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12.6 Homework

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This module provides a homework of F Distribution and ANOVA as a part of Collaborative Statistics collection (col10522) by Barbara Illowsky and Susan Dean.
Use a solution sheet to conduct the following hypothesis tests. The solution sheet can be found in the Table of Contents 14. Appendix.

Three students, Linda, Tuan, and Javier, are given 5 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 average 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

  • H o size 12{H rSub { size 8{o} } } {} : μ L = μ T = μ J size 12{μ rSub { size 8{L} } =μ rSub { size 8{T} } =μ rSub { size 8{J} } } {}
  • df n = 2 size 12{ ital "df" left (n right )=2} {} ; df d = 12 size 12{ ital "df" left (d right )="12"} {}
  • 0.67
  • 0.5305
  • Decision: Do not reject null; Conclusion: Means are same

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 below:

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

Refer to Exercise 13.8.1 . Determine whether or not the variance in weight gain is statistically the same among Javier’s and Linda’s rats.

  • df n = 4 size 12{ ital "df" left (n right )=4} {} ; df d = 4 size 12{ ital "df" left (d right )=4} {}
  • 3.00
  • 2 0 . 1563 = 0 . 3126 size 12{2 left (0 "." "1563" right )=0 "." "3126"} {}
  • Decision: Do not reject null; Conclusion: Variances are same

Refer to Exercise 13.8.2 above . Determine whether or not the variance in mileage driven is statistically the same among the working class and professional (middle income) groups.

For the next two problems, refer to the data from Terri Vogel’s Log Book [link pending].

Examine the 7 practice laps. Determine whether the average lap time is statistically the same for the 7 practice laps, or if there is at least one lap that has a different average time from the others.

  • df n = 6 size 12{ ital "df" left (n right )=6} {} ; df d = 98 size 12{ ital "df" left (d right )="98"} {}
  • 1.69
  • 0.1319
  • Decision: Do not reject null; Conclusion: Average lap times are the same

Examine practice laps 3 and 4. Determine whether or not the variance in lap time is statistically the same for those practice laps.

For the next four problems, refer to the following data.

The following table lists the number of pages in four different types of magazines.

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

Using a significance level of 5%, test the hypothesis that the four magazine types have the same average length.

  • H o size 12{H rSub { size 8{o} } } {} : μ d = μ n = μ h = μ c size 12{μ rSub { size 8{d} } =μ rSub { size 8{n} } =μ rSub { size 8{h} } =μ rSub { size 8{c} } } {}
  • At least one average is different
  • df n = 3 size 12{ ital "df" left (n right )=3} {} ; df d = 16 size 12{ ital "df" left (d right )="16"} {}
  • 8.69
  • 0.0012
  • Decision: Reject null; Conclusion: At least one average is different

Eliminate one magazine type that you now feel has an average length different than the others. Redo the hypothesis test, testing that the remaining three averages are statistically the same. Use a new solution sheet. Based on this test, are the average lengths for the remaining three magazines statistically the same?

Which two magazine types do you think have the same variance in length?

Which two magazine types do you think have different variances in length?
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Source:  OpenStax, Collaborative statistics (mt230 - fall 2014). OpenStax CNX. Aug 16, 2014 Download for free at http://legacy.cnx.org/content/col11403/1.7
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