STAT 101
Topics: Syllabus, Data & Variables, etc.
Handouts: Orange Sheet #1, Syllabus; Assignment Schedule; Anatomy of Statistics: 1) Statistical
1
9.1.2015
Alphabet, 2) Statistical Relationships
Online: All handouts plus PowerPoint for the Nature of Statistics
Course Assignments:
1) Obtain text (see syllabus). Scan through text for general format, etc.
a. Review: Ch. 1, section 1.1
2) Review the terminology on the Anatomy of Statistics sheet.
3) Go online to the Anatomy of Statistics link and look at a couple of these documents.
4) Go online and scan through the second section of the SPSS manual (SPSS Procedures section) to get an idea of the
current manual’s format.
5) PowerPoint slides: if you want a copy go online and obtain the “Nature of Statistics” PowerPoint from the Stat 101
“Supporting Materials” link
6) Items below – be prepared to discuss these items.
Next Class: Nature of Statistics - Terminology
Stat Essentials (What I should know from today): Be able to: 1) define “Data”; 2) define a “Variable”; 2)
distinguish between objective (response) and explanatory variables; and 3) identify variables to be studied when provided a
study scenario.
DATA & VARIABLES:
Data: Data are “factual information (as measurements or statistics) used as a basis for reasoning, discussion, or
calculation” (Merriam-Webster online dictionary definition).
Variables: Variables are pieces of information (characteristics) gathered from people, squirrels, cumquats, fruit flies,
businesses or other sources and which vary from one unit of the population to another. A person’s hair color and
handedness represent variables, as does the circumference of ball bearings.
 There are two basic types of variables:
o Objective Variables (Dependent, Response): These variables represent the characteristics about which you
want to learn – weight, eye color, speed of cars; life span of monarch butterflies.
o Explanatory Variables (Independent, Predictor): These variables help us refine our understanding of the
Objective Variables of interest – gender, age, business size, environmental conditions.
 Variables have Values
o Values may be word or numerical in nature.
o The values of a variable are what are compared via data analysis processes.
Problem 1.1: Nutrition
According to a study published in the Journal of the American Dietetic Association
FOR RELEASE AUGUST 4, 2009 [excerpt from ADA webpage 8.26.2009]
CHICAGO – The intake of added sugars in the United States is excessive, estimated by the US Department of Agriculture in 1999-2002 as
17% of calories a day. Consuming foods with added sugars displaces nutrient-dense foods in the diet. Reducing or limiting intake of added
sugars is an important objective in providing overall dietary guidance. In a study of nearly 30,000 Americans published in the August 2009
issue of the Journal of the American Dietetic Association, researchers report that race/ethnicity, family income and educational status are
independently associated with intake of added sugars. Groups with low income and education are particularly vulnerable to eating diets with
high added sugars.
1. Identify an objective variable for this study. What values could this variable assume? Sugar intake
2. Identify three explanatory variables. What values could these variables assume? Race/ethnicity; education level; family income
Problem 1.2: Diet Calcium & Blood Pressure
A heart researcher is interested in studying the relationship between diets which are high in calcium and blood pressure in adult females. The
researcher randomly selects 20 female subjects who have high blood pressure. Ten subjects are randomly assigned to try a diet which is high
in calcium. The other ten subjects are assigned to a diet with a standard amount of calcium. After one year the average blood pressures for
subjects in both groups will be measured and compared to decide if diets high in calcium decrease the average blood pressure.
1. Identify an objective variable for this study and its associated values. CA level; blood pressure
2. Identify some potential explanatory variables and their associated values (they may not be specifically identified in
the paragraph). Age, socio-economic level; region of country
1
Problem 1.3: Get Married, Gain Weight
Researcher Penny Larson and her associates wanted to determine whether young couples who marry or cohabitate are more likely to gain
weight than those who stay single. The researchers followed 8,000 men and women from 1995 through 2002 as they matured from the teens
to young adults. When the study began, none of the participants were married or living with a romantic partner. By 2002, 14% of the
participants were married and 16% were living with a romantic partner. At the end of the study, married or cohabitating women gained, on
average, nine (9) pounds more than single women, and married or cohabitating men gained, on average, six (6) pounds more than single men.
[p21sullivan]
1. Identify an objective variable for this study and its associated values. Weight gain; weights vary
2. Identify an explanatory variable and its associated values. Marital status/cohabitate; values: married, not married cohabitating
Problem 1.4: Obesity and Artery Calcification
Scientists were interested in learning if abdominal obesity is related to coronary artery calcification (CAC). The scientists studied 2,951
participants in the Coronary Artery Risk Development in Young Adults Study to investigate a possible link. Waist and hip girths were
measured in 1985-86, 1995-96 (year 10) and in 200-01 (waist girth only). CAC measurements were taken in 201-02. The results of the study
indicated that abdominal obesity measured by waist girth is associated with early atherosclerosis as measured by the presence of CAC in
participants. [p21sullivan]
1. Identify an objective variable for this study and its associated values1. Identify an objective variable for this study and its associated
values. Coronary artery calcification; values vary
2. Identify an explanatory variables and its associated values. Waist/hip girth; values vary
Problem 1.5: Hazards: Study Finds That Bike Helmets Invite Close Calls
(By NICHOLAS BAKALAR. Published: September 19, 2006. The New York Times)
A British study suggests that at least in some situations, bicycling with a helmet may be more
dangerous than going without. Dr. Ian Walker, a professor of psychology at the University of
Bath, was his own subject in a study that measured how closely cars drove to bicycles they passed
on the road.
Dr. Walker, using a bicycle fitted with a well-concealed video camera and ultrasonic sensor, measured his distance from cars as
they passed by his bicycle. He rode with and without a helmet, and with and without a wig that made him look like a woman.
He covered 200 miles at various times of day and made more than 2,500 observations. The study will appear in a future issue
of Accident Analysis and Prevention.
Dr. Walker found that cars consistently passed closer to him when he was wearing a helmet than when he was bareheaded, that
trucks passed closer than cars, and that drivers passed closer to him without the wig than when they thought he was a woman.
Cycling farther from the curb, sometimes recommended as a way of keeping cars at a safe distance, did not work. The farther
he rode from the curb, the closer drivers came to his bicycle.
Dr. Walker was hit by a bus and a truck during the study, both times while wearing a helmet. He sustained a minor injury in the
truck accident. But he warned that abandoning headgear was not the answer. “As for helmets,” he said, “the advice goes to the
drivers rather the cyclists — treat them all with lots of care and respect, because no matter how skilled they are, this doesn’t
stop a gust of wind knocking them sideways, or a pedestrian stepping out in front of them.”
So what variables are out there for this study? Distance from curve; Appearance (male/female); Wear helmet
2
2
STAT 101
TOPICS: Nature of Statistics
DOCUMENTS:
 HANDOUTS: Orange #2; Worksheet #1&2 – Twenty-Five Q’s classification AND 50 Greatest

9.3.2015
Athletes of 20th Century
AVAILABLE ONLINE: All handouts listed above; Sampling ppt.
HWK:




Readings: Ch. 1: sections 1.1-1.2; 1.3 (p. 20-24; sampling)
Problems: p. 6 # 1-13, 21,24, 26, 28, 29-32 p. 13 # 1-12, 15, 16, 19–22, 29
Finish Worksheets #1 - 50 Greatest Athletes and #2 - Twenty-Five Questions
Items below
NEXT CLASS: Nature (cont.?); Sampling; Combinations
Stat Essentials (taken from today): Be able to: 1) define terms and relationships as presented on the sheet Anatomy of
the Basics: Statistical Terms and Relationships; 2) identify variables and their characteristics
Problem 2.1: A population is defined by the characteristics that distinguish it from others groups. How would you describe
the members of this class so that it would represent a population and thereby not be confused with other populations?
A statement that would distinguish the population from any other.
Problem 2.2:
FREE SHIPPING on orders $39+*
Code: SHIP39
An 8x12, 20 page Shutterfly photo book costs $29.00. How much would it cost given the above discount?
At 50% off: $29.00*.50 = $14.50; $14.50*.30=$4.35 (the additional 30%); $14.50-$4.35=$10.15 (final price)
Problem 2.3: A heart researcher is interested in studying the relationship between diets which are high in calcium and blood
pressure in adult females. The researcher randomly selects 20 female subjects who have high blood pressure. Ten subjects are
randomly assigned to try a diet which is high in calcium. The other ten subjects are assigned to a diet with a standard amount
of calcium. After one year the average blood pressures for subjects in both groups will be measured and compared to decide if
diets high in calcium decrease the average blood pressure.
1) Identify the population. Adult females
2) What characteristic of the population is being measured? CA & BP relationship
3) Identify the sample. 20 females
4) Is the purpose of this data collection to perform descriptive or inferential statistics?
[P15#1H&M]
5) Could blood pressure be used as an explanatory variable in this situation? No, all BP values may be different
3
Problem 2.4:
Heroin Use: The National Center for Drug Abuse is conducting a study to determine if heroin usage among teenagers has
changed. Historically, about 1.3 percent of teenagers between the ages of 15 and 19 have used heroin one or more times. In a
recent survey of 1,824 teenagers, 37 indicated they had used heroin one or more times.
1) Identify the population. Teenagers 15-19 yrs. old
2) Identify a variable of interest. Heroin use
3) Identify a sample.
1824 teenagers (15-19 yrs old); 37 are the YES respondents (2.085%)
4) Is the purpose of this data collection descriptive or inferential?
Problem 2.5:
Cell Phone Fraud: Lambert and Pinheiro (2006) described a study in which researchers try to identify characteristics of cell
phone calls that suggest the phone is being used fraudulently. For each cell phone call, the researchers recorded information on
its direction (incoming or outgoing), location (local or roaming), duration, time of day, day of week, and whether the call took
place on a weekday or weekend. [WSed3p6]
1) Identify the observational units in this study. Cell phones
2) Identify the qualitative variables and their characteristics.
Direction: qual, nominal
Location: qual, nominal
day of week: qual, nominal
weekend/weekday qual, nominal
3) Identify the quantitative variables and their characteristics.
Duration: quant, cont., ratio
time of day: quant, cont, interval??
4) Would call duration be a good explanatory variable? Why/why not? No – too many values
Problem 2.6:
Student Characteristics: A Case represents all of the information collected from one source, such as a student.
Student #1 is a male who does not smoke, who lives in an urban area, and who would prefer to win an Olympic gold medal over an Academy
Award or Nobel Prize. He indicates that he exercises 10 hours a week, watches television one hour per week, and has a GPA of 3.33. A
resting pulse rate of 58 beats per minute, the oldest of three children and a desire to become a fireman represent other characteristics of this
student.
Identify the variables for which data were obtained and classify them as qualitative (categorical)/quantitative, discrete/continuous,
and provide a measurement level for each variable.
Identify the variables for which data were obtained and classify them as qualitative (categorical)/quantitative, discrete/continuous,
and provide a measurement level for each variable.
Qual, Nominal: Gender; Smoke; Residence/location; Award type; Planned occupation
Qual, Ordinal: position among siblings
Quant, Interval: none
Quant, Discrete, ratio: number of siblings
Quant, continuous, ratio: exercise; TV watching; GPA; heart rate
If similar information were obtained from 49 other students, which variables might most likely be used as explanatory variables?
Nominal and possibly ordinal variables as they have few categories
Problem 2.7:
Iceland: According to World Bank data, 90% of Icelanders have access to the Internet. In order to determine this value, what were the units
from which this figure was obtained? What was the variable of interest (objective variable) and what were the values of this variable?
Identify the variable’s characteristics (Qual/Quant etc.) (L5p.7)
Units Icelanders
Varible: Internet access; qual., nominal (Yes/No)
If one were to look at the number of people worldwide with access to the Internet, we could record the proportion within each country. In
doing so, what would be the population units? What was the variable of interest (objective variable) and what were the values of this
variable? Identify the variable’s characteristics (Qual/Quant etc.)
Units: Countries
Variable: Proportion of country inhabitants with internet access; quant, cont. ratio
4
STAT 101
TOPICS: Nature of Statistics; Sampling
DOCUMENTS:


HANDOUTS: Orange #3; Green #3
AVAILABLE ONLINE: Orange #3; Green #3; PowerPoint placed online (2): Sampling;
Combinations & Permutations
3
9.8.2015
HWK:



