TI-84 Calculator Technology Guide
for
Elementary Statistics:
Looking at the Big Picture
1st EDITION
Nancy Pfenning
University of Pittsburgh
Prepared by
Nancy Pfenning
University of Pittsburgh
Melissa M. Sovak
University of Pittsburgh
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TI-84 Calculator Technology Guide
for Elementary Statistics: Looking at the Big Picture
Preview
The first part of Elementary Statistics: Looking at the Big Picture, on Data Production, does not call for the use of statistical software. For this reason, our first part consists of
basic tips, such as how to enter and manipulate data. Part 2, 3, and 4 of this guide parallel
Parts II, III, and IV of the textbook, presenting examples and activities on Displaying and
Summarizing, Probability, and Inference. Within Part 2 on Displaying and Summarizing,
and Part 4 on Statistical Inference, methods are presented in sequence for each of the five
variable situations: C, Q, C→Q, C→C, Q→Q.
PART 1: WARMING UP WITH THE TI-84
Entering and Manipulating Data
Data is stored in Lists on the TI-84. Lists are essentially columns where we will input the
data. Lists can have user-defined names or users can use the default lists L1-L6. While it is
useful to name variables, it is also useful to use the default lists since shortcut keys can be
used to access them. Data can be entered into lists as single values (each value is typed in
and stored in a list) or in summary form (counts of values are entered). This is useful for
categorical data. We can also use the list like a spreadsheet, and enter data values into one
list and the number of occurrences of that data value into another list.
To access the List Editor, press STAT. You will see three menus listed at the top:
EDIT, CALC and TESTS with EDIT currently selected (see Figure 1). Under the menus,
options are listed. Currently, the options for the EDIT menu should be displayed and
1:Edit... should be selected. Press ENTER. You will now see the List Editor screen,
as shown in Figure 2. Across the top are the names of the lists, starting with the default
L1-L6. If you use the up arrow key to select the list name L1 and right arrow key to scroll
you see all 6 default lists and then finally, a blank name, as in Figure 3. This is where you
can input your own list names if you would like to. To delete a list entirely, highlight the
lists name and press DEL.
Figure 1: TI-84 display after pressing STAT (with TESTS selected)
1
Figure 2: TI-84 List Editor screen
Figure 3: An empty-name list in the List Editor
Examples for Warming Up with the TI-84
Example 1.1: Suppose we want to store heights, in inches, of female class members [59, 65,
60, 66, 62, 66, 66, 65, 68, 64, 63, 65] in list L1. Press the STAT key. Then press ENTER
to select Edit. There should be a dark box under L1. Type 59, ENTER, 65, ENTER, 60,
ENTER, and so on. Note that a height of “5 foot 5” would be entered as 65, and “6 foot
4” would be 76.
To store male heights in list L2, use the arrow keys to navigate to L2 and enter those
data values [76, 68, 75, 66, 67, 68, 71, 72] in this list.
Example 1.2: Now suppose we would like to combine these heights together into one
list called HTS and sort them.
1. Enter the List Editor and use the arrows to navigate to the first list without a name.
2. Press 2nd then ALPHA to enter ALPHA-LOCK mode.
3. Type HTS
4. PressENTER
5. Use the down arrow to navigate to the first data line.
6. Type the appropriate entries.
7. Press STAT
8. Press the down arrow to select the option 2:SortA(
2
9. Press ENTER
10. Press 2nd then STAT
11. Use the down arrow to navigate to HTS
12. While HTS is selected, press ENTER
13. Press ENTER. Once the list is sorted, the display will say Done. To view the sorted
list, enter the list editor.
Lab Activities for Warming Up with the TI-84
1.1. Create a column PG for the lengths, in minutes, of seven movies rated PG: 100, 99,
106, 115, 90, 140, 90. Sort the column in ascending order.
1.2 Create a column R for the lengths, in minutes, of eight movies rated R: 134, 173, 113,
108, 98, 118, 102, 123. Combine the columns of movie lengths, PG and R, into a
column called LEN and sort them in ascending order.
1.3 Create a column PG-13 for the lengths, in minutes, of three movies rated PG-13: 130,
143, 102.
3
PART 2: DISPLAYING AND SUMMARIZING DATA
The remaining examples work with existing data (or subsets of this data). When appropriate,
the data has been summarized and included in the example. You may access the full dataset
at www.cengage.com/statistics/pfenning.
