Unit 3, Statistics
Chapter 11
Objectives:
1. Students will be able to identify the three
types of studies.
2. Students will use the following terms:
Causation and Association in the correct
context.
3. Students will identify types of bias connected
to a study.
Experimental
Observational
Survey
Causation
Association
Bias
Random Sample Treatment Subject
Warm Up
Rules of Exponents:
Product Property
a a a
m
n
mn
Quotient Property
m
a
m n

a
n
a
What is statistics?
What is statistics?
Statistics is a process to make
inferences about population
parameters based on random
population samples.
What is the difference between a
Parameter and a Statistic?
What is the difference between a
Parameter and a Statistic?
Population
Parameter
Measure of Center
Mean
Measure of Spread
Standard deviation
Sample
Statistic

X

Sx
Type of Study Choices, treatments,
or conditions
Experimental Treatments are
applied to subjects
by the researcher
Observational
Treatments are not applied
by the researcher. Subjects
may know they are being
observed but don’t know
what is observed.
Survey
Information about
treatments and/or
results is collected from
the subjects.
Example
What does this diagram of an
experimental study show?
Investigation.
Consider the following:
• Hypothesis: Listening to music while
doing homework will shorten the
time it takes to complete the
assignment.
• Your group will be assigned one of
the three types of studies to test this
hypothesis.
Experiment
If you are
designing an
experimental
study your group
needs to describe
what treatments
will be used and
how subjects will
be assigned to a
treatment.
Observational
Study
If you are
designing an
observational
study your group
needs to describe
what is to be
observed and
measured and
how you’ll decide
which subjects to
observe.
Survey
For the survey,
your group needs
to plan who will
be surveyed, the
method of
survey, and the
exact questions
to be asked.
Causation vs. Association
Causation between two variables can
only be established with an
experimental study.
Association between two variables can
be determined with an observational
study or some type of survey.
Bias
Experimental
Study
The ways subjects are assigned to a
treatment may affect the data.
Observational
Study
When some subjects from the
population are left out of the study.
Survey
1.How the subject chooses to
respond the question.
2.How the question is worded may
influence how the subject
answers the question.
Explain the bias in each method
• The senior class at South High wants to know
how many students plan to attend college
outside the state of Colorado. The following
methods of surveying have been suggested. Each
method is biased in some way.
1. Survey everyone at the homecoming dance.
2. Survey every fifth person buying burritos during
lunch from the burrito venders outside.
3. Survey every student taking Geometry.
4. Survey students that have taken at least 3 AP
classes.
Warm-Up
Power of a Power Property
(a )  a
m n
mn
Simplify the following:
6
2
x y
a.
3 2 3
(x ) y
b.
x x 
4
3 2
1.
2.
3.
4.
Random Rectangles:
Guess
When told to do so flip over the Random
rectangle sheet.
Look at the sheet for 10 seconds and flip it
back over.
Make a guess on what the average area is of
the rectangles.
Calculate the class average.
Expert.
1. Select 5 rectangles that are representative of
all of the rectangles on the page.
2. List the number of each rectangle.
3. Find the area of each rectangle.
4. Calculate the average area of the 5 rectangles
you selected.
73
45
17
3
Example: Number 5
Area
1. Calculate the class average.
Total / 5
Random
1. Select 5 random numbers between 1 and 100
using your calculator. randInt(1,100,5)
2. Find the average area of each of the
randomly selected rectangles.
3. Calculate the class average.
The true average of the rectangles is:
5.27
November 16, 2015
Objectives:
1. Define the statistical measure of Standard
Deviation.
2. Calculate the standard deviation from a set
of data.
3. Review histograms.
Warm-Up
Property of negative exponents.
a
n
1
1
a
n
 n or  n  a and  
a
a
b
Simplify.
 4x 
 3x 


5
2
n
b
 
a
n
• Class survey data.
Standard Deviation
What is the probability of flipping a coin and
getting the first Tail on the 4th flip
1. Use your calculator (random number
generator) to simulate flipping a coin.
Heads = 0 and Tails =1. randint(0,1)
2. Create a relative frequency histogram on
your graph paper to show the distribution of
how many flips of the coin does it take until
the first Tail comes up.
3. Estimate the probability of getting the 1st Tail
on the 4th flip.
November 17, 2015
• Objectives:
1. Students will estimate the center (mean) and
the spread (standard deviation)of a normal
distribution.
2. Students will sketch a graph given the mean
and standard deviation.
Warm-up
Simplify the following:
a.
4x
2
y

5 2
 3xy 
b.  4 
 5x y 
3
3
Normal Distribution Formula
1 x  mean 2
2 stand. dev.
(
1
f ( x) 
e
2 standard Dev.
)
November 19, 2015
Objectives:
1. Students will use the 68-95-99.7 rule to find
the proportion of a distribution with in an
interval of standard deviations.
2. Students will determine how many standard
deviations a data point is from the mean.
3. Students will be able to sketch out a normal
distribution given N     
Warm-Up
a. Factor the polynomial
5 x  50 x  105
2
b. Simplify
 4x y 
 20 x 5 y 3 


3
2
2
• A study of elite distance runners found a mean
body weight of 63.1 kilograms (kg), with a
standard deviation of 4.8 kg.
•
(a) Assuming that the distribution of
weights is Normal, make an accurate sketch of
the weight distribution with the horizontal
axis marked in kilograms.
•
(b) Use the 68–95–99.7 rule to find the
proportion of runners whose body weight is
between 48.7 and 67.9 kg. Show your
method.
The length of human pregnancies from
conception to birth varies according to a
distribution that is approximately Normal with
mean 266 days and standard deviation 16 days.
Use the 68–95–99.7 rule to answer the following
questions. Show your work.
(a) How short are the shortest 2.5% of all
pregnancies?
(b) What percent of pregnancies last between
250 and 298 days?
November 20, 2015
1. Students well determine how far a
data point is from the mean in
terms of standard deviation (zscore).
2. Students will compare different
scores from different distribution
and analyze which is greater.
Warm-Up
Mental math.
Without a calculator, figure out
how much is 45% of 300?
Be prepared to explain how you
calculated your answer.
November 30, 2015
Objectives:
1. Students will compare data from different
distribution by analyzing the standardized
score (z-score).
2. Students will define the meaning of
Confidence Interval and calculate a
confidence interval.
Parameter
Statistic Confidence Interval
Warm-Up
Students at South high want to conduct a study to
determine how students feel about the new
attendance policy. They want to estimate the
proportion of how students feel about the new
attendance policy so they conduct a survey study.
Describe the parameter of interest and the statistic
the students will use to estimate the parameter.
Comparing different scores:
Bob is 68 inches tall and Alice is 64 inches tall.
Who is the tallest given the following statistics:
Men X  70 and   3
Women X  66 and   2
Which gender has the widest range of height and
explain why.
Confidence Interval
• A confidence interval uses sample data to
estimate an unknown population parameter
with an indication of how accurate the
estimate is
estimate  margin of error
estimate  margin of error
z
z
x
x
n
n
The administration what to estimate the mean ACT
score of Juniors is DPS. They use a random sample
of a size of 142 scores with a sample mean of 21
and a standard deviation of 4. With the
information below and the confidence interval
formula, predict the actual population mean with a
99% confidence interval.
Confidence
Interval
Z-value
90%
99%
99.9%
1.645
2.576
3.291
z
z
x
x
n
n