{"id":320,"date":"2021-07-14T15:59:13","date_gmt":"2021-07-14T15:59:13","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/section-exercises\/"},"modified":"2023-12-05T09:53:57","modified_gmt":"2023-12-05T09:53:57","slug":"section-exercises","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/section-exercises\/","title":{"raw":"Section Exercises","rendered":"Section Exercises"},"content":{"raw":"

One-Way ANOVA - Practice<\/h2>\r\nUse the following information to answer the next five exercises.<\/em> There are five basic assumptions that must be fulfilled in order to perform a one-way ANOVA test. What are they?\r\n
\r\n
\r\n\r\n1. Write one assumption.\r\n\r\n<\/div>\r\n
2. Write another assumption.<\/div>\r\n<\/section><\/div>\r\n
\r\n
\r\n\r\n3. Write a third assumption.\r\n\r\n<\/div>\r\n
4. Write a fourth assumption.<\/div>\r\n<\/section><\/div>\r\n
\r\n
\r\n\r\n5. Write the final assumption.\r\n\r\n<\/div>\r\n
6. State the null hypothesis for a one-way ANOVA test if there are four groups.<\/div>\r\n<\/section><\/div>\r\n
\r\n
\r\n\r\n7. State the alternative hypothesis for a one-way ANOVA test if there are three groups.\r\n\r\n<\/div>\r\n
8. When do you use an ANOVA test?<\/div>\r\n<\/section><\/div>\r\n
<\/div>\r\n

The F Distribution and the F-Ratio - Practice<\/h2>\r\n
\r\n

Use the following information to answer the next eight exercises.<\/em> 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. The one-way ANOVA results are shown in the table below.<\/p>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Group 1<\/th>\r\nGroup 2<\/th>\r\nGroup 3<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
216<\/td>\r\n202<\/td>\r\n170<\/td>\r\n<\/tr>\r\n
198<\/td>\r\n213<\/td>\r\n165<\/td>\r\n<\/tr>\r\n
240<\/td>\r\n284<\/td>\r\n182<\/td>\r\n<\/tr>\r\n
187<\/td>\r\n228<\/td>\r\n197<\/td>\r\n<\/tr>\r\n
176<\/td>\r\n210<\/td>\r\n201<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
\r\n
\r\n\r\n9. What is the Sum of Squares Factor?\r\n\r\n<\/div>\r\n
10. What is the Sum of Squares Error?<\/div>\r\n<\/section><\/div>\r\n
\r\n
\r\n\r\n11. What is the df<\/em> for the numerator?\r\n\r\n<\/div>\r\n
12. What is the df<\/em> for the denominator?<\/div>\r\n<\/section><\/div>\r\n
\r\n
\r\n

13. What is the Mean Square Factor?<\/p>\r\n\r\n<\/div>\r\n

14. What is the Mean Square Error?<\/div>\r\n<\/section><\/div>\r\n
\r\n
\r\n\r\n15. What is the F<\/em> statistic?\r\n\r\n<\/div>\r\n
Use the following information to answer the next eight exercises.<\/em> 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. The one-way ANOVA results are shown in the table below.<\/div>\r\n<\/section><\/div>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Team 1<\/th>\r\nTeam 2<\/th>\r\nTeam 3<\/th>\r\nTeam 4<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
1<\/td>\r\n2<\/td>\r\n0<\/td>\r\n3<\/td>\r\n<\/tr>\r\n
2<\/td>\r\n3<\/td>\r\n1<\/td>\r\n4<\/td>\r\n<\/tr>\r\n
0<\/td>\r\n2<\/td>\r\n1<\/td>\r\n4<\/td>\r\n<\/tr>\r\n
3<\/td>\r\n4<\/td>\r\n0<\/td>\r\n3<\/td>\r\n<\/tr>\r\n
2<\/td>\r\n4<\/td>\r\n0<\/td>\r\n2<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
\r\n
\r\n\r\n16. What is SSbetween<\/sub><\/em>?\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n
\r\n
\r\n\r\n17. What is the df<\/em> for the numerator?\r\n\r\n<\/div>\r\n
18. What is MSbetween<\/sub><\/em>?<\/div>\r\n<\/section><\/div>\r\n
\r\n
\r\n\r\n19. What is SSwithin<\/sub><\/em>?\r\n\r\n<\/div>\r\n
20. What is the df<\/em> for the denominator?<\/div>\r\n<\/section><\/div>\r\n
\r\n
\r\n\r\n21. What is MSwithin<\/sub><\/em>?\r\n\r\n<\/div>\r\n
22. What is the F<\/em> statistic?<\/div>\r\n<\/section><\/div>\r\n
\r\n
\r\n\r\n23. Judging by the F<\/em> statistic, do you think it is likely or unlikely that you will reject the null hypothesis?\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n<\/div>\r\n