Summaries of this data are provided for you to complete the examples.
Examples for Part 2: Displaying and Summarizing Data
C Single Categorical Variable
Recall: Pie charts and bar charts are appropriate for displaying single categorical
variables.
Example 2.1:
ences.
Use the TI-84 to produce a bar chart for the students’ color prefer-
1. First, we will input the data into two lists, one indicating the categories (coded
numerically) and the second indicating the counts associated with each category.
2. In L3, input the numbers 1, 2, 3, 4, 5, 6, 7, 8. (In this scheme, 1=Black, 2=Blue,
3=Green, 4=Orange, 5=Pink, 6=Purple, 7=Red, 8=Yellow).
3. In L4, input 35, 193, 64, 13, 37, 53, 35, 16.
4. Press 2nd then Y=
5. Press ENTER to enter the editor window for Plot1
6. Press ENTER to turn the plot on
7. Using the arrow keys, navigate to the icon of the bar chart (the last icon in the
first row)
8. With this icon selected, press ENTER
9. Using the arrow keys, navigate to the entry for Xlist
10. Press 2nd then 3 to change the entry to L3
11. Using the arrow keys, navigate to the entry to Freq
12. Press 2nd then 4, to change the entry to L4
13. Press WINDOW
14. Input the following: Xmin=0, Xmax=9, Xscl=1, Ymin=0, Ymax=200, Yscl=10,
Xres=1
15. Press GRAPH
4
Q Single Quantitative Variable
Recall: Histograms and boxplots are appropriate display methods for single quantitative variables.
For a histogram (A) and boxplot (B) of students’ heights,
Example 2.2A:
1. Press 2nd then Y=
2. Use the arrow keys to navigate to Plot 2 and press ENTER
3. Press ENTER to select On
4. Select the icon for bar from Type and press ENTER
5. Navigate to Xlist
6. Press 2nd then STAT
7. Use the arrow keys to scroll down the HTS and press ENTER
8. Navigate to Freq, type 1 (NOTE: You will need to turn alpha mode off.)
9. Press WINDOW
10. Input the following: Xmin=50, Xmax=80, Xscl=1, Ymin=0, Ymax=5, Yscl=1,
Xres=1
11. Press GRAPH
Example 2.2B:
1. Press 2nd then Y=
2. Use the arrow keys to navigate to PlotsOff and press ENTER
3. Press ENTER
4. Press 2nd then Y=
5. Use the arrow keys to navigate to Plot 3 and press ENTER
6. Press ENTER to select On
7. Select the box plot icon (bottom row, middle icon)
8. Navigate to Xlist
9. Press 2nd then STAT
10. Use the arrow keys to scroll down to HTS and press ENTER
11. Navigate to Freq, type 1
12. Press GRAPH
5
Example 2.2C: This example produces mean, sum of all entries, sum of all entries
squared, sample standard deviation, maximum likelihood estimator for the standard
deviation, sample size n, minimum, Q1, median, Q3, and maximum of the height data.
1. Press STAT
2. Use the right arrow key to navigate to CALC
3. Press ENTER to select 1:1-Var Stats
4. Press 2nd then STAT
5. Scroll to the HTS list
6. Press ENTER
7. Press ENTER
8. Use the down arrow key to scroll through the statistics
Note: If you do not specify a list, the calculations will be performed on the first list,
L1.
C→Q Relationship between Categorical Explanatory and Quantitative Response
Variables
Recall: Side-by-side boxplots are an appropriate display for a categorical explanatory
variable and a quantitative response variable.
Example 2.3: (Two-sample design) To compare heights of students in the two gender
groups with summaries and a side-by-side boxplot, when all heights are entered in
seperate lists,
1. Press 2nd then Y=
2. Navigate to PlotsOff and press ENTER
3. Press ENTER
4. Press 2nd then Y=
5. Press ENTER to select Plot1
6. Press ENTER to turn Plot1 on
7. Select boxplot for Type and press ENTER
8. Navigate to Xlist
9. Press 2nd then 1
10. Type 1 for Freq
11. Use the arrow keys to navigate to Plot2 and press ENTER
12. Press ENTER to turn Plot2 on
13. Select boxplot for Type and press ENTER
6
14. Navigate to Xlist
15. Press 2nd then 2
16. Type 1 for Freq
17. Press GRAPH
Q→Q Relationship between two Quantitative Variables
Recall: A scatterplot is an appropriate display for two quantitative variables.