Text Readings: Ch. 1: pp. 20-24;
Text Problems: p. 6 #14-20, 22, 25, 27, 35, 38; p.13 #17, 18, 23-25, 30
Items below
NEXT CLASS: Extra Credit #1 due; Sampling (cont.); Combinations
Stat Essentials (taken from today): Be able to: 1) think critically when reviewing tables, charts, and other statistical
presentations (assess data presentations for appropriateness of presentation and interpretation); 2) understand relationships
among basic statistical terms. If we get there: Sampling: 1)identify sampling approaches; 3) calculate samples using selected
approaches.
Problem 3.1:
The grade for this course is based upon 400 points. These points are converted to a 100-point base to result in a final course
grade.
1. How many of the 400 points represent one point of the final grade? 4; 400/100 = x/1 > 100x = 400 > x = 4
2.
Extra credit points are added to those you have accrued throughout the course via exams, etc. If you complete ten
extra credit exercises, and receive full credit for them all (i.e. 10 points), by how many points will your final grade
increase? 10/4 = 2.5
3.
Over the course of the semester Elijah elects to not submit three, 12-point class assignments. By how many points
would his final grade decrease as a result of not having submitted these three assignments? 36/4 = 12
Problem 3.2:
Fifty randomly selected Fortune 500 Company CEO’s were asked if they would hire someone who submitted a resume
containing typos. “No” was the response of 58% of the CEO’s.
1) What is the population? Fortune 500 CEO’s (all)
2) What is a unit of the population? CEO
3) What is the sample? 50 Fortune 500 CEO’s
4) What is the variable of interest? Resume Typos
5) What are the likely response options (values)? Yes/No
6) Is the second sentence descriptive or inferential? Desc. 7) If descriptive, can one make an inference? Yes or N
Problem 3.3:
During a prior semester the statistics classes went to the Alumni Field House, flew various types of balsa wood airplanes and
collected information about the flight distances and flight times of these planes. Identify the units of interest for this study
(information source for our study).
A) Class members
B) Balsa wood airplanes
C) Flight distances and times
D) Campus buildings
Problem 3.4:
Burglaries: ADT Security Systems advertised that “when you go on vacation, burglars go to work.” Their ad stated that
“according to FBI statistics, over 26% of home burglaries take place between Memorial Day and Labor Day.” What is
misleading about this statement? (Triola7ed,p15#6)
Approximately 100 days +/- between Memorial Day and Labor Day. One-hundred days is 27.45 of the year, so about ¼ of
burglaries in about ¼ of the year.
5
Problem 3.5:
Election: Review the cartoon to the right. Assume that there
are 100 boys and 100 girls. Demonstrate using these 200
students how this student’s conclusion is either correct or
incorrect. Present your answer using both numerical
computations and sufficient discussion to support your
findings.
21% of 100 boys = 21
30% of 100 girls = 30
Together 51 students/ 200 = 25.64% of all support him
Problem 3.6:
Variables: Identify the explanatory and objective variables in the following pairs of variables.
A) Lung capacity (objective) and number of years smoking cigarettes (explanatory)
B) Blood alcohol content (objective) and the number of alcoholic drinks consumed (explanatory)
C) Year (explanatory) and world record time in a marathon (objective
Problem 3.7:
O-Tiger price hike: For many years Oneonta had a single-A farm team of the NY Yankees, which was followed by a farm team
of the Detroit Tigers. When the Tigers arrived, the prices for seating changed. The following comes from an editorial in the
local newspaper about the rise in ticket prices for the local single-A professional baseball team. “General admission season
passes for adults will be $155, up from $70, in 2009, while six-seat boxes will go up 500 percent, from $300 to $1,500.”
(source: The Daily Star, In Our Opinion column for Feb. 7 & 8, 2009, p D3; this team has since left town)
A) The $85 increase in the single seat price represents how much in terms of a percentage increase?
$85/$70 = 1.21 or 121% increase
B) Demonstrate using a numerical analysis whether or not the cost of a six-seat box increased by 500%.
$1,500 - $300 = $1,200, which is the cost increase;
$1,200/$300 = 4.00 or 400% increase
Problem 3.8:
Seat Belts: Suppose that there are 300 students taking statistics and that they are asked if the always use seat belts.
A) If 27% of the students indicate that they do not always use seat belts, how many students is this?
300 * .27 = 81 students OR
27
X
27 * 300

 X 
 X  81students
100 300
100
B) Suppose that in different course 20% of the students do not use seat belts and that the 20% represents 43 students.
How many students are in this class?
20 43

 20 X  43 *100  20 X  4300  X  215students
100 X
6
4
STAT 101
TOPICS: Sampling; Combinations & Permutations
DOCUMENTS

9.10.2015
HANDOUTS: Orange #4; Green #4A Sampling; #4B Combinations, etc.; Table of
Random Numbers
AVAILABLE ONLINE: Orange #4; Green #4A & 4B; Related Anatomy Sheet: Anatomy of a Systematic Random
Sample, Extra Credit #2.

HWK:

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Text Readings: Ch. 1, section 1.3 – experimental design and sampling; Ch. 3, section 3.4 – combinations, etc.
Text Problems: p. 23 #1-3, 7-10, ODD 19-27
Problems on Green #3 & #4 (As assigned in class)
Items below
Class: EX CR #2 due; Sampling, Combinations (both as needed); Experimental Design (maybe)
Next
Stat Essentials (taken from today): Be able to: 1) describe a probability-based random sample; 2) identify different
sampling approaches; 3) obtain samples using various probability sampling approaches – SRS, Stratified, etc., 4) determine the
number of samples via combinations; 5) calculate permutations, tree diagrams and the multiplication rule for independent
events.
Problem 4.1:
Identify the variables and their characteristics:
1: The number of doctors who wash their hands between patient visits.
2: The majors of randomly selected students at a university.
3: The average weight of mature German Shepherds.
4: The category which best describes how frequently a person eats chocolate: Frequently, Occasionally, Seldom, Never.
5: The temperature this morning at 7:00 a.m.
6: The diameter of major league baseballs.
7: The average horsepower of ten randomly selected 1.6L MINI Cooper engines.
Data Source* Variable
Qual/Quant
Discrete/Cont Nom/Ord/Int/Ratio
1.
2.
3.
4.
5.
6.
7.
doctors
students
dogs
people
thermometer
baseballs
Mini Coopers
wash hands
major
weight
eat chocolate
temperature
ball diameter
engine horsepower
qual.
qual
quant
qual
quant
quant
quant
N/A
N/A
cont
N/A
cont
cont
cont
N
N
R
O
I
R
R
*NOTE: Data Source is the population or sample unit from which you obtain the data, not the variable information (data) collected.
Problem 4.2
The Tax Man Cometh: The Internal Revenue Service wants to sample 1000 tax returns that were submitted last year to
determine the percentage of returns that had a refund. Identify a sampling method that would be appropriate in this situation.
Simple Random Sample (SRS) would work
Problem 4.3
Prescription Drug Program: The director of a hospital pharmacy chooses at random 100 people age 60 or older from each of
three surrounding counties to ask their opinion of a new prescription drug program. Identify the type of sampling used.
Writing descriptive statements:
7
Descriptive statements merely, report data presented in a table or graph/chart. To write a paragraph about a table: 1) introduce
the table; 2) provide descriptive sentences containing statistical data contained within the table/graph; 3) write a summary
sentence.
Example using the table to the right.
[1)Intro=>] The following table presents village residents’ ratings of
life in the village. [2) Descriptives=>] Approximately 78% of surveyed
residents rated life in the village positively (good to excellent). In
contrast, 77 of 347 residents (22.2%) rated life in the village as poor to
fair. [3) Conclusion=>] In general, it would appear that most residents
(77.8%) are satisfied with the quality of life in the village.
Ra ting of qua lity of life in vill age
Valid
Missing
Total
Ex cellent
Very Good
Good
Fair
Poor
Total
Sy stem
Frequency
4
83
183
60
17
347
13
360
Percent
1.1
23.1
50.8
16.7
4.7
96.4
3.6
100.0
Valid Percent
1.2
23.9
52.7
17.3
4.9
100.0
Cumulative
Percent
1.2
25.1
77.8
95.1
100.0
NOTES: The Rating of Quality table is a SPSS generated table.
1) Use the VALID PERCENT column for percentages.
2) If you use words such as most, more than, fewer, approximately, etc., you MUST include supporting statistical
evidence.
3) If you start a sentence with a number write it out (e.g. NOT “7 respondents liked …,” but rather “Seven respondents
liked …”
4) If you include numbers representing counts, also include the associated percentage value (e.g. “Seven respondents
(30%) liked the movie.”)
Seat Belt Usage Among Men and Women
Problem 4.4
Seat Belt Usage: Use the table to the right to determine the
following values.
Not Always
N:
% across:
% down:
Men
2
40
40
Women
3
60
30
Total
5
100
33
Always
N:
% across:
% down:
3
30
60
7
70
70
10
100
67
Total
N:
% across:
% down:
5
33
100
10
67
100
15
100
100
A) Determine the Totals
B) Determine the percent who are: Men 33.33%;
Women 66.66%: Always Use 66.66%; and Don’t
Always Use 33.33%
C) Are men more or less likely to use seat belts? Men
usage (60%;3/5); Women usage (70%;3/10)
D) Write a descriptive statement pertaining to some of the information contained within the table.
Problem 4.5:
Write a paragraph containing: a sentence introducing the table;
two sentences that contain descriptive statements resulting from
the table’s content; and a conclusion you can draw from these data.
Answers vary
8
STAT 101
5
TOPICS: Sampling; Combinations; Experimental Design (?)
DOCUMENTS


HANDOUTS: Orange Sheet #5; Green #5 (Class Assignment #1)
AVAILABLE ONLINE: Orange #5; Green #5; Anatomy of Experimental Terms;
Experimental Design PowerPoint
9.15.2015
HWK:



Text Readings - Review Ch. 1
Text Problems – p. 23 EVEN# 20 - 28; 33 - 36
Class Assignment #1 (bellow)
n!
n!
Combinations: n C r 
(n  r )!
(n  r )! r!
Next Class: CA #1 due; HWK #1 due (see below); Exp. Design (?)
Stat Essentials (taken from today & next class): Be able to: 1) identify terms associated with experimental designs;
FORMULAS: Permutations: n Pr 
2) identify the component parts of a simple experimental design. From Sheet #4: 4) determine the number of samples via
combinations; 5) calculate permutations, tree diagrams and the multiplication rule for independent events.
HOMEWORK ASSIGNMENT #1 [8 points]:


The dice roll is the first item Thursday. Assignments are due at that time.
Assignments for this roll include text assignments for days 2, 3, 4, and 5.
CLASS ASSIGNMENT #1 [12 points]:





COMPLETE ALL PROBLEMS ON THIS SHEET.
THIS ASSIGNMENT IS DUE AT CLASS TIME THURSDAY.
Problem point values are included in brackets [ ].
Please be thorough and neat in the presentation of your responses as they must fit within the space provided.
Grading: -1 for first error; half value (1.5) for multiple errors; 0 minimal effort/not attempted/incorrect.
If your surname (last name) begins with the letter:
“A” through “L,” complete part “A)” of problems 5.2 through 5.4.
“M” through “Z,” complete part “B)” of problems 5.2 through 5.4.
Problem 5.1: (everyone answers this item)
Aging Population [3]: It is predicted that there will be 88,547,000 elderly individuals (65 and over) in the U.S. in
2050 and that they will represent 20.2% of the entire population. What will be the estimated U.S. population?
88547000 20.2

 20.2 x  854700000  x  438,351,485 people
x
100
Problem 5.2: (place answers to your assigned item (A or B) below)
A) Height of CEO’s [3]: An economist suspects that chief executive officers of American companies tend to be taller than
the national average height of 69 inches, so she takes a random sample of 100 CEO’s and records their heights.
[WSeheightd3p7]
What/who are the observational units? Company CEO’s
Identify the variable of interest (OBJECTIVE variable): height
Circle characteristics: Qual. or Quant.
Discrete or Continuous
Nominal, Ordinal, Interval, Ratio
Identify an EXPLANATORY variable that could help us understand the objective variable: Gender
B) Marriage [3]: A psychologist shows a videotaped interview of married couples to a sample of 150 marriage counselors.
Each counselor is asked to predict whether the couple will still be married five years later. The psychologist wants to test
whether marriage counselors make the correct prediction more than half the time. [WSed3p7]
What/who are the observational units? counselors
Identify the variable of interest (OBJECTIVE variable): prediction of couples staying married
Circle characteristics: Qual. or Quant.
N/A Discrete or Continuous
Nominal, Ordinal, Interval, Ratio
Identify an EXPLANATORY variable that could help us understand the objective variable: Gender; yrs experience, …
9
Problem 5.3: Combinations & Permutations
A) Ice Cream [3]: Thirty-one ice cream flavors > three scoops & a banana = one banana split. A) If the order of the
flavors did not matter, how many different combinations of ice cream flavors could be made into a banana split? B)
How many different ways could a banana split be made if order matters?
B) Coca Cola Directors [3]: There are 11 members on the board of directors for the Coca Cola Company. A) If they
must elect a chairperson, first vice president, second vice president; and secretary, how many different slates of four
candidates are possible? B) If they must form a four-member ethics committee, how many different committees are
possible?
A) Ice Cream
31!
31 * 30 * 29 * 28!

