ti-84 calculator technology guide for elementary statistics

TI-84 Calculator Technology Guide

for

Prepared by

Nancy Pfenning University of Pittsburgh

Melissa M. Sovak University of Pittsburgh

Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States

Elementary Statistics: Looking at the Big Picture

1st EDITION

Nancy Pfenning 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 Produc-tion, does not call for the use of statistical software. For this reason, our first part consists ofbasic tips, such as how to enter and manipulate data. Part 2, 3, and 4 of this guide parallelParts II, III, and IV of the textbook, presenting examples and activities on Displaying andSummarizing, 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 fivevariable 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 thedata. Lists can have user-defined names or users can use the default lists L1-L6. While it isuseful to name variables, it is also useful to use the default lists since shortcut keys can beused to access them. Data can be entered into lists as single values (each value is typed inand stored in a list) or in summary form (counts of values are entered). This is useful forcategorical data. We can also use the list like a spreadsheet, and enter data values into onelist 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 and1: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 defaultL1-L6. If you use the up arrow key to select the list name L1 and right arrow key to scrollyou see all 6 default lists and then finally, a blank name, as in Figure 3. This is where youcan input your own list names if you would like to. To delete a list entirely, highlight thelists name and press DEL.

Figure 1: TI-84 display after pressing STAT (with TESTS selected)

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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 ENTERto 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 foot4” would be 76.

To store male heights in list L2, use the arrow keys to navigate to L2 and enter thosedata 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 onelist 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 sortedlist, 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 acolumn 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.

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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 datasetat 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 categoricalvariables.

Example 2.1: Use the TI-84 to produce a bar chart for the students’ color prefer-ences.

1. First, we will input the data into two lists, one indicating the categories (codednumerically) 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 thefirst 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

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http://www.cengage.com/statistics/pfenning

Q Single Quantitative Variable

Recall: Histograms and boxplots are appropriate display methods for single quanti-tative variables.

For a histogram (A) and boxplot (B) of students’ heights,

Example 2.2A:


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


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:


2. Use the arrow keys to navigate to PlotsOff and press ENTER

3. Press ENTER


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)



10. Use the arrow keys to scroll down to HTS and press ENTER

11. Navigate to Freq, type 1

12. Press GRAPH

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Example 2.2C: This example produces mean, sum of all entries, sum of all entriessquared, sample standard deviation, maximum likelihood estimator for the standarddeviation, 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


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 ResponseVariables

Recall: Side-by-side boxplots are an appropriate display for a categorical explanatoryvariable and a quantitative response variable.

Example 2.3: (Two-sample design) To compare heights of students in the two gendergroups with summaries and a side-by-side boxplot, when all heights are entered inseperate lists,


2. Navigate to PlotsOff and press ENTER

3. Press ENTER


5. Press ENTER to select Plot1

6. Press ENTER to turn Plot1 on

7. Select boxplot for Type and press ENTER


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


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 agesof their mothers, first produce a scatterplot (and verify its linearity), then find thecorrelation r and the regression equation, and test if the slope of the regression line isequal to 0 using the following data:

DadAge MomAge51 4558 5447 4944 4049 4847 4755 5243 4351 5051 49

1. First input the data for DadAge into L5 and the data for MomAge into L6


3. Navigate to PlotsOff and press ENTER

4. Press ENTER


6. Press ENTER

7. Press ENTER to turn Plot1 On

8. Select the first icon in Type and press ENTER


10. Press 2nd then 6 then ENTER


12. Press WINDOW

13. Input the following values: Xmin=40, Xmax=60, Xscl=1, Ymin=40, Ymax=60,Yscal=1, Xres=1

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14. Press GRAPH

15. Press STAT

16. Navigate to TESTS

17. Scroll down to F:LinRegTTest...

18. Press 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 thesurveyed students who lived off campus. Consider the following data:

Method CountBike 3Bus 69Car 42

Walk 104

(a) What variable or variables are involved? For each variable, tell whether its typeis quantitative or categorical. If the situation involves two variables, report theexplanatory variable first.