Facts About the F Distribution - Practice<\/h2>\r\n
\r\n
\r\n
\r\n\r\n24. An F<\/em> statistic can have what values?\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n
\r\n
\r\n\r\n25. What happens to the curves as the degrees of freedom for the numerator and the denominator get larger?\r\n\r\n<\/div>\r\n
Use the following information to answer the next seven exercises.<\/em> Four basketball teams took a random sample of players regarding how high each player can jump (in inches). The results are shown in the table below.<\/div>\r\n<\/section><\/div>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Team 1<\/th>\r\nTeam 2<\/th>\r\nTeam 3<\/th>\r\nTeam 4<\/th>\r\nTeam 5<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
36<\/td>\r\n32<\/td>\r\n48<\/td>\r\n38<\/td>\r\n41<\/td>\r\n<\/tr>\r\n
42<\/td>\r\n35<\/td>\r\n50<\/td>\r\n44<\/td>\r\n39<\/td>\r\n<\/tr>\r\n
51<\/td>\r\n38<\/td>\r\n39<\/td>\r\n46<\/td>\r\n40<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
\r\n
\r\n\r\n26. What is the df(num)<\/em>?\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n
\r\n
\r\n\r\n27. What is the df(denom)<\/em>?\r\n\r\n<\/div>\r\n
28. What are the Sum of Squares and Mean Squares Factors?<\/div>\r\n<\/section><\/div>\r\n
\r\n
\r\n\r\n29. What are the Sum of Squares and Mean Squares Errors?\r\n\r\n<\/div>\r\n
30. What is the F<\/em> statistic?<\/div>\r\n<\/section><\/div>\r\n
\r\n
\r\n\r\n31. What is the p<\/em>-value?\r\n\r\n<\/div>\r\n
32. At the 5% significance level, is there a difference in the mean jump heights among the teams?<\/div>\r\n
<\/div>\r\n
Use the following information to answer the next seven exercises.<\/em> 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. The results are shown in the table below.<\/div>\r\n<\/section><\/div>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Group A<\/th>\r\nGroup B<\/th>\r\nGroup C<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
101<\/td>\r\n151<\/td>\r\n101<\/td>\r\n<\/tr>\r\n
108<\/td>\r\n149<\/td>\r\n109<\/td>\r\n<\/tr>\r\n
98<\/td>\r\n160<\/td>\r\n198<\/td>\r\n<\/tr>\r\n
107<\/td>\r\n112<\/td>\r\n186<\/td>\r\n<\/tr>\r\n
111<\/td>\r\n126<\/td>\r\n160<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
\r\n
\r\n\r\n33. What is the df(num)<\/em>?\r\n\r\n<\/div>\r\n
34. What is the df(denom)<\/em>?<\/div>\r\n<\/section><\/div>\r\n
\r\n
\r\n\r\n35. What are the SSbetween<\/sub><\/em> and MSbetween<\/sub><\/em>?\r\n\r\n<\/div>\r\n
36. What are the SSwithin<\/sub><\/em> and MSwithin<\/sub><\/em>?<\/div>\r\n<\/section><\/div>\r\n
\r\n
\r\n\r\n37. What is the F<\/em> Statistic?\r\n\r\n<\/div>\r\n
38. What is the p<\/em>-value?<\/div>\r\n<\/section><\/div>\r\n
\r\n
\r\n