Example 2.4: To examine the relationship between ages of students fathers and ages
of their mothers, first produce a scatterplot (and verify its linearity), then find the
correlation r and the regression equation, and test if the slope of the regression line is
equal to 0 using the following data:
DadAge MomAge
51
45
58
54
47
49
44
40
49
48
47
47
55
52
43
43
51
50
51
49
1. First input the data for DadAge into L5 and the data for MomAge into L6
2. Press 2nd then Y=
3. Navigate to PlotsOff and press ENTER
4. Press ENTER
5. Press 2nd then Y=
6. Press ENTER
7. Press ENTER to turn Plot1 On
8. Select the first icon in Type and press ENTER
9. Navigate to Xlist
10. Press 2nd then 6 then ENTER
11. Press 2nd then 5 then ENTER
12. Press WINDOW
13. Input the following values: Xmin=40, Xmax=60, Xscl=1, Ymin=40, Ymax=60,
Yscal=1, Xres=1
7
14. Press GRAPH
15. Press STAT
16. Navigate to TESTS
17. Scroll down to F:LinRegTTest...
18. Press ENTER
19. Press 2nd then 6 then ENTER
20. Press 2nd then 5 then ENTER
21. Navigate to β & ρ: and select 6= 0 and press ENTER
22. Navigate to Calculate and press ENTER
Example 2.4 (continued): To graph the regression line on the scatterplot:
1. Press Y=
2. Type 3.825+.960*X
3. Press GRAPH
Lab Activities for Part 2: Displaying and Summarizing Data
2.1. This activity considers method of transportation (bike, bus, car, or walking) for the
surveyed students who lived off campus. Consider the following data:
Method
Bike
Bus
Car
Walk
Count
3
69
42
104
(a) What variable or variables are involved? For each variable, tell whether its type
is quantitative or categorical. If the situation involves two variables, report the
explanatory variable first.
• first variable:
• second variable (if there are two):
type:
type:
(b) Use Example 2.1 to produce an appropriate display and summaries; report
the proportion in each category: bike
, bus
, car
, walk
.
(c) Summarize your findings in one or two sentences. Be sure to express your results
specifically in terms of the variable(s) of interest, and mention to what extent the
results match your guesses in (b).
8
2.2 This activity considers how many credits surveyed students were taking. Use the
following data: 13, 14, 17, 16, 15, 16, 17, 16, 16, 15.
(a) What variable or variables are involved? For each variable, tell whether its type
is quantitative or categorical. If the situation involves two variables, report the
explanatory variable first.
• first variable:
• second variable (if there are two):
type:
type:
(b) Before you even look at the data, try to make a rough guess for each of the
following: [If you have no idea, just answer with a “?”.]
i. (center) mean:
median:
ii. (spread) standard deviation:
iii. shape:
Do you expect outliers? (Explain briefly.)
range:
to
(c) Use Example 2.2 to produce an appropriate display and summaries; report the
following:
Five Number Summary:
mean
standard deviation
shape
(d) Summarize your findings in one or two sentences. Be sure to express your results
specifically in terms of the variable(s) of interest, and mention to what extent the
results match your guesses in (b).
2.3 For surveyed students, how do the shoe sizes of males compare to those of females?
Use the following data:
Male Female
11
8
11
8
12
6
11
8
10
8
9
9
13
9
12
7
12
10
10
8
(a) What variable or variables are involved? For each variable, tell whether its type
is quantitative or categorical. If the situation involves two variables, report the
explanatory variable first.
• first variable:
type:
9
• second variable (if there are two):
type:
(b) Before you even look at the data, try to make a reasonable guess for each of
the following:
i. Which group will have a higher center (or about the same)?
ii. Which group will have more spread (or about the same)?
iii. What shapes do you expect?
Do you expect outliers?
(c) Use Example 2.3 to produce an appropriate display and summaries to make a
comparison:
i. Does one group have a considerably higher center?
ii. Does one group have more spread?
iii. Compare the shapes.
(d) Summarize your findings in one or two sentences. Be sure to express your results
specifically in terms of the variable(s) of interest, and mention to what extent the
results match your guesses in (b).
2.4 How are surveyed students’ heights and weights related? Use the following data:
Observation
1
2
3
4
5
6
7
8
9
10
Height Weight
59
115
76
165
65
125
60
105
66
117
62
107
66
125
66
145
65
112
68
175
(a) What variable or variables are involved? For each variable, tell whether its type
is quantitative or categorical. If the situation involves two variables, report the
explanatory variable first.