 26970 banana splits
(31  3)!
28!
31!
31 * 30 * 29 * 28! 31 * 5 * 29


 4495 banana splits
31 C3 
(31  3)!3!
28!*3 * 2 * 1
1
P 
31 3
B) Coca Cola
11!
11 * 10 * 9 * 8 * 7!

 7920 possible election orders
(11  4)!
7!
11!
11 * 10 * 9 * 8 * 7! 11 * 10 * 3


 330 possible committees
11 C 4 
(11  4)!4!
7!*4 * 3 * 2 * 1
1
P 
11 4
Problem 5.4: Sampling
Stratified Sampling: Include a table with a title, column headings for frequency of occurrence and relative frequency, numeric
calculations, the calculation process used to obtain the sample AND the resulting sample, again in a table format.
A) Hotels [3]: A random sample of 80 hotels is to be taken from a population consisting of 3,500 hotels. The hotels have
been separated into four strata: Five Star properties, consisting of 600 units; Four Star Properties, consisting of 1,800
units; Three Star Properties, consisting of 900 units; and Unacceptable Properties, consisting of 200 units. How many
hotels will be selected from each property type?
B) Thanksgiving Past [3]: This past fall semester the college elected to have the Thanksgiving break start on
Wednesday rather than take a full week off. To determine the opinion of students regarding this holiday break time
frame, the Student Association proposed to survey 450 students. To do so it was determined that the student body
should be stratified into four groups: 1) Campus Residents (n = 3200); 2) Off-Campus Students (n = 2400); 3)
Commuters (n = 240); and 4) International Students (n = 125). Determine the number of students to be surveyed from
each strata.
Hotel Sample
Population: N =3500
Level
f
Five Star
600
Four Star
1800
Three Star
900
Unacceptible
200
Total:
3500
Thanksgivinng Sample
Population: N =5965
Student
f
On-campus
3200
Off-campus
2400
Commuters
240
Interntional
125
Total:
5965
rf
0.171
0.514
0.257
0.057
1.000
Sample: n = 80
Level
f
f rounded
Five Star
13.71429
14
Four Star
41.14286
41
Three Star
20.57143
21
Unacceptible 4.571429
5
Total:
80
81
rf
0.171
0.514
0.257
0.057
1.000
rf
0.536
0.402
0.040
0.021
1.000
Sample: n = 450
Level
f
f rounded
Five Star
241.4082
241
Four Star
181.0562
181
Three Star
18.10562
18
Unacceptible 9.430008
10
Total:
450
450
rf
0.536
0.402
0.040
0.021
1.000
shaded numbers were/may be adjusted
10
6
STAT 101
TOPICS: Experimental Design (finally); Qualitative Data (?)
DOCUMENTS
9.17.2015
 HANDOUTS: Orange Sheet #6
AVAILABLE ONLINE: Orange #6; Qualitative PowerPoint; Anatomy Sheets (5): Experimental
Terms; Qualitative Frequency Table; Pie Chart; Bar Chart; Pareto Chart;
HWK:




Text Readings - Ch. 2 – p. 56-57 (qualitative graphs)
Text Problems: p. 23 #11 – 18, 33 – 36; p.29 Chapter 1 Review #1 - 20
Green #5: Experimental Designs – items not done in class
Items below
Class: Qualitative Data; Quiz #2 (topics: sampling approaches; combinations/permutations; exp. design)
Next
Stat Essentials (taken from today & next class): For Experimental Designs be able to: 1) identify terms associated
with experimental designs; 2) identify the component parts of a simple experimental design. For Qualitative Data be able to: 1)
calculate relative frequency for response values; 2) build a qualitative frequency table; 3) build charts appropriate for
qualitative data (pie, bar, pareto).
Problem 6.1:
In 2005 a television advertisement for Allstate Auto Insurance noted that last year (2004) 1.3 million
people switched to Allstate. Anything missing here?
Do not know how many left Allstate
Problem 6.2:
Permutations & Combinations: You have ten paintings to hang, but only space to hang three. How many different ways
could these paintings be hung if order matters? If order didn’t matter, how many different groups of three paintings could
occur?
10
P3 
10!
10 * 9 * 8 * 7!

 720
(10  3)!
7!
10
C3 
10!
10 * 9 * 8 * 7! 10 * 3 * 4


 120
(10  3)!3!
7!*3 * 2 * 1
1
Problem 6.3:
Ra ting of qua lity of life in vill age
Village Life: Identify the variable characteristics below.
Variable: Quailty of life in village
Valid
Qual/Quan: qualitative
Measurement Level: ordinal
Missing
Total
Ex cellent
Very Good
Good
Fair
Poor
Total
Sy stem
Frequency
4
83
183
60
17
347
13
360
Percent
1.1
23.1
50.8
16.7
4.7
96.4
3.6
100.0
Valid Percent
1.2
23.9
52.7
17.3
4.9
100.0
Cumulative
Percent
1.2
25.1
77.8
95.1
100.0
Problem 6.4:
Earth: Using the table below, write a paragraph containing an
introductory statement, two descriptive sentences using table data,
and a summary statement. [Remember to use the valid percent
column for percentages.]
Answers vary
e.g.: The following table presents the responses to a survey
question regarding the earth being like a spaceship with
limited room and resources. Among respondents, 22% indicated a level of disagreement with this statement. In contrast, 58 %
agreed at some level with the statement. Overall, it would appear that a large percentage of respondents are aware of and concerned
about the physical space and resources the planet.
11
7
STAT 101
TOPICS: Qualitative Data, Quantitative Data, SPSS
DOCUMENTS
9.22.2105
HANDOUTS: Orange #7; Green #7 (Qualitative Data)
AVAILABLE ONLINE: Orange #7; Green #7; PowerPoint (2): Qualitative; Quantitative;
Anatomy Sheets (5): Qualitative Frequency Table; Pie Chart; Bar Chart; Pareto Chart; Contingency Tables


HWK:




Text Read: Ch. 2 sections 2.1, 2.2.
Text Problems: p. 62 #15, 23, 25 (make rel. freq. bar chart instead of a pareto chart), 33, 36-38. (repeated)
Green #7 as assigned in class.
Items below.
Class: Quantitative Data, SPSS
Next
Stat Essentials (taken from today: Qualitative Data: Be able to: 1) build a qualitative frequency table; 2) build charts
appropriate for qualitative data (pie, bar, pareto); 3) obtain a frequency table and appropriate charts using SPSS.
Problem 7.1:
What do Alligators eat? The chart below depicts the
food choices by volume for 100 alligators. Respond to
the following two questions by referencing this chart.
7.1A) [1] The primary food choice is:
A) Categorical B) Quantitative
yummy
7.1B) [1] About what percent of alligators had fish as
their primary food choice? __42%_____ (within+/- 3%)
Problem 7.2: Obtaining statistical output
and providing analysis
SPSS: During the spring semester of 2013 an
environmental sustainability survey was conducted
among Oneonta students. Open the SPSS data file Environmental Sustainability SP2013.sav. Using SPSS build a frequency
table, a pie chart, a bar chart, and a pareto chart of the variable Q1, “Approaching the limit of people earth can support.” The
“how to” for these charts is noted below. Further examples are available in the online SPSS reference manual.
Finding the data file:
Go to my web page > Stat 101: Intro > Data Files > select the file Environmental Sustainability SP2013
How to obtain:
Frequency Table: Analyze > Descriptive Statistics > Frequency > move variable Q1 (approaching limit of people
earth can support) to right cell > Ok.
Pie Chart: Graphs > Legacy Dialog > Pie> Define (leave as is) > move variable Q1 to the Define Slices by cell >
OK.
Bar Chart: Graphs > Legacy Dialog > Bar> Define (leave as is) > move variable Q1 to the Category Axis cell > OK
Pareto Chart: Analyze > Quality Control > Pareto > Define (leave as is) > move variable Q1 to the Category Axis
cell > OK.
Descriptive Analysis:
1) Open a Word document.
2) Place a copy of the frequency table and the pie chart in the document. (I will show you how in class – be sure to take
some notes on this process)
3) In Word, write a descriptive paragraph containing an introductory sentence, descriptive statements, and a conclusion.
4) Print out the document.
12
STAT 101
TOPICS: SPSS; Quantitative Tables & Charts
DOCUMENTS:
8
9.24.2015
HANDOUTS: Orange #8; Green #8
AVAILABLE ONLINE: Orange #8, Green #8; Quantitative Data ppt.; Contingency Tables ppt.
ANATOMY REFERENCE SHEETS: Contingency Tables; Anatomy sheets: 1) Quantitative Frequency Table; 2)
Histogram 3) Dot plot 4) Stem-and-Leaf plot



HWK:



Text Reading: Ch. 2, review sections 2.1-2.2
Text Problems: p. 47 #1-5, 11, 15, 19, 29, 37
Items below AND item 7.2 (SPSS)
Class: Quantitative Tables & Charts (cont.); Ex. Cr. #3 due; CA #2 distributed
Next
Stat Essentials (taken from today & next class): Be able to: 1) build a frequency table appropriate for the
presentation of quantitative data; 2) identify frequency table components – classes, boundaries, etc.; 3) build charts/graphs
appropriate to quantitative data – histogram, dot plot, stem-and-leaf, frequency polygon, ogive; 4) use SPSS.
Problem 8.1:
Sampling Approaches:
1.
A college faculty consists of 400 men and 250 women. The college administration wants to obtain a sample of 65 faculty members
to ask their opinion about a new parking fee. They obtain a sample of 40 men and another of 25 women. What sampling approach
has been used? Stratified with proportional allocation
2.
Police at a sobriety checkpoint stop every fifth car to determine whether the driver is sober. What sampling approach has been
used? Systematic
3.
A pollster walks around a shopping mall and approached people passing by to ask them how often they shop at the mall. What
sampling approach has been used, convenience
Problem 8.2:
Nutrition Bars: (NOTE: Lower Class Limits shown)
Nutrition Bars: (Lower Class Limits shown)
How many values are in the data set? 75
How many classes are there? 11
What is the width of a class? 50
How many milligrams of sodium are in the nutrition bar
with the highest value? >500
Explain how a relative frequency histogram would differ
from the displayed chart. (Hint: Think about how
frequency and relative frequency bar charts differ?)
CHANGE OF Y-AXIS LABEL AND SCALE
13
Problem 8.3:
Ideal Weight: Twenty five students reported their ideal weights (in most cases, not their current weight).
Weights (lb):
110
120
110
115
110
123
120
130
150
105
110
119
130
130
120
125
118
120
120
115
135
120
130
120
135
Create a frequency table containing five classes
Based upon your table make the following tables (NOTE: do only those demonstrated today)
 Histogram
 Dot plot
IDEAL WEIGHTS
 Stem and Leaf
 Frequency Polygon
 Ogive
Weight (lb.)
f
rf
cf
105-114
115-124
125-134
135-144
145-154
Totals:
5
12
5
2
1
25
0.20
0.48
0.20
0.08
0.04
1.00
5
17
22
24
25
-
crf
0.20
0.58
0.88
0.96
1.00
-
double] Stem-and-leaf of weight lb.
N = 25
Leaf Unit = 1.0
10
11
11
12
12
13
13
14
14
15
5
0000
5589
00000003
5
0000
55
0
Frequency polygon and ogive not available. See class notes.
14
STAT 101
TOPICS: Quantitative Tables & Charts & data collection
DOCUMENTS:



9
9.29.2015
HANDOUTS: Orange #9
AVAILABLE ONLINE: Orange #9
ANATOMY REFERENCE SHEETS: Contingency Tables; Quantitative Frequency Table; Histogram; Dot plot;
Stem-and-Leaf plot; Line Chart
HWK:


Text Readings: Ch. 2, 2.3 (2.1-2.2- review charts); Contingency Tables p. 551; Line Chart (Time Series Chart) p. 59
Text Problems:; Problem p. 62 #22 Housefly Life Spans (in addition to the dot plot, using these data, make a
frequency table containing 6 classes, and both a histogram and an ogive based upon your table)
 Class Assignment #2 (on this sheet)
Next Class: Contingency tables; Time Series Charts; Distribution Shapes; Sigma; Arithmetic Mean; CA #2 due
Stat Essentials (taken from today & next class): Be able to: 1) build a frequency table appropriate for the
presentation of quantitative data; 2) identify frequency table components – classes, boundaries, etc.; 3) build charts/graphs
appropriate to quantitative data – histogram, dot plot, stem-and-leaf, frequency polygon, ogive.
CLASS ASSIGNMENT #2 [12 points; due next class]:
GENERAL INSTRUCTIONS:
1) Complete the Problem Set to which you have been assigned.
2) Open a Word document:
a. On the first line place your name and the date
b. On the second line place: Class Assignment #2: Problem Set # <one
assigned to you>
3) Obtain the required SPSS frequency table. All SPSS data files are located on the
STAT 101 Data Files link. If you get stuck, recall that there is a SPSS manual
online.
4) Place the table obtained from SPSS into the document.
5) Type a paragraph discussing the table (refer to Orange #4). When discussing the
contents of a table/chart/graph remember to use the data rather than just words such
as “more” and “majority.”
6) Answer all other questions on the printout sheet so that you are handing in one piece
of paper (two sides). A penalty of one (1) point will be assessed any assignment
exceeding one page.
7) Grading: Item values for this 12 point assignment are located within [ ]. For
individual items: -.5 for first error; -1.5 partial credit (beyond one error); 0 not
attempted.
Problem Set #1: CEREAL DATA
CLASS ASSIGNMENT #2
8:30
10:00
Problem Set #1
Brown, C
Brandifino
Brown, N
Gaines
Davis
Lee
DeFazio
Lin
Neider
Preiss
Perez
Sanders
Salaway
Valenti
Tompkins
Valoroso
Walsh
Problem Set #2
Carney
DeMarzo
Conrade
Dolce
DiTommaso
Gaynor
Hicks
Greene
O'Brien
Korankyi
Prickett
Pace
Sutton
Salomone
Vavoules
Zuckerman
Problem Set #3
Guidetti
Alix
Kodya
Asfand
Layman
Bartlett
Malventano
Christofel
1) [3] Open the Cereals.sav SPSS data file and make a frequency table of
the variable MANUFACTURER, which represents the number of
cereals made by the various cereal companies. Place this table into the
Word document and write a paragraph which introduces the table and
discusses information contained within the table. Incorporate statistics
Provost
Companion
into your written presentation.
Randell
Fancher
2) [3] Bar Chart: Using SPSS make a frequency bar chart of the data
provided in the variable MANUFACTURER. Include counts and
Swan
Mecca
percentage values on the chart (double click to go to the editor; select
Williams
Minasi
the bar chart icon). Place this chart into your document.
3) [3] Pie Chart: On the paper, by hand, create a pie chart. Include a title and the count and percent values on
the chart. In a separate presentation demonstrate how the slice arc degrees are calculated.
4) [3] Pareto Chart: On the paper, by hand, create a pareto chart. Include all appropriate labels and the ogive.
15
Problem Set #2: NUTRITION BARS DATA
1) [3] Open the NutritionBars.sav SPSS data file and make a frequency table of the variable CLASS, which
represents the number of nutrition bars within selected bar categorizations. Place this table into the Word
document and write a paragraph which introduces the table and discusses information contained within the
table. Incorporate statistics into your written presentation.
2) [3] Bar Chart: Using SPSS make a frequency bar chart of the data provided in the variable CLASS. Include
counts and percentage values on the chart (double click to go to the editor; select the bar chart icon). Place
this chart into your document.
3) [3] Pie Chart: On the paper, by hand, create a pie chart. Include a title and the count and percent values on
the chart. In a separate presentation demonstrate how the slice arc degrees are calculated.
4) [3] Pareto Chart: On the paper, by hand, create a pareto chart. Include all appropriate labels and the ogive.
Problem Set #3: LEISURE TIME DATA
1) [3] Open the Leisure_F2005-SP2008.sav SPSS data file and make a frequency table of the variable
LEISURE1, which represents the opinion of students as to how productively they use their leisure time.
Place this table into the Word document and write a paragraph which introduces the table and discusses
information contained within the table. Incorporate statistics into your written presentation.
2) [3] Bar Chart: Using SPSS make a frequency bar chart of the data provided in the variable LEISURE1.
Include counts and percentage values on the chart (double click to go to the editor; select the bar chart icon).
Place this chart into your document.
3) [3] Pie Chart: On the paper, by hand, create a pie chart. Include a title and the count and percent values on
the chart. In a separate presentation demonstrate how the slice arc degrees are calculated.
4) [3] Pareto Chart: On the paper, by hand, create a pareto chart. Include all appropriate labels and the ogive.
For CA #2 see returned assignment
m&m’s data collection
Include in the table below the m&m’s data from your bag of m&m’s
Blue
Brown
Green
Orange
Red
Yellow
Total
16
STAT 101:
TOPICS: Contingency Tables, Line Charts, Distribution Shapes, m&m’s, Sigma (?)
DOCUMENTS:


10
10.1.2015
HANDOUTS: Orange sheet #10; Green #10; Green 10B (m&m’s)
AVAILABLE ONLINE: Orange #10; Green #10; Green 10B; PowerPoints for: 1) Distributions, 2) Sigma, 3)
Contingency tables, 4) Line Charts, Frequency Polygons, & Ogives (quant.); Anatomy sheets: Contingency tables,
Sigma
HWK:

PRINT OUT THE LAST THREE SIGMA POWERPOINT SLIDES AS FULL-PAGE SHEETS. They are our
worksheets for this statistical symbol.
 Text Readings: Ch. 2, p. 59 (Time Series), Ch. 10 p. 551 (Contingency Table), section 2.3
 Text Problems: p. 31 Chapter 1 Quiz; p. 48 #21, 23, 39; p. 61 #17 (single stem), 18 (double stem), 29, 32, 34 (part c
only)
 Items below
NEXT CLASS: (Sigma) Measures of Center; Quiz #3, ExCr #4 distributed
Stat Essentials (taken from today): Be able to: TABLES & CHARTS: 1) build a contingency table; 2) build a line
chart (time series presentation). DISRIBUTIONS: 1) distinguish between common distribution shapes (uniform, normal, and
skewed); 2) calculate the degree of a distribution’s skewness (Pearson’s I). SIGMA: 1) understand what the symbol  (Sigma)
means; 2) successfully demonstrate the application of Distributions: 1) distinguish between.
Problem 10.1: (refer to the online contingency table ppt. or anatomy sheet for a “how to read this table.”)
Contingency Tables: Using the table below, find the requested percentages or counts. The data present three cities in which
houses were sold and during which month the houses sold. An explanation and practice on how to read contingency tables is
available in the PowerPoint listing, the online SPSS manual and in the online Anatomy sheets.
1) What is the size of this contingency
table? __4__ by _3___
2) Among houses sold in Arlington, what
percent were sold in June and July?
48.6%
3) During August 32.3% of the houses
were sold in Fort Worth.
4) Among all houses 11.2% were sold in
Dallas during September.
5) Looking at the right marginal totals
column what does the 131 value
represent? Houses sold in July
6) T or F: Thirty percent of the houses
sold in June were sold in Dallas.
7) T or F: Thirty-two percent of the houses
were sold in Fort Worth.
8) T or F: Of the houses sold in July, approximately 25% were sold in Dallas.
17
Problem 10.2:
An introductory statistics class had three exams for which the distributions of each is presented below.
For each exam describe the distribution’s shape and comment on the exam.
Distribution Shape
Difficulty (easy, average, hard)
Exam #1:
right or positively skewed
hard
Exam #2:
normal distribution
average
Exam #3:
left or negatively skewed
easy
18
STAT 101:
TOPICS: Sigma, Measures of Center, Balance data
DOCUMENTS:


HANDOUTS: Orange sheet #11; Green #11
AVAILABLE ONLINE: Orange #11; Green #11; PowerPoints: SIGMA,
Measures of Center; Measures of Variation
11
10.6.2015
HWK:





Text Readings: Ch. 2, sections 2.3 – 2.4
Text Problems: p. 72 # 1 – 19, 23
Complete balance of Sigma PowerPoint problems.
Extra Credit #4: Titanic
Hwk #2 roll. Be sure you have addressed the following assignments: Text assignments for days #6 through #11 and
Orange Sheet #8. (Yes, that is seven assignments, one which will be dropped before the roll.)
n
 xi
n
xi

n 1
i 1
i 1
FORMULAS:
Median: Q 
Sample Mean
Population Mean  
x
2
2
N
n
NEXT CLASS: Lab #1 in MILNE 108; Hwk roll #2; ExCr #4 due
Stat Essentials (taken from today): ). SIGMA: 1) understand what the symbol  (Sigma) means; 2) successfully
demonstrate the application of Measures of Center: 1) identify basic distribution shapes and how the mean and median are
affected by the shape of a distribution; 2) understand the differences between the mean, median and mode, and where and how
each apply to data; 3) calculate mean and median.
Problem 11.1:
SIGMA: Given the following data for X and Y, determine the values of S yy and r.
X
Y
20
38
10
68
104
87
4
10
2
8
28
23
Answers:
(y)

2
S
yy
r
 y
2
n
 559.5
nxy  (x)(y )
[nx  (x) 2 ][ ny 2  (y ) 2 ]
2
 .926
19
STAT 101:
TOPICS: Lab #1
DOCUMENTS:


HANDOUTS: Orange sheet #12; Green #12; Twenty-Five Q’s Survey
AVAILABLE ONLINE: Orange #12; Green #12; PowerPoints (3): Measures of
Center, Variation, Position
12
10.8.2015
HWK:


Complete Lab #1
Complete Class Assignment #3 (on Green #12)
NEXT CLASS: Measures of Center & Variation; DUE: Lab #1 AND CA #3
Stat Essentials (taken from today): Application of descriptive statistics.
STAT LAB #1: CLASS SURVEY & RANDOM ACTS
Course Component value: 12
Data Files:

Class_Survey (F2010-Sp2015).sav
Objectives:




To gain some familiarity with accessing SPSS.
To gain some familiarity with utilizing SPSS to analyze data.
To create a document using the transfer of SPSS tables and chrts.
To describe what the data presentations tell one about the data collected.
SPSS REVIEW & DEMONSTRATION: Cars.sav






Frequency Table [Analyze > Descriptive Statistics > Frequencies]: Obtain a frequency table of a qualitative, nominal
variable.
Pie Chart [Graphs > Legacy Dialogs > Pie (or other graph)]: From the class survey, identify a qualitative, ordinal level
variable. From the Graph menu select the “Pie” chart option.
Contingency Tables [Analyze > Descriptive Statistics > Crosstabs]: From the Class Survey, create a 4x2 contingency
table (Crosstabs Table) of the variables ANXIETY (row, dependent variable) and GENDER (column, independent
variable) and include column percents in the table.
Statistics [Analyze > Descriptive Statistics > Frequencies > Statistics button]: Mean, Median, etc. via frequency tables
options.
Word: Transferring data into a Word Document.
Data Manipulation: Split File.
LAB #1, PART 1: Class Survey Data – Variable Identification and Presentation
LAB NOTES:
1) Use the yellow sheet as a survey reference sheet.
2) Remember to use COPY SPECIAL (Metafile) when transferring tables/charts from SPSS to Word.
3) Lab response is limited to one sheet of paper (two sides), so shrink the tables and charts once placed into Word.
Word: Open a Word document and enter the following highlighted information:
 Name(s): __________
 STAT Lab #1 – SPSS Oct. 8, 2015
ENTER HEADING ALONG THE LEFT SIDE LABELED “CLASS SURVEY.”
1) [2] Frequency Table: From the class survey, identify one qualitative, ordinal variable. Obtain a frequency table for that
variable.
 Transfer only the frequency table into the Word document.
 Write two sentences that describe what the table tells you about some aspect(s) of the variable.
20
2) [2] Bar Chart: From the class survey, identify a second qualitative variable with more than two, but less than ten response
values . From the Graph menu, Legacy Dialogs listing select the Bar chart option. Before making the chart, enter an
appropriate title for it (Titles button). Add to your chart percentages via the chart editor.
 Transfer only the bar chart into the Word document.
 Write a sentence or two that describes what the chart tells you about some aspect of the variable.
3) [2] Crosstabs: From the class data, create a contingency table (Crosstabs Table) of the variables DRIVER by GENDER
and include only row percents in the table (no column or totals percent). (Remember to determine the independent
variable and place it in the column location.)
 Transfer only this table into the Word document.
 Write two sentences that compare the percent of males vs. females with regard to their perceived driving ability.
4) [2] Split File: Using the Split File command, select “Compare Groups” and move the variable GENDER into the “Groups
based on:” box and then select “Okay.” Use the “Statistics” option on the Frequency Table dialog box to obtain the
mean, median and range for the variable HEIGHT.
 Transfer only the Statistics table into the Word document.
 Write two sentences that describe what the table tells you about some aspect of the variable.
 NOTE: When you are done, go back to the Split File command and select “Analyze all cases.”
LAB #1, Part 2: Random Acts of Kindness Data Analysis
ENTER IN YOUR WORD DOCUMENT A LEFT SIDE HEADING LABELED “RANDOM ACTS.”
Throughout life we perform random acts of kindness for strangers – hold a door, smile or say hello, help rebuild after a flood or
earthquake. This survey contained three questions, #6, #11, & #24 (see arrows in margin) that reflect random acts of kindness,
each involving greater commitment than the prior one. How did respondents do in these areas?
5) [2] Frequency Tables: Obtain a frequency table for each of these three variables (survey items: #6 – would give the time;
#11 – would help pick up items; #24 – would loan your cell phone). Enter these tables in order into the Word
document and after the third table, discuss any trend you see occurring across the three variables.
6) [2] Crosstabs: Using GENDER as an independent variable (column), examine the trend for the random act of loaning a
cell phone (row). Create a contingency table, include column percentages. Provide a sentence introducing the table
followed by a minimum of two sentences discussing findings and finish with a summary/concluding statement.
Remember to cite percentages in your discussion.
ITEMS TO SUBMIT:

BEFORE PRINTING, CONSERVE PAPER by shrinking tables and charts down. Your lab printout may not
exceed one sheet of paper (2-sided; -1 point if > one sheet of paper). Before printing be sure that the print
process is set to two-sided.