39. At the 10% significance level, are the scores among the different groups different?<\/p>\r\n\r\n<\/div>\r\n

\u00a0Use the following information to answer the next three exercises.<\/em> Suppose a group is interested in determining whether teenagers obtain their driver's 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 driver's licenses.<\/div>\r\n<\/section><\/div>\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
<\/th>\r\nNortheast<\/th>\r\nSouth<\/th>\r\nWest<\/th>\r\nCentral<\/th>\r\nEast<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
<\/td>\r\n16.3<\/td>\r\n16.9<\/td>\r\n16.4<\/td>\r\n16.2<\/td>\r\n17.1<\/td>\r\n<\/tr>\r\n
<\/td>\r\n16.1<\/td>\r\n16.5<\/td>\r\n16.5<\/td>\r\n16.6<\/td>\r\n17.2<\/td>\r\n<\/tr>\r\n
<\/td>\r\n16.4<\/td>\r\n16.4<\/td>\r\n16.6<\/td>\r\n16.5<\/td>\r\n16.6<\/td>\r\n<\/tr>\r\n
<\/td>\r\n16.5<\/td>\r\n16.2<\/td>\r\n16.1<\/td>\r\n16.4<\/td>\r\n16.8<\/td>\r\n<\/tr>\r\n
[latex]\\overline{x}[\/latex]=<\/td>\r\n________<\/td>\r\n________<\/td>\r\n________<\/td>\r\n________<\/td>\r\n________<\/td>\r\n<\/tr>\r\n
[latex]{s}_{2}[\/latex]=<\/td>\r\n________<\/td>\r\n________<\/td>\r\n________<\/td>\r\n________<\/td>\r\n________<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nEnter the data into your calculator or computer.\r\n
\r\n
\r\n\r\n40. p<\/em>-value = ______\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n\u00a0State the decisions and conclusions (in complete sentences) for the following preconceived levels of \u03b1<\/em>.\r\n
\r\n
\r\n\r\n41.\u00a0\u03b1<\/em> = 0.05\r\n\r\na. Decision: ____________________________\r\n

b. Conclusion: ____________________________<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

\r\n
\r\n\r\n42. \u03b1<\/em> = 0.01\r\n

a. Decision: ____________________________<\/p>\r\n

b. Conclusion: ____________________________<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n<\/section><\/div>\r\n