• first variable:
• second variable (if there are two):
type:
type:
(b) Before you even look at the data, try to make a reasonable guess for each of
the following: [If you have no idea, just answer with a “?”.]
i. form (linear or curved):
ii. direction (positive, negative, or none):
10
iii. strength (strong, moderate, or weak):
Do you expect outliers or influential observations? (Explain briefly.)
(c) Use Example 2.4 to produce an appropriate display and summaries in order to
answer the following:
Does the form appear roughly linear?
What is the regression line equation?
What is the value of the correlation r?
(d) Summarize your findings in one or two sentences. Be sure to express your results
specifically in terms of the variable(s) of interest, and mention to what extent the
results match your guesses in (b).
Exercises to Try
For more practice with techniques from this section, try these exercises from your text:
(Note: Data may not be well-suited for input into the TI-84)
Exercises
Exercises
Exercises
Exercises
Exercises
4.13
4.41
4.65
4.85
4.98
-
4.16,
4.45,
4.67,
4.86,
4.99,
Exercises
Exercises
Exercises
Exercises
Exercises
11
5.84 - 5.90,
5.99 - 5.101,
5.115 - 5.119,
8.65 - 8.68,
8.80 - 8.83
PART 4: STATISTICAL INFERENCE
Note: Examples will be provided for situations where descriptive statistics are available.
Examples for lists of data input directly into the TI-84 can be found in the Appendix.
Examples for Part 4: Statistical Inference
C Single Categorical Variable
Recall: A Z-test is used when testing hypotheses about population proportions.
Example 4.1A: Use the TI-84 to do inference about the population proportion of
males/females; specifically, test if the sample represent a population with less than 40%
who are male given the following data: Total sample size=446, Number of males=164,
Number of females=282.
1. Press STAT
2. Navigate to TESTS
3. Scroll down to 5:1-PropZTest...
4. Press ENTER
5. For p0 type .4 and press ENTER
6. For x type 64 and press ENTER
7. For n type 446 and press ENTER
8. Check that 6=p0 is selected
9. Navigate to Calculate
10. Press ENTER (Note: p provides the p value for the test).
Example 4.1B: Use the TI-84 to test if the population proportion preferring the
color green could be one-eighth (0.125) given the information we stored in L3 and L4.
Note that green (coded 3) has 64 observations.
1. Press STAT
2. Navigate to TESTS
3. Scroll down to 5:1-PropZTest...
4. Press ENTER
5. for p0 type .125 and press ENTER
6. For x type 64 and press ENTER
7. For n type 446 and press ENTER
8. Check that 6=p0 is selected
12
9. Navigate to Calculate
10. Press ENTER
Q Single Quantitative Variable
Recall: A Z-test is used to test hypotheses about a single population mean (or
construct confidence intervals) when σ is known. A t-test is used to test hypotheses
about a population mean (or construct confidence intervals) when σ is unknown.
Example 4.2A: (σ known) Assume we have a random sample of Verbal SAT scores of
students taken from scores of all students at a particular university, whose mean score
is unknown and standard deviation is 100. Use the following information to obtain
a 90% confidence interval for the unknown population mean score, after producing a
histogram of the scores. The sample contained 391 students and had the sample mean
Verbal SAT score was 591.84.
NOTE: If you would like to complete this test with a list of data rather than summary
statistics, follow the procedure outlined in Appendix A Example Ap 4.2A.
1. Press STAT
2. Navigate to TESTS
3. Scroll down to 7: ZInterval...
4. Press ENTER
5. Navigate to Stats
6. Press ENTER
7. For σ : type 100 and press ENTER
−
8. For x: type 591.84 and press ENTER
9. For n: type 391 and press ENTER
10. For C-Level: type .90 and press ENTER
11. While Calculate is selected press ENTER
Next, test the null hypothesis that Verbal SAT scores of surveyed students are a random
sample taken from a population with mean 600 against the alternative that the mean
is less than 600. Assume the population standard deviation to be 100. [If population
standard deviation were not assumed to be known, a 1-Sample t test would be used,
and Standard deviation would not be specified.]
