11.5 Exercises

1. Three different traffic routes are tested for mean driving time. The entries in the table are the driving times in minutes on the three different routes. At the 5% significance level, test if the mean driving time for the three routes are the same.

Route 1 Route 2 Route 3
30 27 16
32 29 41
27 28 22
35 36 31

 

2. Suppose a group is interested in determining whether teenagers obtain their drivers licenses at approximately the same average age across the country. Suppose that the following data are randomly collected from five teenagers in each region of the country. The numbers represent the age at which teenagers obtained their drivers licenses.  At the 5% significance level, determine if the mean age is the same in the different regions of the country.
Northeast South West Central East
16.3 16.9 16.4 16.2 17.1
16.1 16.5 16.5 16.6 17.2
16.4 16.4 16.6 16.5 16.6
16.5 16.2 16.1 16.4 16.8

 

3. Groups of men from three different areas of the country are to be tested for mean weight. The entries in the table are the weights for the different groups. At the 5% significance level, test if the average weight for men is the same for the three groups.

Group 1 Group 2 Group 3
216 202 170
198 213 165
240 284 182
187 228 197
176 210 201

 

4. Girls from four different soccer teams are to be tested for mean goals scored per game. The entries in the table are the goals per game for the different teams. At the 5% significance level, test if the mean goal scored per game is the same for the four teams.
Team 1 Team 2 Team 3 Team 4
1 2 0 3
2 3 1 4
0 2 1 4
3 4 0 3
2 4 0 2
5. Four basketball teams took a random sample of players regarding how high each player can jump (in inches).  At the 5% significance level, is there a difference in the mean jump heights among the teams?
Team 1 Team 2 Team 3 Team 4 Team 5
36 32 48 38 41
42 35 50 44 39
51 38 39 46 40
6. A video game developer is testing a new game on three different groups. Each group represents a different target market for the game. The developer collects scores from a random sample from each group. At the 5% significance level, are the scores among the different groups different?
Group A Group B Group C
101 151 101
108 149 109
98 160 198
107 112 186
111 126 160

7. Three students, Linda, Tuan, and Javier, are given five laboratory rats each for a nutritional experiment. Each rat’s weight is recorded in grams. Linda feeds her rats Formula A, Tuan feeds his rats Formula B, and Javier feeds his rats Formula C. At the end of a specified time period, each rat is weighed again, and the net gain in grams is recorded. Using a significance level of 5%, determine if the three formulas produce the same mean weight gain.

Weights of Student Lab Rats
Linda’s rats Tuan’s rats Javier’s rats
43.5 47.0 51.2
39.4 40.5 40.9
41.3 38.9 37.9
46.0 46.3 45.0
38.2 44.2 48.6

8. A grassroots group opposed to a proposed increase in the gas tax claimed that the increase would hurt working-class people the most, since they commute the farthest to work. Suppose that the group randomly surveyed 24 individuals and asked them their daily one-way commuting mileage.  Using a 5% significance level, test if the three mean commuting mileages are the same.

working-class professional (middle incomes) professional (wealthy)
17.8 16.5 8.5
26.7 17.4 6.3
49.4 22.0 4.6
9.4 7.4 12.6
65.4 9.4 11.0
47.1 2.1 28.6
19.5 6.4 15.4
51.2 13.9 9.3

 

9. The following table lists the number of pages in four different types of magazines. Using a significance level of 5%, test if the four magazine types have the same mean length.  Assume that all distributions are normal, the four population standard deviations are approximately the same, and the data were collected independently and randomly
home decorating news health computer
172 87 82 104
286 94 153 136
163 123 87 98
205 106 103 207
197 101 96 146

 

10. A researcher wants to know if the mean times (in minutes) that people watch their favorite news station are the same. At the 5% significance level, test if the mean times that people watch their favorite news station are the same.  Assume that all distributions are normal, the three population standard deviations are approximately the same, and the data were collected independently and randomly
CNN FOX Local
45 15 72
12 43 37
18 68 56
38 50 60
23 31 51
35 22

11. Are the means for the final exams the same for all statistics class delivery types?  The table shows the scores on final exams from several randomly selected classes that used the different delivery types.  Assume that all distributions are normal, the four population standard deviations are approximately the same, and the data were collected independently and randomly.  Use a 5% significance level.