Test of Two Variances - Practice<\/h2>\r\n
\r\n\r\nUse the following information to answer the next two exercises.<\/em> There are two assumptions that must be true in order to perform an F<\/em> test of two variances.\r\n
\r\n
\r\n\r\n43. Name one assumption that must be true.\r\n\r\n<\/div>\r\n
44. What is the other assumption that must be true?<\/div>\r\n<\/section><\/div>\r\n
<\/div>\r\nUse the following information to answer the next five exercises.<\/em> 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\u2019s times have a variance of 12.1. The second worker\u2019s times have a variance of 16.9. The first worker thinks that he is more consistent with his commute times and that his commute time is shorter. Test the claim at the 10% level.\r\n
\r\n
\r\n\r\n45. State the null and alternative hypotheses.\r\n\r\n<\/div>\r\n
46. What is s<\/em>1<\/sub> in this problem?<\/div>\r\n<\/section><\/div>\r\n
\r\n
\r\n\r\n47. What is s<\/em>2<\/sub> in this problem?\r\n\r\n<\/div>\r\n
48. What is n<\/em>?<\/div>\r\n<\/section><\/div>\r\n
\r\n
\r\n\r\n49. What is the F<\/em> statistic?\r\n\r\n<\/div>\r\n
50. What is the p<\/em>-value?<\/div>\r\n<\/section><\/div>\r\n
\r\n
\r\n\r\n51. Is the claim accurate?\r\n\r\n<\/div>\r\n
<\/div>\r\n<\/section><\/div>\r\n
Use the following information to answer the next four exercises.<\/em> 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\u2019s grades have a standard deviation of 38.1. The second student\u2019s grades have a standard deviation of 22.5. The second student thinks his scores are lower.<\/div>\r\n
\r\n
\r\n\r\n52. State the null and alternative hypotheses.\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n
\r\n
\r\n\r\n53. What is the F<\/em> Statistic?\r\n\r\n<\/div>\r\n
54. What is the p<\/em>-value?<\/div>\r\n<\/section><\/div>\r\n
\r\n
\r\n\r\n55. At the 5% significance level, do we reject the null hypothesis?\r\n\r\n<\/div>\r\n
<\/div>\r\n<\/section><\/div>\r\n
Use the following information to answer the next three exercises.<\/em> 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. The cyclists want to see if their variances are the same or different.<\/div>\r\n
\r\n
\r\n\r\n56. State the null and alternative hypotheses.\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n
\r\n
\r\n\r\n57. What is the F<\/em> Statistic?\r\n\r\n<\/div>\r\n
58. At the 5% significance level, what can we say about the cyclists\u2019 variances?<\/div>\r\n<\/section><\/div>\r\n<\/div>\r\n
\r\n

One-Way ANOVA - Homework<\/h2>\r\n<\/div>\r\n
\r\n
\r\n
\r\n\r\n59. 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. The one-way ANOVA results are shown in the table below.\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Route 1<\/th>\r\nRoute 2<\/th>\r\nRoute 3<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
30<\/td>\r\n27<\/td>\r\n16<\/td>\r\n<\/tr>\r\n
32<\/td>\r\n29<\/td>\r\n41<\/td>\r\n<\/tr>\r\n
27<\/td>\r\n28<\/td>\r\n22<\/td>\r\n<\/tr>\r\n
35<\/td>\r\n36<\/td>\r\n31<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nState SS<\/em>between<\/sub>, SS<\/em>within<\/sub>, and the F<\/em> statistic.\r\n\r\n<\/div>\r\n
60. Suppose a group is interested in determining whether teenagers obtain their driver's 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 driver's licenses.<\/div>\r\n<\/section><\/div>\r\n<\/section>\r\n
\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Northeast<\/th>\r\nSouth<\/th>\r\nWest<\/th>\r\nCentral<\/th>\r\nEast<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
16.3<\/td>\r\n16.9<\/td>\r\n16.4<\/td>\r\n16.2<\/td>\r\n17.1<\/td>\r\n<\/tr>\r\n
16.1<\/td>\r\n16.5<\/td>\r\n16.5<\/td>\r\n16.6<\/td>\r\n17.2<\/td>\r\n<\/tr>\r\n
16.4<\/td>\r\n16.4<\/td>\r\n16.6<\/td>\r\n16.5<\/td>\r\n16.6<\/td>\r\n<\/tr>\r\n
16.5<\/td>\r\n16.2<\/td>\r\n16.1<\/td>\r\n16.4<\/td>\r\n16.8<\/td>\r\n<\/tr>\r\n
[latex]\\overline{x}[\/latex]=<\/td>\r\n________<\/td>\r\n________<\/td>\r\n________<\/td>\r\n________<\/td>\r\n________<\/td>\r\n<\/tr>\r\n
[latex]{s}_{2}[\/latex]=<\/td>\r\n________<\/td>\r\n________<\/td>\r\n________<\/td>\r\n________<\/td>\r\n________<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

State the hypotheses.<\/p>\r\n

H0<\/sub><\/em>: ____________<\/p>\r\nHa<\/sub><\/em>: ____________\r\n\r\n<\/div>\r\n