SUBMIT: Word document containing tables, charts and discussion. If you work with someone
please submit only one lab printout per group. Be sure that all names are on the printout.
else,
21
STAT 101:
13
NAME: _______________
TOPICS: Median; Variation; Exam Review
DOCUMENTS:


HANDOUTS: Orange sheet #13; Green #13a & 13b (Review Sheets)
AVAILABLE ONLINE: Orange #13; Green #13a & 13b (with answer keys)
HWK:



Review Ch. 1, Ch. 2 through section 2.3
Green Sheet #13a & 13b, as needed - finish off review problems (answers online)
Exam #1 take-home portion
FORMULAS: Available on prior orange sheets
NEXT CLASS: Exam #1; Exam #1 Take-home section due at beginning of class
10.15.2015
EXAM #1 Take-Home
8:30
10:00
Data Set #1 Exercise
Brown, C
Brandifino
Brown, N
Gaines
Davis
Lee
DeFazio
Lin
Neider
Preiss
Stat Essentials (taken from today): Be able to: 1) obtain a median; 2) determine which
Perez
Sanders
statistic, mean or median, might be the better one to use as a measure of center in a given situation.
A review of sample items representing potential exam topics.
Salaway
Valenti
Tompkins
Valoroso
Exam 1 Topic Areas for Review:
Potential exam topics:
See Handouts through today and related online materials.
1. Terms and their relationships
2. Assessing table & chart content for accuracy
3. Interpretation & discussion of table & chart content
4. Recognition of appropriate/inappropriate data presentation
5. Sampling techniques – identification and calculation
6. Combinations, permutations, multiplication rule
7. Reading contingency tables
8. Building qualitative tables (2 types) and charts (pie, pareto, bar)
9. Building quantitative tables (2 types) and charts (histogram, dot plot, stem-and-leaf, ogive,
frequency polygon)
10. Statistics: mode, median, mean, midrange, minimum, maximum, range, skewness.
11. Calculation of distribution skew (Pearson’s I)
12. Distribution shapes
13. Sigma
Formulas: Any necessary formulas for the classroom portion of the exam will be provided.
EXAM #1 TAKE-HOME PROBLEMS [16pts.]: On this sheet,
complete the problems on the reverse and submit this sheet at the beginning
of class #14 (exam day). (Grading for these problems are noted with the
problems.)
Walsh
Data Set #2 Shot Size
Carney
DeMarzo
Conrade
Dolce
DiTommaso
Gaynor
Hicks
Greene
O'Brien
Korankyi
Prickett
Pace
Sutton
Salomone
Vavoules
Zuckerman
Data Set #3 Tip Size (%)
Guidetti
Alix
Kodya
Asfand
Layman
Bartlett
Malventano
Christofel
Provost
Companion
Randell
Fancher
Swan
Mecca
Williams
Minasi
Data Set #1: Weekend Exercise
The following are data on weekend exercise time for 20 females consistent with summary quantities in the paper :An
Ecological Momentary Assessment of the Physical Activity and Sedentary Behavior Patterns of University Students” (Health
Education Journal [2010])
Weekend Exercise (minutes): 84.0 27.0 82.5 0.0 5.0 13.0 44.5 3.0 0.0 14.5
45.5 39.5 6.5
34.5 0.0 14.5 40.5 44.5 54.0 0.0
Data Set #2: Alcohol Poured
The following data are consistent with summary statistics that appeared in the paper “Shape of Glass and Amount of Alchol
Poured: Comparative Study of Effect of Practice and Concentration? (British Madical Journal) [2005]). Data represent the
alcohol amount (in ml) poured into a tall, slender glass for individuals asked to pour a “shot” of alcohol (44.3 ml or 1.5 oz.).
Shot Size (ml): 44.0 49.6 62.3 28.4 39.1 39.8 60.5 73.0 57.5
56.5 65.0 56.2 57.7 73.5 66.4 32.7 40.4 21.4
Data Set #3: Restaurant Tipping (%)
The following data represent the tipping rate for 19 restaurant tables, consistent with summary statistics given in the paper
“Beauty and the Labor Market: Evidence from Restaurant Servers” (unpublished manuscript [2007]}.
Tip Size (%):
0.0
5.0
45.0 32.8
13.9
10.4
55.2
50.0
10.0 14.6
38.4 23.0 27.9
27.9
19.0
10.0
32.1
11.1
15.0
REMEMBER, This sheet must be submitted at the BEGINNING of the exam period. It will not be accepted after that
point in time. Problems completed on another sheet (e.g. notebook page) will not be accepted.
22
Data assignment: See the front of this sheet for identification of the data set to which you have been assigned.
Exam #1, Problems:
1) [3] Identify HERE the characteristics of the variable for your data set. [Circle three choices, 1 pt. each]
[Qualitative
Quantitative]
[Discrete
Continuous
N/A]
[Nominal
Ordinal
Ratio]
2) [2] Show how you calculated the class width for your data set. (See the next item for specifications)
3) [5] Create a grouped frequency table of your data set having five classes with the lower class limit of the first class at:
 0.0 for Weekend Exercise; round width up to a multiple of 5 (e.g. round 7.2 up to 10 add to width by5’s if needed –
width to 15, 20, etc.)
 105.0 for Shot Size (Alcohol Poured); round width up to a multiple of 5 (e.g. round 7.2 up to 10 add to width by5’s if
needed – width to 15, 20, etc.)
 0.0 for Tip Size; round up width to a multiple of 4 (e.g. round 7.2 up to 8 add to width by 4’s if needed – width to 12, 16,
etc.)
4) [3] Create an ogive of the data contained within the frequency table you have made.
5) [3] SPSS –based Statistics: Determine the statistics listed below by using SPSS. HOW: Open SPSS > close the initial
dialog box > enter data values into the first column (on data view tab) > Analyze > Descriptive Stats > Frequency > get stats
Cell #1) PLACE CLASS WIDTH CALCULATIONS HERE [2;
Cell #2) PLACE THE FREQUENCY TABLE HERE [4;
grading: 0 nothing; 1 partially complete; 2 complete presentation of process)]
grading: 3 one error; 2 > one error; 0 no table]
Cell #3) PLACE THE OGIVE HERE [4;
Cell #4) PLACE SPSS STATISTICS HERE [3;
grading: 3 one error; 2 > one error; 0 no chart]
grading: 1.5 incomplete listing; 0 no statistics]
Minimum: _____
Maximum: _____
Median: _____
Mean: _____
Range: _____
Standard Deviation: _____
x: _____
Skewness: _____
23
14
STAT 101
TOPICS: EXAM #1
DOCUMENTS:
10.20.2015

HANDOUTS: Orange #14
 AVAILABLE ONLINE: Orange #14
 HWK: Review text sections 2.4, 2.5
NEXT CLASS: Measures of Variation, Position, Box Plots, etc.
Stat Essentials (taken from today): Application of statistical analysis
Portion sizes increase in 'Last Supper' paintings
By Nanci Hellmich, USA TODAY (3/23/2010)
If your food portions seem to have
grown larger over the years, you have
some blessed company.
Two researchers analyzed the food and
plate sizes in 52 of the most famous
paintings of The Last Supper and found
that the portion sizes in the paintings
have increased dramatically over the
past millennium, from years 1000 to
2000.
Using a computer program, they
compared the size of loaves of bread,
main dishes and plates to the size of the
heads of the disciples and Jesus in the
artwork, including Leonardo da Vinci's
famous depiction of the event.
ABOVE: "The Last Supper" painting by Duccio, 1308-11. Note the size of the food and drink on
the table compared to the size of the heads of Jesus and his disciples.
BELOW: "The Last Supper" painting by Tiziano Vecellio Titian.
Findings published in April's
International Journal of Obesity: Over
that 1,000-year period, the main course size increased by 69%, plate size 66% and
loaves of bread 23%. The biggest increases in size came after 1500.
The researchers used paintings of this event "because it is the most famous supper
in history," which artists have been painting for centuries, so the paintings provide
information about plate and entree sizes over time, says Brian Wansink, director of
the Cornell (University) Food and Brand Lab in Ithaca, N.Y. One possible reason
for the increase: Food may have become more available and less expensive, he
says.
He did the research with his brother, Craig, a professor of religious studies at
Virginia Wesleyan College in Norfolk, and a Presbyterian minister.
The three Gospels (Matthew, Mark and Luke), which include descriptions of The
Last Supper, mention only bread and wine, but many of the paintings have other
foods, such as fish, lamb, pork and even eel, says Craig Wansink.
The use of fish in the meals is symbolic because it's an image that is used to
represent Christianity, he says. Among the reasons for the symbolism: A number of
the disciples were fishermen, and Jesus told them "to be fishers of men," he says.
Plus, he says, Jesus performed several miracles with fishes and loaves.
As Easter approaches, he says, people may want to study the paintings because
they illustrate one of the "most important moments in Christianity. It's both
beautiful and haunting."
24
15
STAT 101
TOPICS: Measures of Variation; Measures of Position
DOCUMENTS:


10.22.2015
HANDOUTS: Orange sheet #15
AVAILABLE ONLINE: Orange #15, Measures of Variation ppt; Measures of Position ppt; Anatomy sheets related
to: Summary Statistics; Symmetry & Skewness; Standard Deviation
HWK:




Text Readings: review, yet again, ch. 2, sections 2.4 & 2.5
Text Problems: none
Complete the back side of Green Sheet #11 (printed on orange paper)
Items Below (Only ones covered in class)
FORMULAS:
Mean
Variance
Standard Deviation
n
Sample (by definition formula):
Sample (by computational formula):
z-score: z 
x

x
x
i 1
_
i
n
Pearson’s
I
2
s
nx 2  (x) 2
s 
n(n  1)
n x 2  (x) 2
s
n(n  1)
2
above
 ( x  x)
( x  x ) 2
s2 
n 1
3( x  median )
s
CVAR 
n 1
s
_
* 100%
x
NEXT CLASS: Measures of position (cont.); Correlation (?)
Stat Essentials (taken from today): Be able to: Variation: 1) explain what a standard deviation represents; 2) obtain a
standard deviation using either formula (definition or computational); 3) interpret what the standard deviation represents in a
given situation; 4) Empirical Rule; Position: 1) Five-number-summary; 2) Calculating Quartiles.
CRICKETS:
THE DATA: Temperature vs. Cricket Chirps: Crickets make a chirping noise by sliding their wings over each other.
Perhaps you have noticed that the number of chirps seems to increase with the temperature. The following data list the
temperature (Fahrenheit) and the number of chips per second for the striped ground cricket.
X: Temperature (Fo): 69.4 69.7 71.6 75.2 76.3 79.6 80.6 80.6 82.0 82.6 83.3 83.5 84.3
Y: Chirps/second:
15.4
14.7 16.0 15.5 14.4 15.0 17.1 16.0 17.1 17.2 16.2 17.0
18.4
Given: xxyyxy
88.6
20.0
93.3
19.8
Problem 15.1:
Determine the mean, median, mode for both of these variables.
Modes:
Temp: 80.6 degrees F
Chirps: 16.0/sec; 17.1/sec. (bimodal)
Temp Chirp
IQR
1.5(IQR)
LL
UL
8.3
12.45
62.75
95.95
1.8
2.7
12.7
19.9
25
Problem 15.2:
Using the computational formula, determine the standard deviations for these two variables.
s.d. listed in prior table
Problem 15.3: (z-score)
A temperature of 93.3o is how many standard deviations away from the mean? Sixteen chirps per second is how many
standard deviations away from the mean?
Temp: z = (93.3 – 80.04)/6.707 = 1.977 s.d above mean
Chirps: z = (16 – 16.65)/1.70 = -.38 s.d below mean
Problem 15.4: (skewness of distribution)
3( x  median )
Determine using Pearson’s I, where I 
, whether or not the data distributions are skewed.
s
Temp: I = (3(80.04-80.6))/6.71 = -.25 yes
Chirps: I = (3(16,65-16.2))/1.7 = .79 yes
Despite a skew value, both would be considered normally distributed.
Problem 15.5: (variability measure)
Using the Coefficient of Variation formula, determine which of these two variables demonstrated the greatest variability.
Variation:
Temp: CVAR = (6.71/80.04)*100 = 8.4%
Chirps: CVAR = (1.7/16.65)*100 = 10.2%
Chirps has greater variability
Problem 15.6: (visual presentation of distribution; save this one
until we do box plots)
Create a box plot for each of the variables.
26
16
STAT 101
TOPICS: Box plots; z-score; Pearson’s I, Coefficient of Variability (CVAR)
DOCUMENTS:


10.27.2015
HANDOUTS: Orange #16; Green #16
AVAILABLE ONLINE: Orange #16; Green #16; Measures of Position ppt.
HWK:



Text Readings: Ch. 9,sections 9.1, 9.2; Ch. 2 scatter plot p. 58
Text Problems: p. 107 #7 – 14, 21, 25, 26, 31, 35, 61.
Items below
FORMULAS: Mean, median, quartiles, variance, standard deviation on prior sheets
z-score: z 
x
Pearson’s

I
3( x  median )
s
CVAR 
s
_
* 100%
x
NEXT CLASS: Correlation & Regression; ExCr #5 due
Stat Essentials (taken from today): Be able to: 1) obtain the five-number-summary; 2) build a box plot; 3) determine
variability measures: skew (Pearson’s I), Coefficient of Variability, z-score.
THE DATA
Woodpeckers: Forest managers are increasingly concerned about the damage done to animal populations when forests are
clear-cut. Woodpeckers are a valuable forest asset, both because they provide nest and roost holes for other animals and birds
and because they prey on many forest insect pests. The article “Artificial Trees as a Cavity Substrate for Woodpeckers,”
(Journal of Wildlife Management [1983]) reported on a study of how woodpeckers behaved when provided with polystyrene
cylinders as an alternative roost and nest cavity substrate. Noted below are selected values of X = ambient temperature (oC)
and Y = cavity depth (in centimeters). [Devore & Peck p. 558]
Observation:
1
Temperature (oC): -6
Hole Depth (cm): 21.1
2
-3
26.0
Given: n = 12  x = 131
3
-2
18.0
4
1
19.2
y = 196.3
5
6
16.9
6
10
18.1
 x2 = 2939
7
11
16.8
8
19
11.8
 y2 = 3445.25
9
21
11.0
10
23
12.1
11
25
14.8
12
26
10.5
 xy = 1622.3
16.1) [1] Using the computational formula, determine the standard deviation for the variables.
[Note: x, etc. listed above with data values]
Temperature
s
n  x 2  ( x ) 2
n( n  1)
12( 2939)  1312
35268  17161
18107



 137.17  11.71Celcius
12(11)
132
132
Hole Depth
s
n  y 2  ( y ) 2
n( n  1)

12(3445.25)  196.32

12(11)
41343  38533.69

132
2809.31
 21.28  4.61cm
132
16.2) [1] Determine, using Pearson’s I, whether or not the variable to which you were assigned is skewed.
TEMP:
3( x  median) 3(10.9167  10.5)
1.2501
I


 .1067
s
11.71214
11.71214
DEPTH:
I
3( x  median) 3(16.3583  16.85)  1.4751


 .3197
s
4.61331
4.61331
Yes No (circle one): Given the value of “I,” we would consider this
variable approximately normally distributed.
Both would be considered approximately normally distributed
27
16.3) [1] For the variable’s maximum value, determine how many standard deviations it is away from the mean.
TEMP:
z
x  x 26  10.92

 1.29
s
11.71
DEPTH:
z
x  x 26  16.36

 2.09
s
4.61
16.4) [1] Determine the variability of the variable.
TEMP: CVAR 
s
_
x
*100 
11.71
*100  107.23%
10.92
DEPTH: CVAR 
s
_
*100 
x
4.61
*100  28.18%
16.36
As a result of comparing variability via CVAR, it appears that ______________ has greater variability than ___________.
16.5) [5]Create a modified box plot for each variable. Although you may not need these values, calculate the IQR, upper limit,
and lower limit.
Temperature (C): -6
-3
-2
1
ALL MEASURES IN DEGREES CELCIUS
Min: -6 Q1: -1.25 Q2: 10.5 Q3: 22.5
6
MAX: 26
10
11
IQR: 23.75
19
21
L. Limit: -36.875
23
25
26
U. Limit: 58.125
Hole Depth (cm): 21.1
26.0
18.0
19.2
16.9
18.1
16.8
11.8
11.0
12.1
14.8
ALL MEASURES IN CM
Ordered: 10.5 11.0 11.8 12.1 14.8 16.8 16.9 18.0 18.1 19.2 21.1 26.0
Min: 10.5 Q1: 11.875 Q2: 16.85 Q3: 18.925 MAX: 26 IQR: 7.05 L. Limit: 1.3 U. Limit: 29.5
10.5
28
STAT 101
17
NAME: _____________________
TOPICS: Correlation & Regression
DOCUMENTS:



10.29.2015
HANDOUTS: Orange #17; Green #17
AVAILABLE ONLINE: Orange #17; Green #17; Correlation ppt. & Regression ppt.
TABLE: Pearson Correlation Coefficient table distributed on day #4 (on yellow sheet w/ Table of Random Numbers)
HWK:



Text Readings: Ch. 9, sections 9.1, 9.2, & 9.3 pp. 513-514 only; Ch. 2 p. 58 (scatter plot)
Text Problems: p. 495 #1-4, 9-12, 15-21
Items below (Class Assignment #4)
FORMULAS:
Hypotheses: Null Hypothesis (H0) vs. Alternative Hypothesis (H1) for correlations:
Statistically:
H0:   0 ( rho  0 )
H1:
 0
In Words:
H0: There is no linear relationship between variable X and variable Y.
( rho  0 ) H1: There is a linear relationship between variable X and variable Y.
Correlation: r 
nxy  (x)(y )
nx  (x) 2 ny 2  (y ) 2
2
Regression:
nxy  (x)(y )
n ( x 2 )  ( x ) 2
Additional formulas located on prior sheets

y  b0  b1 x
b1 
b0  y  b1 x
or
b0 
(y)(x 2 )  (x)(xy)
n(x 2 )  (x)2
NEXT CLASS: Correlation & Regression; QUIZ #4; ASSIGNMENTS: DUE CA #4; Hwk #3
Stat Essentials (taken from today): 1) Be able to: 1) identify the steps leading to correlation and regression; 2)
Conducting a correlation by hand and via SPSS; 3) Scatter Plot – building and interpreting; 4) Basics of Regression.
HOMEWORK #3: Selected from:
1) Green 13A through problem #16 (sigma)
2) Green 13B front side
3) Orange #15
4) Text Problems listed on Orange #16
5) Green #16A back side
6) Text Problems listed on Orange #17
CLASS ASSIGNMENT #4
Crickets Data
Woodpeckers Data
8:30
10:00
8:30
10:00
Brown, C Alix
Conrade
Asfand
Brown, N Brandifino Guidetti
Bartlett
Carney
DeMarzo Kodya
Christofel
Davis
Dolce
Layman
Companion
DeFazio
Gaines
Malventano
Fancher
DiTommasoGreene
Prickett
Gaynor
Hicks
Lin
Provost
Korankyi
Neider
Preiss
Randell
Mecca
O'Brien
Sanders
Sutton
Minasi
Perez
Valenti
Swan
Pace
Salaway
Valoroso Vavoules
Salomone
Tompkins Walsh
Williams
Zuckerman
CLASS ASSIGNMENT #4 [12]
GENERAL INSTRUCTIONS:





ON THIS SHEET Complete the Problem Set to which you have been assigned. The data are located on Orange
sheets #15 and #16, as well as available online.
DUE DATE: 11.3.2015
Item values for this assignment are located within [ ].
Remember labels, where appropriate.
CADE TUTORS: This assignment is for the student to do, not you. Assistance may be provided by using problems
on Green Sheet #17 (student has a copy).
29

ASSIGNED DATA SET (circle one):
CRICKETS
WOODPECKERS
1) [1] What is being studied? Relationship between ____________________________________
______________________________________________________________________________
2) [1] Does it make sense to study a relationship between these two variables?
_____
Why? ________________________________________________________________________
______________________________________________________________________________
3) [3] Make a scatter plot of these variables.
4) [2] State in words the null and alternative correlation hypotheses to be tested.
H
0
: r  0 ___________________________________________________________
H
1
: r  0 ___________________________________________________________
5) [3] Given that the scatter plot indicates a relationship between these two variables. Calculate the
correlation for the two variables.
r = _________
6) [1] Determine if the correlation is statistically significant: not sig.
 = .05
 = .01
(Use: Critical Values for the Pearson’s Correlation Coefficient Table; text page A26)
30
STAT 101
18
TOPICS: Correlation & Regression; da Vinci handout
DOCUMENTS:


HANDOUTS: Orange #18
AVAILABLE ONLINE: Orange #18; Normal Distribution ppt.
11.3.2015
HWK:



Text Readings: Ch. 5, sections 5.1, 5.2
Text Problems: p. 505 #7-12, 17
Problem 18.1 below
FORMULAS:
Correlation & Regression on prior sheet
SSExplained
where:
SSTo
SSE  1  [ SS Re s  y 2  ay  bxy]
Coefficient of Determination = Correlation, r, squared (r2)
SSTo  y 2 
(y ) 2
n
SS Re s  y 2  ay  bxy
( where, a  y  int; b  slope )
or
r2 
( where, a  y  int; b  slope )
NEXT CLASS: Normal Distribution
Stat Essentials (taken from today): Review from prior classes 1) Steps leading to correlation and regression; 2)
Scatter Plot – building and interpreting; Today: 3) Regression – developing the regression equation; 4) terminology related to
correlation & regression.
Problem 18.1:
Given the following data set obtain: 1) in words identify what the null and
alternative hypotheses state for this set of data; 2) a correlation coefficient; 3)
the significance level of the correlation; 4) the coefficient of determination; 5)
the regression equation for the line of best fit; 6) Add the regression line to the
scatter plot to right (approximate location); and 7) calculate values for Yogi and
Booboo. You may do this problem by manually calculating the values on the
back of this sheet or using SPSS.
Lengths & Weights of Male Bears
Length (in.):
53.0 67.5 72.0 72.0 73.5 68.5 73.0 37.0
Weight (lbs.): 80
344 416 348 262 360 332 34
Given:  x = 516.5 x2 = 34525.8 y = 2176 y2 = 728520 xy = 151879
In words state the null and alternative hypotheses for these two variables.
H
0
:   0 ______There is no relationship between length and weight.
H
1
:   0 ______There is a relationship between length and weight.
r = .897
Sig. level of r = .01
Regression Equation: y-hat = -351.59 + 9.659(x)
Given the regression equation you identified estimate the weight of the following two bears:
Yogi who is 76.0 inches long.
Booboo (aka Bobo) who is 43 inches long.
Estimated weight: outside data range
Estimated weight: 63.747 lb.
31
19
STAT 101
TOPICS: Standard Normal Table, Normal and Non-Standard Normal Distributions
DOCUMENTS:
11.5.2015
HANDOUTS: Orange #19, Green #19; Standard Normal Distribution Table; Practice
Sheets
AVAILABLE ONLINE: Orange #19; Green #19; Normal Distribution and
Distribution of Sample Means PowerPoints; Anatomy (2): Normal Distribution, Standard Normal


HWK:



Text Readings: –Ch. 5, sections 5.1 – 5.3;
Text Problems - p. 246 #19–30; p. 252 #1, 2, 7, 8; p. 505 #18; p. 112 #62
Items below.
FORMULAS:

Probability Rules: 1) P ( X )  1
z
2) 0  P ( X )  1
x

z
xx
s
NEXT CLASS: Normal Distribution; Distribution of Sample Means; ExCr #6 due
LAB #2 DATE CHANGED FROM NOV. 10 TO NOV. 12; MILNE 108
Statistics Essentials: Know: 1) the characteristics of a standard normal distribution; 2) how to identify a probability
distribution; 3) find an area associated with a z-score (use the standard normal table); 4) find a z-score associated with an area
(use the standard normal table); and 5) determine the probability of occurrence specified by an area under the standard normal
curve.
Problem 19.1: Identify the area associated
with the following z-scores.
Problem 19.2: Identify the z-score associated
with the following areas.
1) z = -1.54: area = .0618
2) z = .50: area = .6915
1) area = .0207: z = -2.04
3) z = 2.33: area = .9901
4) z = -1.645: area = .0500
3) area = .9500: z = 1.645
2) area = .5000: z = 0
4) area = .9900: z = 2.33
Draw the area under the standard normal curve and determine the probability noted.
Problem 19.3: P(z  1.62)
Problem 19.4: P(-.42  z or z  .42)
ANSWER:
.3372*2 =
.6744
1.0000
-.9474
.0526
.3372
.6628
.9474
.3372
Problem 19.5: P(1.00  z  2.50)
.9938
-.8413
.1525
.9938
Problem 19.6: P(-.26  z  0.00)
.5000
-.3974
.1026
.5000
?
.8413
?
.3974
32
STAT 101
20
TOPICS: Non-Standard Normal Distributions; Distribution of Sample Means; Central
Limit Theorem
DOCUMENTS:


HANDOUTS: Orange #20; Green #20
AVAILABLE ONLINE: Orange #20, Green #20; Dist. Of Sample Means ppt.
11.10.2015
HWK:




Text Readings: Ch. 5, sections 5.4
Text Problems: p. 262 #33, 34; p. 274 #1-8, 1317; Prior Topics: p. 505 #19; p. 110 #39, 44
Problems from Green #20 – any we do not get to in class
Items below
FORMULAS: See Orange #19; Dist. Of Sample Means:

x


x


n
z
x

n
NEXT CLASS: LAB IN MILNE 108; CA#5 distributed
Statistics Essentials: Know: 1) the characteristics of the distribution of sample means; 2) the Central Limit Theorem.
Problem 20.1
Driven to distraction: It seems almost silly to say: Keep your eyes on the road. But with cars now more than ever resembling
mobile offices, massive entertainment centers, telephone booths and lunch counters – well, the road is sometimes the last thing
we’re looking at. It’s much more interesting to jabber away on the cell phone or toy with your iPod – but those distractions
can cut your reaction time in half. And with most accidents occurring within a few seconds, you need all the time you can get.
So hang up, find a radio station you like and keep looking forward. (Source: MetLife yourlife, Summer 2007; italics added)
So what do you know? Assume it takes you 2 seconds to react and apply the brakes when driving and paying
attention to the road. How long will it take you to react while being distracted by food, phone, etc?
Problem 20.2
Marriage Patterns: Are more people living together before getting married? The results of a recent survey indicated that
48% of respondents indicated that they were in an unwed relationship and that forty percent of these couples marry within three
years. If there were 1200 respondents to the survey, how many of the respondents would marry within three years?
1200*.48 = 576; 576*.40 =230.4 couples
Problem 20.3
Education and self-employment: According to a recent Current Population Reports, the
population distribution of number of years of education for self-employed individuals in
the United States has a mean if 13.6 and a standard deviation of 3.0.
If one self-employed person was randomly selected, what would be the probability that
he/she would have an education level less than 11 years?
z
x


11  13.6  2.6

 .87
3
3
prob. associated with -.87 = .1922
Find the mean and standard error (standard deviation) of the sampling distribution of the mean for a random sample of size
100.

x
   13.6 years

x


n

3
3

 .3
100 10
If a sample of 100 self-employed individuals is selected, find the probability that their mean education level is less than 11.0
z
years.
x

n

11  13.6  2.6

 8.66
3
.3
probability essentially 0
100
33
21
STAT 101
TOPICS: Lab #2: Correlation & Regression via SPSS
DOCUMENTS:


11.12.2015
HANDOUTS: Orange #21 (Lab #2); Green 21A (CA#5)
AVAILABLE ONLINE: Orange #21; Green #21A (CA#5) & 21B; Confidence Intervals ppt.
HWK:



Complete Class Assignment #5 (see reverse)
Complete the lab.
Complete problems 7 & 8 on Green #19
NEXT CLASS: Dist. Sample Mean; Confidence Intervals (?); DUE: Lab #2, CA#5; Quiz #5 (topic: normal dist.)
Stat Essentials (taken from today): Application using SPSS.
STAT 101 Lab #2: Correlation & Regression [12pts.]
Filename: daVinci_Sp2011_Thru_F2015.sav (N=740).
References: See the online SPSS manual for Correlation and Regression topics
Lab Report:
 All responses must be placed in a Word document.
 One two-sided sheet max.
 When copying tables and charts use the Copy Special (Metafile) option so that you can control size and location
of the tables and charts.
 In the report please number your responses to correspond with the numbers below.
 NO MORE THAN TWO INDIVIDUALS PER WORKING GROUP (One report copy per group).
Demonstration: Use of SPSS to address data analysis within the lab.
LAB #2:
CORRELATION & REGRESSION
1.
[1] Does it make sense that there might be a relationship between Height and Arm_span? (Yes/No with any relevant
discussion of why.)
2.
[1] Before you make a scatter plot, let us assume that we believe one of these variables can be used to predict the other
one. Which variable is X and which is Y? What logic did you use to identify one of the two variables as the
independent (predictor) variable X and the other as the dependent variable Y? (Flipped a coin is not an option here.)
3.
[2] Create a scatter plot of the two variables you are studying. Include a fit line on the scatter plot. Include this plot
in your document. Briefly discuss what this scatter plot suggests to you (e.g. direction of the correlation, strength,
etc.).
4.
[2] In your report state in both statistical form and in words the null and alternative hypotheses for the two variables.
5.
[2] Determine the correlation for the variables under study and place in your report both the correlation table for these
two variables and a statement identifying the correlation and its level of significance.
6.
[1] Determine the value of the coefficient of determination. What does this statistic tell us about the relationship (i.e.
explain what this statistic means)? What other factors might affect the dependent variables?
Coefficient of Determination: explained variation/total variation
^
r2 

( y  y ) 2
OR
r2

( y  y ) 2
7.
[3] Obtain the equation for the regression line of best fit, place it in your report and estimate the Arm_span of a person
with a Height of 169.50 cm. [Under the column headed by a “B” in the fourth regression table are the values for the
y-intercept (labeled “constant”) and slope.] Check the data file to determine if there was anyone 169.50 cm tall. If so,
what was his/her arm-span? Does it match your estimate? Why/why not?
34
Class Assignment #5
The problems for this assignment are located online as Green #21B, which is an excel file.
Specific assigned problems are noted here on Orange #21.
Instructions:
This assignment requires completion of two correlation &
regression problems.
The first problem is required and will be the basis for
most of your grade. Look at the number following your
name - that is your required problem. Go to Green
#21B, located online, for the problem information.
The second problem, worth one (1) point, is required in
order to receive a grade on the first problem. You may
select from among problems #8, 9, 10, 14, or 15 to
complete this portion of the assignment.
Both problems must be completed on the distributed
Class Assignment #5 sheet (Green #21A).
Please:
1) place your answers in the designated spaces.
2) be organized and neat in the presentation of your
calculations.
3) know that the second problem has to be complete in
its entirety, as appropriate, in order to receive
credit for the first problem.
CLASS ASSIGNMENT #5 FALL 2015
Must complete two (2) problems.
1) Required problem number located after name.
2) Your choice selected from five specified problems.
Problems located on Green #21B
8:30 AM
10:00 AM
Brown C
Brown N
Carney
Conrade
Davis
DeFazio
DiTommaso
Guidetti
Hicks
Kodya
Layman
Malventano
Neider
O'Brien
Perez
Prickett
Provost
Randell
Salaway
Sutton
Swan
Tompkins
Vavoules
Williams
Alix
Asfand
Bartlett
Brandifino
Christofel
Companion
DeMarzo
Dolce
Fancher
Gaines
Gaynor
Greene
Korankyi
Lin
Mecca
Pace
Preiss
Salomone
Sanders
Valenti
Valoroso
Venditti
Walsh
Zuckerman
#1) Required
1
2
#2) Select
choose
one from
3
problems
4
#8, 9, 10,
5
14, or 15
6
1
2
3
4
5
6
1
2
3
4
5
6
1
2
3
4
5
6
35
STAT 101
22
TOPICS: Distribution of Sample Means; Confidence Intervals
DOCUMENTS:



HANDOUTS: Orange #22; Green #22 & #23
11.17.2015
AVAILABLE ONLINE: Orange #22; Green #22 & #23; Anatomy Sheets; Confidence
Intervals ppt.
RELEVANT ANATOMY SHEETS (4): Z, Confidence Intervals for Small Samples, Large Samples, &
Proportions
HWK:


Text Readings: – Ch. 6, sections 6.1 – 6.3
Text Problems: -p. 274 (repeated) #1 – 8, 13, 14, 17; Review: p. 263 #31; p. 505 #21; p. 112 #57 [do box plot for
“You” data only]
 Selected items from Worksheet #22 & #23
 Item(s) below.
FORMULAS: Confidence Intervals & sample sizes [NOTE: see probabilities on Orange #19]
  
x  z 

2
 n
 s 
x  z 

2 n 


p  z 
2


 s 
x  t ,df 

2
 n

C onfidence Intervals for a Mean
_
X % C .I. =( x 
known:
s known:
(unknown)

z
x  t
2
2
, df
2
 z 
n  pˆ qˆ  2 
 E 


2


_
X % C .I. = ( p  E    p 
E  x E )
30
x 
 z  
 2 
n
 E 


C onfidence Intervals for a P roportion
S ample S ize


pq 

n 


30

  


n 

x 
 s 


 n
 s 
x  z 

2 n 
z
2
  


n 

p
z



2


E)
 
pq 

n 

NEXT CLASS: Confidence Intervals for Means &Proportions; ExCr #7 available
Statistics Essentials for Confidence Intervals: Know: 1) what a confidence interval represents and how to calculate
one for specific conditions; 2) what a margin of error is and how to obtain it; 3) the table above; 4) obtaining Z critical
values.
Problem 22.1
Pregnancy Duration: The lengths of pregnancies are normally distributed with
a mean of 268 days and a standard deviation of 15 days.
1) Wanda has been pregnant for a really, really long time. So long in fact that
only one-half of a percent of women have been pregnant longer. For how many
days has Wanda been pregnant?
.5% = .005 area; every area has a z-score; 1.0000 - .0050 = .9950; look up
the z-score associated with an area of .9950 (area to left)
x    z  268  (2.575)(15)  306.625days
2) Find the mean and standard error (standard deviation) of the sampling distribution of the mean for a random sample 10
pregnancies.

x
   268days

x


n

15
 4.74( prob.essentiall y 0)
10
3) A sample of 10 pregnant woman is selected. Find the probability that their mean pregnancy is greater than 283 days.
x
283  268
15

 3.16 associated area = .9992; > 283 days: 1.0000 - .9992 =.0008 prob.