• first variable: type:

• second variable (if there are two): type:

(b) Use Example 2.1 to produce an appropriate display and summaries; reportthe proportion in each category: bike , bus , car

, walk .

(c) Summarize your findings in one or two sentences. Be sure to express your resultsspecifically in terms of the variable(s) of interest, and mention to what extent theresults match your guesses in (b).

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2.2 This activity considers how many credits surveyed students were taking. Use thefollowing data: 13, 14, 17, 16, 15, 16, 17, 16, 16, 15.




(b) Before you even look at the data, try to make a rough guess for each of thefollowing: [If you have no idea, just answer with a “?”.]

i. (center) mean: median:

ii. (spread) standard deviation: range: to

iii. shape:Do you expect outliers? (Explain briefly.)

(c) Use Example 2.2 to produce an appropriate display and summaries; report thefollowing:Five Number Summary:mean standard deviationshape

(d) Summarize your findings in one or two sentences. Be sure to express your resultsspecifically in terms of the variable(s) of interest, and mention to what extent theresults 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 Female11 811 812 611 810 89 913 912 712 1010 8



9


(b) Before you even look at the data, try to make a reasonable guess for each ofthe 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 acomparison:

i. Does one group have a considerably higher center?

ii. Does one group have more spread?

iii. Compare the shapes.


2.4 How are surveyed students’ heights and weights related? Use the following data:

Observation Height Weight1 59 1152 76 1653 65 1254 60 1055 66 1176 62 1077 66 1258 66 1459 65 11210 68 175




(b) Before you even look at the data, try to make a reasonable guess for each ofthe following: [If you have no idea, just answer with a “?”.]

i. form (linear or curved):

ii. direction (positive, negative, or none):

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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 toanswer the following:Does the form appear roughly linear?What is the regression line equation?What is the value of the correlation r?


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 4.13 - 4.16,Exercises 4.41 - 4.45,Exercises 4.65 - 4.67,Exercises 4.85 - 4.86,Exercises 4.98 - 4.99,

Exercises 5.84 - 5.90,Exercises 5.99 - 5.101,Exercises 5.115 - 5.119,Exercises 8.65 - 8.68,Exercises 8.80 - 8.83

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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 ofmales/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


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 thecolor 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


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

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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 (orconstruct confidence intervals) when σ is known. A t-test is used to test hypothesesabout 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 ofstudents taken from scores of all students at a particular university, whose mean scoreis unknown and standard deviation is 100. Use the following information to obtaina 90% confidence interval for the unknown population mean score, after producing ahistogram of the scores. The sample contained 391 students and had the sample meanVerbal SAT score was 591.84.

NOTE: If you would like to complete this test with a list of data rather than summarystatistics, follow the procedure outlined in Appendix A Example Ap 4.2A.

1. Press STAT


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 randomsample taken from a population with mean 600 against the alternative that the meanis less than 600. Assume the population standard deviation to be 100. [If populationstandard 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


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



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 studentsmembers to be a random sample taken from scores of all students at a particularuniversity, whose mean and standard deviation are unknown. The sample standarddeviation is 73.24. Use sample descriptives to obtain a 99% confidence interval for thepopulation mean score.

Note: If you would like to complete this test with a list of data rather than summarystatistics, follow the procedure outlined in Appendix A Example Ap 4.2B

1. Press STAT


3. Scroll down to 8: TInterval...

4. Press ENTER

5. Navigate to Stats and press ENTER


7. For sx: type 73.24 and press ENTER


9. For C-Level: type .99 and press ENTER

10. Press ENTER

C→Q Relationship between Categorical Explanatory and Quantitative ResponseVariables

Recall: A paired t-test is used to test hypotheses involving two population meanswhen the two samples involved are dependent. A two-sample t-test is used to testhypotheses involving two population means when the two samples involved are inde-pendent. An ANOVA is used to test hypotheses involving more than two populationmeans.