1. Press STAT
2. Navigate to TESTS
3. Select 1:Z-Test... and press ENTER
4. Navigate to Stats
13
5. Press Enter
6. For µ0 : type 600 and press ENTER
7. For σ : type 100 and press ENTER
−
8. For x: type 591.84 and press ENTER
9. For n: type 391 and press ENTER
10. Navigate to < µ0 and press ENTER
11. Navigate to Calculate and Press ENTER
Example 4.2B: (σ unknown) Now assume Verbal SAT scores of surveyed students
members to be a random sample taken from scores of all students at a particular
university, whose mean and standard deviation are unknown. The sample standard
deviation is 73.24. Use sample descriptives to obtain a 99% confidence interval for the
population mean score.
Note: If you would like to complete this test with a list of data rather than summary
statistics, follow the procedure outlined in Appendix A Example Ap 4.2B
1. Press STAT
2. Navigate to TESTS
3. Scroll down to 8: TInterval...
4. Press ENTER
5. Navigate to Stats and press ENTER
−
6. For x: type 591.84 and press ENTER
7. For sx: type 73.24 and press ENTER
8. For n: type 391 and press ENTER
9. For C-Level: type .99 and press ENTER
10. Press ENTER
C→Q Relationship between Categorical Explanatory and Quantitative Response
Variables
Recall: A paired t-test is used to test hypotheses involving two population means
when the two samples involved are dependent. A two-sample t-test is used to test
hypotheses involving two population means when the two samples involved are independent. An ANOVA is used to test hypotheses involving more than two population
means.
Example 4.3A: (Paired design) Do students’ dads tend to be older than their moms?
Test the null hypothesis that the mean of differences (ages of dads minus ages of moms)
for the larger population is zero, against the alternative that the mean of differences is
14
positive using the following information. The mean of Dad ages is 50.83 and the mean
of Mom ages is 48.37 so the mean difference is 2.45. The standard deviation of the
difference is 3.88 and sample size is 431.
Note: If you would like to complete this test with a list of data rather than summary
statistics, follow the procedure outlined in Appendix A Example Ap 4.3A.
1. Press STAT
2. Navigate to TESTS
3. Scroll down to 2: T-Test...
4. Press ENTER
5. Navigate to Stats and press ENTER
6. For µ0 : type 0 and press ENTER
−
7. For x: type 2.45 and press ENTER
8. For sx: type 3.88 and press ENTER
9. For n: type 431 and press ENTER
10. Navigate to > µ0 and press ENTER
11. Navigate to Calculate and press ENTER
Example 4.3B: (Two-sample design)
Use the TI-84 to check if, on average, there is a difference between amount of cash
carried by female and male students using the following information. The average
amount of cash carried by the 159 males sampled was 34.19 with a standard deviation
of 58.387. The average amount of cash carried by the 280 females sampled was 23.96
with a standard deviation of 39.576. Procedure may or may not be pooled.
Note: If you would like to complete this test with a list of data rather than summary
statistics, follow the procedure outlined in Appendix A Example Ap 4.3B.
1. Press STAT
2. Navigate to TESTS
3. Scroll down to 4: 2-SampTTest...
4. Press ENTER
5. Navigate to Stats and press ENTER
−
6. For x 1 : type 23.96 and press ENTER
7. For sx1: type 39.576 and press ENTER
8. For n1: type 280 and press ENTER
−
9. For x 2 : type 34.19 and press ENTER
15
10. For sx2: type 58.387 and press ENTER
11. for n2: type 159 and press ENTER
12. Navigate to > µ2 and press ENTER
13. Navigate to No for Pooled: and press ENTER
14. Navigate to Calculate and press ENTER
15. Repeat the same procedure, except choose Yes for Pooled this time.
Example 4.3C: (Several-sample design) Use the TI-84 to see if there is a significant
difference in mean earnings of freshmen, sophomores, juniors, and seniors in the class
using the following information:
Freshman
2
0
22
3
2
3
1
1
0
13
Sophomores Juniors
1
6
0
1
3
4
2
4
3
4
0
9
1
0
2
1
2
2
2
5
Seniors
0
15
5
3
2
9
1
2
6
0
1. First enter the Freshman data in a list called E1
2. Enter the Sophomore data in a list called E2
3. Enter the Junior data in a list called E3
4. Enter the Senior data in a list called E4
5. Press STAT
6. Navigate to TESTS
7. Scroll down to H: ANOVA(
8. Press ENTER
9. Press 2nd then STAT
10. Scroll down to E1
11. Press ENTER
12. Press ,
13. Press 2nd then STAT and select E2 then press ,
14. Press 2nd then STAT and select E3 then press ,
15. Press 2nd then STAT and select E4 then press )
16
16. Press ENTER
C→C Relationship between two Categorical Variables
Recall: A χ2 test is used to determine if there two categorical variables are independent or dependent.