The F Distribution and the F-Ratio - Homework<\/h2>\r\n
Use the following information to answer the next three exercises.<\/em> Suppose a group is interested in determining whether teenagers obtain their driver's 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 driver's licenses.\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
<\/th>\r\nNortheast<\/th>\r\nSouth<\/th>\r\nWest<\/th>\r\nCentral<\/th>\r\nEast<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
<\/td>\r\n16.3<\/td>\r\n16.9<\/td>\r\n16.4<\/td>\r\n16.2<\/td>\r\n17.1<\/td>\r\n<\/tr>\r\n
<\/td>\r\n16.1<\/td>\r\n16.5<\/td>\r\n16.5<\/td>\r\n16.6<\/td>\r\n17.2<\/td>\r\n<\/tr>\r\n
<\/td>\r\n16.4<\/td>\r\n16.4<\/td>\r\n16.6<\/td>\r\n16.5<\/td>\r\n16.6<\/td>\r\n<\/tr>\r\n
<\/td>\r\n16.5<\/td>\r\n16.2<\/td>\r\n16.1<\/td>\r\n16.4<\/td>\r\n16.8<\/td>\r\n<\/tr>\r\n
[latex]\\overline{x}[\/latex]=<\/td>\r\n________<\/td>\r\n________<\/td>\r\n________<\/td>\r\n________<\/td>\r\n________<\/td>\r\n<\/tr>\r\n
[latex]{s}_{2}[\/latex]<\/td>\r\n________<\/td>\r\n________<\/td>\r\n________<\/td>\r\n________<\/td>\r\n________<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nH0<\/sub><\/em>: \u00b5<\/em>1<\/sub> = \u00b5<\/em>2<\/sub> = \u00b5<\/em>3<\/sub> = \u00b5<\/em>4<\/sub> = \u00b5<\/em>5<\/sub>\r\n

H\u03b1<\/em>: At least any two of the group means \u00b5<\/em>1<\/sub>, \u00b5<\/em>2<\/sub>, \u2026, \u00b5<\/em>5<\/sub> are not equal.<\/p>\r\n\r\n

\r\n
\r\n

61. degrees of freedom \u2013 numerator: df<\/em>(num<\/em>) = _________<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

\r\n
\r\n\r\n62. degrees of freedom \u2013 denominator: df<\/em>(denom<\/em>) = ________\r\n\r\n<\/div>\r\n
63.\u00a0<\/span>F<\/em> statistic = ________<\/div>\r\n<\/section>\r\n
\r\n

Facts About the F Distribution - Homework<\/h2>\r\n
\r\n
\r\n
DIRECTIONS<\/div>\r\n<\/header>
\r\n

Use a solution sheet to conduct the following hypothesis tests. The solution sheet can be found in Appendix E<\/a>.<\/p>\r\n\r\n<\/section><\/div>\r\n