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

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positive using the following information. The mean of Dad ages is 50.83 and the meanof Mom ages is 48.37 so the mean difference is 2.45. The standard deviation of thedifference is 3.88 and sample size is 431.

Note: If you would like to complete this test with a list of data rather than summarystatistics, follow the procedure outlined in Appendix A Example Ap 4.3A.

1. Press STAT


3. Scroll down to 2: T-Test...

4. Press ENTER


6. For µ0 : type 0 and press ENTER


8. For sx: type 3.88 and press ENTER


10. Navigate to > µ0 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 cashcarried by female and male students using the following information. The averageamount of cash carried by the 159 males sampled was 34.19 with a standard deviationof 58.387. The average amount of cash carried by the 280 females sampled was 23.96with 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 summarystatistics, follow the procedure outlined in Appendix A Example Ap 4.3B.

1. Press STAT


3. Scroll down to 4: 2-SampTTest...

4. 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

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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


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 significantdifference in mean earnings of freshmen, sophomores, juniors, and seniors in the classusing the following information:

Freshman Sophomores Juniors Seniors2 1 6 00 0 1 1522 3 4 53 2 4 32 3 4 23 0 9 91 1 0 11 2 1 20 2 2 613 2 5 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


7. Scroll down to H: ANOVA(

8. Press ENTER


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 )

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16. Press ENTER

C→C Relationship between two Categorical Variables

Recall: A χ2 test is used to determine if there two categorical variables are indepen-dent or dependent.

Example 4.4: Use the TI-84 to check for a relationship between major being decidedor not, and living situation (on or off campus) using the following information.

LiveOff On

Dec?No 82 124Yes 141 97

1. First, manually create a table of expected counts as below:

LiveOff On

Dec?No 103.5 102.5Yes 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 97ENTER

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 ENTER119.5 ENTER 118.5 ENTER

11. Press STAT


13. Navigate to C:χ2-Test...

14. Check that [A] is selected for Observed and [B] is selected for Expected

15. Press ENTER


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Lab Activities for Part 4: Statistical Inference

4.1 The proportion of American adults who smoked at the time the students were surveyedwas 0.25. Was the proportion significantly lower for university students? Use thefollowing data:

Number of students surveyed: 446 Number who smoked: 85 Number who did notsmoke: 361




(b) Before you even look at the data, give a rough guess for the populationproportion of students who smoked . Then formulate null and al-ternative hypotheses to test if the population proportion was necessarily less than0.25.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 forthe unknown population proportion.Test your hypotheses, making sure to opt for the correct alternative: the P -valueis . Do you reject H0?

(d) State your results: since you did or did not reject H0, what do you concludeabout the unknown population proportion? Be sure to express your results specif-ically in terms of the variable(s) of interest, and mention to what extent the resultsmatch your suspicions in (b).

4.2A (σ known) Math SAT scores are assumed to have a standard deviation of 100. Is themean Math SAT score of all intro Stat students at a particular university 600? Use

the following information:−x=610.44 and n=390.




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(b) Before you even look at the data, formulate null and alternative hypotheses aboutthe 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 optfor the correct alternative (<, 6=, or >); include a display of the data. What isthe P -value?Do you reject H0?Give a 95% confidence interval for µ:[Note: this was automatically provided if your alternative was 6=; otherwise, repeatthe procedure, this time opting for a two-sided alternative.]

(d) State your results: based on the outcome (you did or did not reject H0), whatdo you conclude about the unknown population mean? Be sure to express yourresults specifically in terms of the variable(s) of interest, and mention to whatextent 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.




(b) Before you even look at the data, formulate null and alternative hypothesesabout 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 at 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 ofthe data. What is the P -value?Do you reject H0?Give a 95% confidence interval for µ: [Note: this was auto-matically 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), whatdo 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 whatextent the results match your suspicions in (b).

4.3A Overall, is there a positive mean difference between the number of minutes studentsspend on the computer versus the number of minutes they spend exercising? (Theinitial suspicion is that students spend more time on the computer than they do exer-cising.) Use the following data: the mean difference between computer and exercisingis 41.285, the standard deviation of the difference is 99.493 and n=441.