Example 4.4: Use the TI-84 to check for a relationship between major being decided
or not, and living situation (on or off campus) using the following information.
Dec?
No
Yes
Live
Off On
82 124
141 97
1. First, manually create a table of expected counts as below:
Live
Off
On
No 103.5 102.5
Dec?
Yes 119.5 118.5
2. Press 2nd then x−1
3. Navigate to EDIT, select 1:[A] and press ENTER
4. Press 2 then ENTER, 2 then ENTER to set the dimension
5. Input the matrix as above by typing 82 ENTER 124 ENTER 141 ENTER 97
ENTER
6. Press 2nd then x−1
7. Navigate to EDIT
8. Navigate to 2:[B] and press ENTER
9. Press 2 then ENTER, 2 then ENTER
10. Input the expected matrix as above by typing 103.5 ENTER 102.5 ENTER
119.5 ENTER 118.5 ENTER
11. Press STAT
12. Navigate to TESTS
13. Navigate to C:χ2 -Test...
14. Check that [A] is selected for Observed and [B] is selected for Expected
15. Press ENTER
16. Navigate to Calculate and press ENTER
17
Lab Activities for Part 4: Statistical Inference
4.1 The proportion of American adults who smoked at the time the students were surveyed
was 0.25. Was the proportion significantly lower for university students? Use the
following data:
Number of students surveyed: 446 Number who smoked: 85 Number who did not
smoke: 361
(a) What variable or variables are involved? For each variable, tell whether its type
is quantitative or categorical. If the situation involves two variables, report the
explanatory variable first.
• first variable:
• second variable (if there are two):
type:
type:
(b) Before you even look at the data, give a rough guess for the population
proportion of students who smoked
. Then formulate null and alternative hypotheses to test if the population proportion was necessarily less than
0.25.
H0 :
Ha :
Do you suspect that there will be enough evidence to reject H0 ?
(c) Use Example 4.1 to display the data, then find a 95% confidence interval for
the unknown population proportion.
Test your hypotheses, making sure to opt for the correct alternative: the P -value
is
. Do you reject H0 ?
(d) State your results: since you did or did not reject H0 , what do you conclude
about the unknown population proportion? Be sure to express your results specifically in terms of the variable(s) of interest, and mention to what extent the results
match your suspicions in (b).
4.2A (σ known) Math SAT scores are assumed to have a standard deviation of 100. Is the
mean Math SAT score of all intro Stat students at a particular university 600? Use
−
the following information: x=610.44 and n=390.
(a) What variable or variables are involved? For each variable, tell whether its type
is quantitative or categorical. If the situation involves two variables, report the
explanatory variable first.
• first variable:
• second variable (if there are two):
18
type:
type:
(b) Before you even look at the data, formulate null and alternative hypotheses about
the population mean µ.
H0 :
Ha :
Do you suspect that there will be enough evidence to reject H0 ?
(c) Use Example 4.2A to carry out a z test, specifying σ and making sure to opt
for the correct alternative (<, 6=, or >); include a display of the data. What is
the P -value?
Do you reject H0 ?
Give a 95% confidence interval for µ:
[Note: this was automatically provided if your alternative was 6=; otherwise, repeat
the procedure, this time opting for a two-sided alternative.]
(d) State your results: based on the outcome (you did or did not reject H0 ), what
do you conclude about the unknown population mean? Be sure to express your
results specifically in terms of the variable(s) of interest, and mention to what
extent the results match your suspicions in (b).
4.2B (σ unknown) Adults in the U.S. average 7 hours of sleep a night. Is this also the mean
−
for the population of students at a particular university? Use the following data: x=
7.12, s=1.424 and n=445.
(a) What variable or variables are involved? For each variable, tell whether its type
is quantitative or categorical. If the situation involves two variables, report the
explanatory variable first.
• first variable:
• second variable (if there are two):
type:
type:
(b) Before you even look at the data, formulate null and alternative hypotheses
about the population mean µ.
H0 :
Ha :
Do you suspect that there will be enough evidence to reject H0 ?