15
4.74
n
10
Problem 22.2
z

Critical Value of za/2: Calculate the za/2 critical value associated with the following Confidence Levels.
92%: za/2 = 1.75
96%: za/2 = 2.05
90%: za/2 = 1.645
98%: za/2 = 2.33
36
STAT 101
23
TOPICS: Confidence Intervals: Means for large samples, small samples ( dist.) &
proportions
11.19.2015
DOCUMENTS:


HANDOUTS: Orange #23; Green #23 (distributed on day 22)
AVAILABLE ONLINE: Orange #23; Green #23; Ex. Cr. #7; Hypothesis Testing ppt.
HWK:

Text Readings: Ch. 6, 6.2 (tC onfidence Intervals for a Mean
C onfidence Intervals for a P roportion


_
_
distribution), 6.3 (proportions)
(
x

E



x

E
)
X % C .I. =
X % C .I. = ( p  E    p  E )
 Text Problems: p. 311 #ODD
S ample S ize
 30
problems 1 – 9, 13, 15, 17, 19; [only
 30


 pq 
p z 
if we get to proportions: p. 332 #1 –
  

known:
  
x  z


n 
x




z
n 



n 

3, 7, 11
s


 Green #23: determine the appropriate s known:
 s 
x  z 
x t



(unknown)
2 n 
 n
formula for items #1 – 17; Calculate
CI’s for problems #2, 4, 10
 Print out as full pages the last three Hypothesis Testing PowerPoint slides. They are our working examples.
 Items below.
FORMULAS: Listed in grid
NEXT CLASS: Confidence Intervals (proportions); Hypothesis Testing (intro); DUE: Quiz #6; Hwk #4, ExCr #7




2

2
2
 , df
2
Statistics Essentials for Confidence Intervals: Know: 1) what a confidence interval represents and how to calculate
one given specific conditions; 2) what a margin of error is and how to obtain it; 3) how determine the mean and margin of error
if given a confidence interval; 4) how to determine which formula to use based upon provided data.; 5) the table above.
HOMEWORK #4: Randomly selected from following assignments.
1. Text problems from Orange #18
2. Text problems from Orange #19
3. Text problems from Orange #20 (ONLY NEED problems from pages 110, 262, 505; p. 274 problems are part
of Orange #22)
4. Text problems from Orange #22 (includes problems on p. 274)
5. Text problems from Orange #23
6. Green #19 problems #6 & 7
Problem 23.1
A few classes ago we collected data on the length of time one could stand on
one foot with one’s eyes closed. Using the data provided in the
accompanying table for female class members, build 95% confidence
intervals about the observed means for left foot up and right foot up.
Assuming data are approximately normally distributed
(they are)
Left foot up:
17.28548
  
x  z 
)  20.768  (1.96)(3.966)  20.768  7.772
  20.768  (1.96)(
2 n 
19
95% CI = 20.768±7.772 seconds
Right foot up:
OR
95% CI = (12.996, 28.54) seconds
16.5216
  
x  z 
)  23.0437  (1.96)(3.9)  23.0437  7.429
  23.0437  (1.96)(
2 n 
19
95% CI = 23.0437±7.429 seconds
OR
95% CI = (15.61,30.47) seconds
37
24
STAT 101
TOPICS: Confidence Intervals for Proportions; Hypothesis Testing (intro)
11.24.2015
DOCUMENTS:
 HANDOUTS: Orange #24; Green #24
 AVAILABLE ONLINE: Orange #24; Green #24; Hypothesis Testing ppt.
HWK:



Text LARSON: Ch. 7, section 7.1 – 7.3
Green #23: problems #4 - 6, 10, 13, 14
Class Assignment #6 (problems on green #24B)
FORMULAS:
Hypothesis Testing
z
x

0
t
x
Null Hypothesis
TRUE
FALSE
Decision:
RETAIN
^
z
0
s
n
Testing a Hypothesis
n
p p
pq
n
REJECT
Correct
Decision
Type II Error
b
Type I Error

Correct
Decision
Steps in testing a hypothesis:
1.
2.
3.
4.
5.
6.
7.
8.
9.
List the given information
State in statistical and word format the null hypothesis and the alternative hypothesis
a. Identify the “claim”
Determine if the test is one-tailed (left or right) or two-tailed
Identify the critical value for the test (or the stated p-value level at which the test is being conducted)
Draw a picture containing the critical value(s) and, after testing, the test statistic
Identify the statistical test
Conduct the test and obtain the test statistic (place it on your drawing)
Analyze your results (relationship between critical value and test statistic (or p-values comparison)
State a conclusion. Include a statement of the null hypothesis, the level at which it was tested, and whether it was retained
or rejected.
NEXT CLASS: Hypothesis Testing; CA #6 due
Statistics Essentials for Confidence Intervals (proportions): Know: 1) how to identify a confidence interval for
proportion; 2) Calculating the interval
Statistics Essentials Hypothesis Testing: Know: 1) how to write hypotheses in statistical format and in written
format; 2) what statistical significance means; 3) what terms associated with hypothesis testing mean – e.g. critical value(s),
test statistic, p value, etc.; 4) how to conduct a hypothesis test and interpret the results.
CLASS ASSIGNMENT #6:
Problem 24.1 (Correlation)(These data are from problem #7 on green 21B)
These data were obtained from a survey of the number of years people smoked
Sum
and the percentage of lung damage they sustained.
Years, x
Damage, y
x2
22
20
484
14
14
196
31
54
961
36
63
1296
9
17
81
41
71
1681
19
23
361
172
262
5060
y2
400
196
2916
3969
289
5041
529
13340
xy
440
196
1674
2268
153
2911
437
8079
a) Calculate the correlation coefficient and determine if the variables have a sig. corr.
b) Find the equation of the regression line.
c) Construct a scatter plot of the data.
d) Predict the percentage of lung damage for a person who has smoked for 30 years.
38
a)
nxy  (x)(y)
r
b)
[nx2  (x)2 ][ny2  (y)2 ]

(7  8079)  (172  262)
[(7  5060)  1722 ][(7 13340)  2622 ]
nxy  (x)(y) (7  8079)  (172  262) 11489


 1.9686
n(x 2 )  (x) 2
(7  5060)  1722
5836
b1 
11489
5836 24736
y  37.43
 .95622
x  24 . 57

b 0  y  b1 x  37 . 43  (1 . 9686 )( 24 . 57 )   10 . 94
c)

y  b 0  b 1 x   10 . 94  1 . 9686 x
Scatterplot of years vs. damage
70
60
Damage
50
40
30
20
10
10
15
20
25
Years
30
35
40
45
d) -10.94+(1.9686)(30 years)=48.118 percent damage
Problem 24.2 (Confidence Interval)
Health Clubs: A random sample of 60 female members of health clubs in Los Angles showed that they spend on
average 4 hours per week doing physical exercise with a standard deviation of .75 hours. Find a 95% confidence
interval for the population mean 
  
.75
95%C.I .  x  z 
  4.0  1.96(
)  4.0  .19  (3.81,4.19)
2
60
 n
Problem 24.3: (Normal Distribution)
Tall Clubs International: Tall Clubs International is a social organization for tall people. It has a requirement that
men must be at least 74 inches tall, and women must be at least 70 inches tall. Man’s heights are normally distributed
with a mean of 69 inches and a standard deviation of 2.8 inches. Women’s heights are normally distributed with a
mean of 63.6 inches and a standard deviation of 2.5 inches.
A) What percent of men meet the requirement?
B) What percent of women meet the requirement?
C) Are the height requirements for men and women fair? Why or why not?
x
74  69
 1.785 Area to right = .0367 or 3.67% (using z=1.79)

2.8
x   70  63.6

 2.56 Area to right = .0052 or .52%
B) z 

2.5
C) Not fair as a larger proportion of males are eligible for membership.
A) z 

Problem 24.4 (Hypothesis Testing): (probably on hold for next class)
Cigarette Tar: A simple random sample of 25 filtered 100 mm cigarettes was obtained and the tar content of each
cigarette was measured. The sample has a mean of 13.2 mg and a standard deviation of 3.7 mg. At the = .05
significance level, test the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg, which is
the mean for unfiltered king size cigarettes.
Cigarette Tar
H o :   21.1
H a :   21.1
The mean amount of tar in 100mm filtered cigarettes is  21.1 mg.
The mean amount of tar in 100mm filtered cigarettes is < 21.1 mg. CLAIM
Reject
_
x = 13.2 mg
x
Given:
t
0
s
 = 21.1 mg
= -10.67 (Test Stat.)
s = 3.7 mg
n = 25
 = .05
Left-tailed test
Retain
Critical Value = -1.711
n
Conclusion: Reject null. At the  = .05 significance level the data provide sufficient evidence
to reject the null hypothesis that the mean amount of tar in 100 mm filtered cigarettes is 21.1 mg.
TS = -10.67
CV = -1.711
39
Class Assignment #6
NAME: __________________________
Stat 101, Spring 2015 [value: 12]
Class (circle one):
Assigned Problem: # ____
8:30
10:00
Selected Problem (#1, 2, or 3); # ______
Part A) [2]:
Part A) [2]:
Part B) [2]:
Part B) [2]:
Part C) [2]:
Part C [2]:
40
Class Assignment #6
Name: _______________________
The problems for this assignment are located online as Green #24B, which is a Word document.
Instructions:
This assignment requires completion of two confidence
interval problems. The first has been assigned to you.
The second problem can be selected from problems #1,
2, or 3.
Both problems must be completed on the distributed
reverse of this sheet or a downloaded copy thereof.
Please:


place your answers in the designated spaces.
be organized and neat in the presentation of
your calculations.
CLASS ASSIGNMENT #6 FALL 2015
Must complete two (2) problems.
1) Required problem number located after name.
2) Your choice selected from three specified problems.
Problems located on Green #24B
8:30 AM
10:00 AM
Brown C
Brown N
Carney
Conrade
Davis
DeFazio
DiTommaso
Guidetti
Hicks
Kodya
Layman
Malventano
Neider
O'Brien
Perez
Prickett
Provost
Randell
Salaway
Sutton
Swan
Tompkins
Vavoules
Williams
Alix
Asfand
Bartlett
Brandifino
Christofel
Companion
DeMarzo
Dolce
Fancher
Gaines
Gaynor
Greene
Korankyi
Lin
Mecca
Minasi
Pace
Preiss
Salomone
Sanders
Valenti
Valoroso
Venditti
Walsh
Zuckerman
#1) Required
7
#2) Select
choose
8
one from
9
problems
10
#1, 2, or 3
11
12
8
9
10
11
12
7
9
10
11
12
7
8
10
11
12
7
8
9
9
41
25
STAT 101
TOPICS: Hypothesis Testing
DOCUMENTS:
 HANDOUTS: Orange #25
 AVAILABLE ONLINE: Orange #25
12.1.2015
HWK:

Problems from green #24 and this sheet
FORMULAS: Hypothesis Testing general process on prior sheet. z  x   0

n
t
x
s
n
^
0
z
p p
pq
n
NEXT CLASS: Hypothesis Testing; Test review
Statistics Essentials: Know: 1) how to write hypotheses in statistical format and in written format; 2) what statistical
significance means; 3) what terms associated with hypothesis testing mean – e.g. critical value(s), test statistic, p value, etc.; 4)
how to conduct a hypothesis test and interpret the results.
Problem 25.1:
Global Warming: As part of a Pew Research Center poll, subjects were asked if there is solid evidence that the earth is getting
warmer. Among 1501 respondents, 20% said that there is not such evidence. At the  = .01 significance level test the claim
that less than 25% of the population believes that there is not solid evidence that the earth is getting warmer.
Problem 25.2:
Toxic Mushrooms: Cadmium, a heavy metal, is toxic to animals. Mushrooms, however, are able to absorb it and
accumulate cadmium at high concentrations. The Czech and Slovak governments have set a safety level for cadmium
in dry vegetables at 0.5 parts per million (ppm). A sample of 12 Boletus piniletus pinicola mushrooms has a mean
cadmium level of .53 ppm and a standard deviation of 0.37 ppm. At the = .05 significance level, do the data provide
sufficient evidence to conclude that the mean cadmium level in Boletus piniletus pinicola mushrooms is greater than the
government’s recommended limit of .5 ppm?
Problem 25.3
Acid Rain and Lake Acidity: Acid rain from the burning of fossil fuels has caused many lakes around the world to
become acidic. A lake is classified as non-acidic if it has a pH greater than 6. Scientists obtained water samples from 15
high mountain lakes in the Southern Alps. The mean pH of these lakes was 6.6 with a standard deviation was 0.672. At
the = .05 significance level, do the data provide sufficient evidence that, on average, high mountain lakes in the
Southern Alps are non-acidic (i.e., greater than a pH of 6)?
42
Format for the take-home portion of Exam #2
A) [ ] State the null and alternative hypotheses in both statistical form and written form.
Statistically:
In Words:
Ho: _________________
Ho: _________________________________________________________
Ha: _________________
Ha: _________________________________________________________
B) [ ] List the GIVEN information:
C) [ ] The hypothesis test is (circle one):
left-tailed
right-tailed
two-tailed
D) [ ] Identify the Critical Value(s) for the test.
C.V. = __________
[may ask about p-value as well]
item E
EE
E) [ ] Draw a detailed picture displaying the
region(s) of retention and rejection of the null
hypothesis. Include the location of the Critical
Value(s) and Test Statistic (once calculated).
F) [ ] Present the formula to be used, determine the
Test Statistic and locate the T.S. on the picture.
Test Statistic: _________
Formula & Calculations:
G) [ ] State a conclusion that includes the level at which the null hypothesis was tested and whether you have retained or
rejected the null hypothesis using the original statements of the hypotheses.
43