(b) Before you even look at the data, formulate null and alternative hypothesesabout 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 forthe correct alternative (<, 6=, or >); include a display of the data. What is theP -value?Do you reject H0?

(d) State your results: based on the outcome (you did or did not rejectH0), what doyou conclude about the unknown population mean difference? Be sure to expressyour results specifically in terms of the variable(s) of interest, and mention towhat 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 aparticular 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


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(b) Before you even look at the data, formulate null and alternative hypothesesabout the difference µ1 − µ2 between population means for the two groups. [Thenull 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 optfor the correct alternative (<, 6=, or >); include a display of the data. What isthe P -value?Do you reject H0?

(d) State your results: based on the outcome (you did or did not reject H0), whatdo you conclude about the unknown difference between population means? Besure to express your results specifically in terms of the variable(s) of interest, andmention 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, orneither? Use the following data:

Contacts Glasses Neither19.67 18.50 19.0820.08 19.75 19.6718.50 20.25 20.4219.17 20.42 19.4219.17 22.25 19.1719.67 19.25 19.0819.42 20.17 19.3320.83 19.50 19.8325.50 31.75 19.33




(b) Before you even look at the data, formulate null and alternative hypothesesabout the population means.H0 :Ha :Do you suspect that there will be enough evidence to reject H0?

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(c) Use Example 4.3C to carry out an ANOVA procedure; include a display of thedata. What is the P -value?Do you reject H0?

(d) State your results: based on the outcome (you did or did not reject H0), whatdo you conclude about the various population means? Be sure to express yourresults specifically in terms of the variable(s) of interest, and mention to whatextent the results match your suspicions in (b).

4.4 Is there a statistically significant relationship between whether or not a student smokesand whether the student lives on or off campus? Use the following information:

LiveOff On

SmokeNo 162 198Yes 61 24




(b) Before you even look at the data, formulate null and alternative hypothesesabout 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), doyou conclude that those variables are related? Be sure to express your resultsspecifically in terms of the variable(s) of interest, and mention to what extent theresults match your suspicions in (b).

4.5 Is there a relationship between the heights of students’ fathers and mothers? Use thefollowing data:

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DadHeight MomHeight73 6275 6669 6969 6171 6270 6369 6372 6473 6470 64




(b) Before you even look at the data, formulate null and alternative hypothesesabout 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 reasonablylinear. Then carry out a regression procedure to test your hypotheses. What isthe P -value?Do you reject H0?

(d) State your results: based on the outcome (you did or did not reject H0), doyou conclude that the population variables are related? Be sure to express yourresults specifically in terms of the variable(s) of interest, and mention to whatextent 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 9.32 - 9.35,Exercises 9.68 - 9.71,Exercises 9.93 - 9.95,Exercises 10.73 -10.85,Exercises 11.50 - 11.51,

Exercises 11.70 - 11.73,Exercises 11.80 - 11.103,Exercises 12.44 - 12.54,Exercises 13.50 - 13.58

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APPENDIX A

Example Ap 4.2A To find a confidence interval for a population mean when the data issaved in a list,

1. Store the data in a list of your choice

2. Press STAT


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,


2. Press STAT


4. Select 1:Z-Test... 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

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Example Ap 4.2B To find a confidence interval for a population mean when the datais saved in a list and the value for σ is unknown,


2. Press STAT


4. Select 8:TInterval... and press ENTER


6. Enter the appropriate list

7. Enter the appropriate confidence level in C-Level


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


4. Select 2:T-Test... and press ENTER


6. Enter the appropriate test value for µ0

7. Enter the appropriate list



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


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4. Select 4:2-SampTTest... and press ENTER


6. Enter the first list for List1

7. Enter the second list for List2


9. Select the appropriate response for Pooled


Return to Example 4.3B

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ti-84 calculator technology guide for elementary statistics

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