(c) Note: When σ is unknown, you should carry out a test of your hypotheses using a
t procedure, not z. Use Example 4.2B to carry out the one-sample t procedure,
making sure to opt for the correct alternative (<, 6=, or >); include a display of
the data. What is the P -value?
Do you reject H0 ?
Give a 95% confidence interval for µ:
[Note: this was automatically provided if your alternative was 6=; otherwise, repeat the t procedure,
this time opting for a two-sided alternative.]
(d) State your results: based on the outcome (you did or did not reject H0 ), what
do you conclude about the unknown population mean? Be sure to express your
19
results specifically in terms of the variable(s) of interest, and mention to what
extent the results match your suspicions in (b).
4.3A Overall, is there a positive mean difference between the number of minutes students
spend on the computer versus the number of minutes they spend exercising? (The
initial suspicion is that students spend more time on the computer than they do exercising.) Use the following data: the mean difference between computer and exercising
is 41.285, the standard deviation of the difference is 99.493 and n=441.
(a) What variable or variables are involved? For each variable, tell whether its type
is quantitative or categorical. If the situation involves two variables, report the
explanatory variable first.
• first variable:
• second variable (if there are two):
type:
type:
(b) Before you even look at the data, formulate null and alternative hypotheses
about the population mean difference µd .
H0 :
Ha :
Do you suspect that there will be enough evidence to reject H0 ?
(c) Use Example 4.3A to carry out a paired t procedure, making sure to opt for
the correct alternative (<, 6=, or >); include a display of the data. What is the
P -value?
Do you reject H0 ?
(d) State your results: based on the outcome (you did or did not reject H0 ), what do
you conclude about the unknown population mean difference? Be sure to express
your results specifically in terms of the variable(s) of interest, and mention to
what extent the results match your suspicions in (b).
4.3B Is the mean number of credits taken the same for all on- and off-campus students at a
particular university? Use the following data:
Number of off-campus students surveyed: 223
Mean number of credits for off-campus students: 14.910
Standard deviation for off-campus students: 2.429
Number of on-campus students surveyed: 222
Mean number of credits for on-campus students: 15.595
Standard deviation for on-campus students: 1.451
(a) What variable or variables are involved? For each variable, tell whether its type
is quantitative or categorical. If the situation involves two variables, report the
explanatory variable first.
20
• first variable:
• second variable (if there are two):
type:
type:
(b) Before you even look at the data, formulate null and alternative hypotheses
about the difference µ1 − µ2 between population means for the two groups. [The
null hypothesis usually states that this difference is zero.]
H0 :
Ha :
Do you suspect that there will be enough evidence to reject H0 ?
(c) Use Example 4.3B to carry out a two-sample t procedure, making sure to opt
for the correct alternative (<, 6=, or >); include a display of the data. What is
the P -value?
Do you reject H0 ?
(d) State your results: based on the outcome (you did or did not reject H0 ), what
do you conclude about the unknown difference between population means? Be
sure to express your results specifically in terms of the variable(s) of interest, and
mention to what extent the results match your suspicions in (b).
4.3C In general, is mean age the same for students who wear contact lenses, glasses, or
neither? Use the following data:
Contacts Glasses
19.67
18.50
20.08
19.75
18.50
20.25
19.17
20.42
19.17
22.25
19.67
19.25
19.42
20.17
20.83
19.50
25.50
31.75
Neither
19.08
19.67
20.42
19.42
19.17
19.08
19.33
19.83
19.33
(a) What variable or variables are involved? For each variable, tell whether its type
is quantitative or categorical. If the situation involves two variables, report the
explanatory variable first.
• first variable:
• second variable (if there are two):
type:
type:
(b) Before you even look at the data, formulate null and alternative hypotheses
about the population means.
H0 :
Ha :
Do you suspect that there will be enough evidence to reject H0 ?
21
(c) Use Example 4.3C to carry out an ANOVA procedure; include a display of the
data. What is the P -value?
Do you reject H0 ?
(d) State your results: based on the outcome (you did or did not reject H0 ), what
do you conclude about the various population means? Be sure to express your
results specifically in terms of the variable(s) of interest, and mention to what
extent the results match your suspicions in (b).
4.4 Is there a statistically significant relationship between whether or not a student smokes
and whether the student lives on or off campus? Use the following information:
Live
Off On
No 162 198
Smoke
Yes 61 24
(a) What variable or variables are involved? For each variable, tell whether its type
is quantitative or categorical. If the situation involves two variables, report the
explanatory variable first.