Online Hybrid Face-to-Face
72 83 80
84 73 78
77 84 84
80 81 81
81 86
79
82

12. Are the mean numbers of daily visitors to a ski resort the same for the three types of snow conditions? The table shows the results of a study.  Assume that all distributions are normal, the four population standard deviations are approximately the same, and the data were collected independently and randomly. Use a 5% significance level.

Powder Machine Made Hard Packed
1,210 2,107 2,846
1,080 1,149 1,638
1,537 862 2,019
941 1,870 1,178
1,528 2,233
1,382

13.  Two coworkers commute from the same building. They are interested in whether or not there is any variation in the time it takes them to drive to work. They each record their times for 20 commutes. The first worker’s times have a variance of 12.1. The second worker’s times have a variance of 16.9. At the 5% significance level, test if the variation in the first worker’s commute time is smaller than the second worker’s.

 

14. Two students are interested in whether or not there is variation in their test scores for math class. There are 15 total math tests they have taken so far. The first student’s grades have a standard deviation of 38.1. The second student’s grades have a standard deviation of 22.5. At the 5% significance level, determine if the variation in the second student’s scores are lower than the first student’s.

 

15. Two cyclists are comparing the variances of their overall paces going uphill. Each cyclist records his or her speeds going up 35 hills. The first cyclist has a variance of 23.8 and the second cyclist has a variance of 32.1. At the 5% significance level, is there a difference in the variance in the cyclists’ speeds?

 

16. Students Linda and Tuan are given five laboratory rats each for a nutritional experiment. Each rat’s weight is recorded in grams. Linda feeds her rats Formula A and Tuan feeds his rats Formula B. At the end of a specified time period, each rat is weighed again and the net gain in grams is recorded.

Linda’s rats Tuan’s rats
43.5 47.0
39.4 40.5
41.3 38.9
46.0 46.3
38.2 44.2
  1. Construct a 98% confidence interval for the ratio of the variance in the net weight gain for Linda’s and Tuan’s rats.
  2. Interpret the confidence interval found in part (a).
  3. Is there evidence to suggest that the variance in the net weight gain for Linda and Tuan’s rats is the same?  Explain.
17. A grassroots group opposed to a proposed increase in the gas tax claimed that the increase would hurt working-class people the most, since they commute the farthest to work. Suppose that the group randomly surveyed 16 individuals and asked them their daily one-way commuting mileage. The results are as follows.  Determine whether or not the variance in mileage driven is statistically the same among the working class and professional (middle income) groups. Use a 5% significance level.
working-class professional (middle incomes)
17.8 16.5
26.7 17.4
49.4 22.0
9.4 7.4
65.4 9.4
47.1 2.1
19.5 6.4
51.2 13.9

18. A researcher wants to study the amount of money, in dollars, that shoppers spend on Saturdays and Sundays at the mall.  A sample of shoppers is taken, and the amount of money they spent at the mall on Saturday or Sunday is recorded in the table below.
Saturday Sunday Saturday Sunday
75 44 62 137
18 58 0 82
150 61 124 39
94 19 50 127
62 99 31 141
73 60 118 73
89
  1. Construct a 93% confidence interval for the ratio of the variances for the amount of money spent on Saturdays and Sundays at the mall.
  2. Interpret the confidence interval found in part (a).
  3. Is there evidence to suggest that variance in the amount of money spent on Saturdays and Sundays at the mall is different?  Explain.

19. Are the variances for incomes on the East Coast and the West Coast the same? The table shows the results of a study. Income is shown in thousands of dollars. Assume that both distributions are normal. Use a 5% level of significance.

East West
38 71
47 126
30 42
82 51
75 44
52 90
115 88
67

Attribution

“Chapter 13 Homework” and “Chapter 13 Practice” in Introductory Statistics by OpenStax is licensed under a Creative Commons Attribution 4.0 International License.

License

Icon for the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License

Introduction to Statistics Copyright © 2022 by Valerie Watts is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.