\r\n
\r\n

64. 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 10%, test the hypothesis that the three formulas produce the same mean weight gain.<\/p>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Weights of Student Lab Rats<\/span><\/caption>\r\n
Linda's rats<\/th>\r\nTuan's rats<\/th>\r\nJavier's rats<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
43.5<\/td>\r\n47.0<\/td>\r\n51.2<\/td>\r\n<\/tr>\r\n
39.4<\/td>\r\n40.5<\/td>\r\n40.9<\/td>\r\n<\/tr>\r\n
41.3<\/td>\r\n38.9<\/td>\r\n37.9<\/td>\r\n<\/tr>\r\n
46.0<\/td>\r\n46.3<\/td>\r\n45.0<\/td>\r\n<\/tr>\r\n
38.2<\/td>\r\n44.2<\/td>\r\n48.6<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n
<\/div>\r\n<\/section><\/div>\r\n<\/section>\r\n
\r\n
\r\n\r\n65. 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. The results are in the table below. Using a 5% significance level, test the hypothesis that the three mean commuting mileages are the same.\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
working-class<\/th>\r\nprofessional (middle incomes)<\/th>\r\nprofessional (wealthy)<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
17.8<\/td>\r\n16.5<\/td>\r\n8.5<\/td>\r\n<\/tr>\r\n
26.7<\/td>\r\n17.4<\/td>\r\n6.3<\/td>\r\n<\/tr>\r\n
49.4<\/td>\r\n22.0<\/td>\r\n4.6<\/td>\r\n<\/tr>\r\n
9.4<\/td>\r\n7.4<\/td>\r\n12.6<\/td>\r\n<\/tr>\r\n
65.4<\/td>\r\n9.4<\/td>\r\n11.0<\/td>\r\n<\/tr>\r\n
47.1<\/td>\r\n2.1<\/td>\r\n28.6<\/td>\r\n<\/tr>\r\n
19.5<\/td>\r\n6.4<\/td>\r\n15.4<\/td>\r\n<\/tr>\r\n
51.2<\/td>\r\n13.9<\/td>\r\n9.3<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/section><\/div>\r\n
\r\n
\r\n\r\nExamine the seven practice laps from Appendix C.<\/a> Determine whether the mean lap time is statistically the same for the seven practice laps, or if there is at least one lap that has a different meantime from the others.\r\n\r\n<\/div>\r\n
Use the following information to answer the next two exercises.<\/em>\u00a0The table below lists the number of pages in four different types of magazines.<\/div>\r\n<\/section><\/div>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
home decorating<\/th>\r\nnews<\/th>\r\nhealth<\/th>\r\ncomputer<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
172<\/td>\r\n87<\/td>\r\n82<\/td>\r\n104<\/td>\r\n<\/tr>\r\n
286<\/td>\r\n94<\/td>\r\n153<\/td>\r\n136<\/td>\r\n<\/tr>\r\n
163<\/td>\r\n123<\/td>\r\n87<\/td>\r\n98<\/td>\r\n<\/tr>\r\n
205<\/td>\r\n106<\/td>\r\n103<\/td>\r\n207<\/td>\r\n<\/tr>\r\n
197<\/td>\r\n101<\/td>\r\n96<\/td>\r\n146<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
\r\n
\r\n\r\n66. Using a significance level of 5%, test the hypothesis that the four magazine types have the same mean length.\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n
\r\n
\r\n\r\n67. Eliminate one magazine type that you now feel has a mean length different from the others. Redo the hypothesis test, testing that the remaining three means are statistically the same. Use a new solution sheet. Based on this test, are the mean lengths for the remaining three magazines statistically the same?\r\n\r\n<\/div>\r\n
68. A researcher wants to know if the mean times (in minutes) that people watch their favorite news station are the same. Suppose that the\u00a0table below shows the results of a study.<\/div>\r\n<\/section><\/div>\r\n
\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
CNN<\/th>\r\nFOX<\/th>\r\nLocal<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
45<\/td>\r\n15<\/td>\r\n72<\/td>\r\n<\/tr>\r\n
12<\/td>\r\n43<\/td>\r\n37<\/td>\r\n<\/tr>\r\n
18<\/td>\r\n68<\/td>\r\n56<\/td>\r\n<\/tr>\r\n
38<\/td>\r\n50<\/td>\r\n60<\/td>\r\n<\/tr>\r\n
23<\/td>\r\n31<\/td>\r\n51<\/td>\r\n<\/tr>\r\n
35<\/td>\r\n22<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

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 level of significance of 0.05.<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

\r\n
\r\n\r\n69. Are the means for the final exams the same for all statistics class delivery types? The table below shows the scores on final exams from several randomly selected classes that used the different delivery types.\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Online<\/th>\r\nHybrid<\/th>\r\nFace-to-Face<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
72<\/td>\r\n83<\/td>\r\n80<\/td>\r\n<\/tr>\r\n
84<\/td>\r\n73<\/td>\r\n78<\/td>\r\n<\/tr>\r\n
77<\/td>\r\n84<\/td>\r\n84<\/td>\r\n<\/tr>\r\n
80<\/td>\r\n81<\/td>\r\n81<\/td>\r\n<\/tr>\r\n
81<\/td>\r\n<\/td>\r\n86<\/td>\r\n<\/tr>\r\n
<\/td>\r\n<\/td>\r\n79<\/td>\r\n<\/tr>\r\n
<\/td>\r\n<\/td>\r\n82<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