• first variable:
• second variable (if there are two):
type:
type:
(b) Before you even look at the data, formulate null and alternative hypotheses
about the relationship between those variables.
H0 :
Ha :
Do you suspect that there will be enough evidence to reject H0 ?
(c) Use Example 4.4 to carry out a chi-square test. What is the P -value?
Do you reject H0 ?
(d) State your results: based on the outcome (you did or did not reject H0 ), do
you conclude that those variables are related? Be sure to express your results
specifically in terms of the variable(s) of interest, and mention to what extent the
results match your suspicions in (b).
4.5 Is there a relationship between the heights of students’ fathers and mothers? Use the
following data:
22
DadHeight MomHeight
73
62
75
66
69
69
69
61
71
62
70
63
69
63
72
64
73
64
70
64
(a) What variable or variables are involved? For each variable, tell whether its type
is quantitative or categorical. If the situation involves two variables, report the
explanatory variable first.
• first variable:
• second variable (if there are two):
type:
type:
(b) Before you even look at the data, formulate null and alternative hypotheses
about the slope β1 of the population regression line.
H0 :
Ha :
Do you suspect that there will be enough evidence to reject H0 ?
(c) Use Example 2.5 to display the data and verify that the form is reasonably
linear. Then carry out a regression procedure to test your hypotheses. What is
the P -value?
Do you reject H0 ?
(d) State your results: based on the outcome (you did or did not reject H0 ), do
you conclude that the population variables are related? Be sure to express your
results specifically in terms of the variable(s) of interest, and mention to what
extent the results match your suspicions in (b).
Exercises to Try
For more practice with techniques from this section, try these exercises from your text:
(Note: Data may not be well-suited for input in the TI-84)
Exercises
Exercises
Exercises
Exercises
Exercises
9.32 - 9.35,
9.68 - 9.71,
9.93 - 9.95,
10.73 -10.85,
11.50 - 11.51,
Exercises
Exercises
Exercises
Exercises
23
11.70
11.80
12.44
13.50
-
11.73,
11.103,
12.54,
13.58
APPENDIX A
Example Ap 4.2A To find a confidence interval for a population mean when the data is
saved in a list,
1. Store the data in a list of your choice
2. Press STAT
3. Navigate to TESTS
4. Select 7:ZInterval... and press ENTER
5. Select Data and press ENTER
6. Enter the appropriate value for σ
7. For List, select the appropriate list
8. For C-Level, type the appropriate confidence level
9. Highlight Calculate and press ENTER
To run a hypothesis test for a population mean when the data is saved in a list,
1. Store the data in a list of your choice
2. Press STAT
3. Navigate to TESTS
4. Select 1:Z-Test... and press ENTER
5. Select Data and press ENTER
6. Enter the appropriate test value for µ0
7. Enter the appropriate value for σ
8. Select the appropriate list
9. Select the appropriate alternate hypothesis
10. Select Calculate and press ENTER
Return to Example 4.2A
24
Example Ap 4.2B To find a confidence interval for a population mean when the data
is saved in a list and the value for σ is unknown,
1. Store the data in a list of your choice
2. Press STAT
3. Navigate to TESTS
4. Select 8:TInterval... and press ENTER
5. Select Data and press ENTER
6. Enter the appropriate list
7. Enter the appropriate confidence level in C-Level
8. Select Calculate and press ENTER
Return to Example 4.2B
Example Ap 4.3A To run a t-test for paired design when the data is saved in a list,
1. Enter the differences of the paired samples in a list of your choice
2. Press STAT
3. Navigate to TESTS
4. Select 2:T-Test... and press ENTER
5. Select Data and press ENTER
6. Enter the appropriate test value for µ0
7. Enter the appropriate list
8. Select the appropriate alternate hypothesis
9. Select Calculate and press ENTER
Return to Example 4.3A
Example Ap 4.3B To run a 2-sample t-test when the data is saved in a list,
1. Enter the data for the two samples in two lists of your choice
2. Press STAT
3. Navigate to TESTS
25
4. Select 4:2-SampTTest... and press ENTER
5. Select Data and press ENTER
6. Enter the first list for List1
7. Enter the second list for List2
8. Select the appropriate alternate hypothesis
9. Select the appropriate response for Pooled
10. Select Calculate and press ENTER
Return to Example 4.3B
26