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 level of significance of 0.05.<\/p>\r\n\r\n<\/div>\r\n

70. Are the mean number of times a month a person eats out the same for Whites, Blacks, Hispanics, and Asians? Suppose that the table below shows the results of a study.<\/div>\r\n<\/section><\/div>\r\n
\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
White<\/th>\r\nBlack<\/th>\r\nHispanic<\/th>\r\nAsian<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
6<\/td>\r\n4<\/td>\r\n7<\/td>\r\n8<\/td>\r\n<\/tr>\r\n
8<\/td>\r\n1<\/td>\r\n3<\/td>\r\n3<\/td>\r\n<\/tr>\r\n
2<\/td>\r\n5<\/td>\r\n5<\/td>\r\n5<\/td>\r\n<\/tr>\r\n
4<\/td>\r\n2<\/td>\r\n4<\/td>\r\n1<\/td>\r\n<\/tr>\r\n
6<\/td>\r\n<\/td>\r\n6<\/td>\r\n7<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

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 level of significance of 0.05.<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

\r\n
\r\n

71. Are the mean numbers of daily visitors to a ski resort the same for the three types of snow conditions? Suppose that the table below shows the results of a study.<\/p>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Powder<\/th>\r\nMachine Made<\/th>\r\nHard Packed<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
1,210<\/td>\r\n2,107<\/td>\r\n2,846<\/td>\r\n<\/tr>\r\n
1,080<\/td>\r\n1,149<\/td>\r\n1,638<\/td>\r\n<\/tr>\r\n
1,537<\/td>\r\n862<\/td>\r\n2,019<\/td>\r\n<\/tr>\r\n
941<\/td>\r\n1,870<\/td>\r\n1,178<\/td>\r\n<\/tr>\r\n
<\/td>\r\n1,528<\/td>\r\n2,233<\/td>\r\n<\/tr>\r\n
<\/td>\r\n1,382<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

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 level of significance of 0.05.<\/p>\r\n\r\n<\/div>\r\n

72. Sanjay made identical paper airplanes out of three different weights of paper: light, medium, and heavy. He made four airplanes from each of the weights and launched them himself across the room. Here are the distances (in meters) that his planes flew.<\/div>\r\n<\/section><\/div>\r\n
\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Paper Type\/Trial<\/th>\r\nTrial 1<\/th>\r\nTrial 2<\/th>\r\nTrial 3<\/th>\r\nTrial 4<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
Heavy<\/td>\r\n5.1 meters<\/td>\r\n3.1 meters<\/td>\r\n4.7 meters<\/td>\r\n5.3 meters<\/td>\r\n<\/tr>\r\n
Medium<\/td>\r\n4 meters<\/td>\r\n3.5 meters<\/td>\r\n4.5 meters<\/td>\r\n6.1 meters<\/td>\r\n<\/tr>\r\n
Light<\/td>\r\n3.1 meters<\/td>\r\n3.3 meters<\/td>\r\n2.1 meters<\/td>\r\n1.9 meters<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
\"the<\/span><\/figure>\r\n
    \r\n \t
  1. Take a look at the data in the graph. Look at the spread of data for each group (light, medium, heavy). Does it seem reasonable to assume a normal distribution with the same variance for each group? Yes or No.<\/li>\r\n \t
  2. Why is this a balanced design?<\/li>\r\n \t
  3. Calculate the sample mean and sample standard deviation for each group.<\/li>\r\n \t
  4. Does the weight of the paper have an effect on how far the plane will travel? Use a 1% level of significance. Complete the test using the method shown in the bean plant example in Example<\/a>.\r\n