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13.7 Homework

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This module provides a homework of F Distribution and One-Way 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 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

  • 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: There is insufficient evidence to conclude that the means are different.
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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. Using a 5% significance level, test the hypothesis that the 3 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

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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"} {} . Using the TI-83+/84+ function 2-SampFtest, you get the the test statistic as 2.9986 and p-value directly as 0.3127. If you input the lists in a different order, you get a test statistic of 0.3335 but the p-value is the same because this is a two-tailed test.
  • Decision: Do not reject null; Conclusion: There is insufficient evidence to conclude that the variances are different.
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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.

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For the next two problems, refer to the data from Terri Vogel’s Log Book.
http://cnx.org/content/m17132/latest/?collection=col10522/latest/

Examine the 7 practice laps. Determine whether the mean lap time is statistically the same for the 7 practice laps, or if there is at least one lap that has a different mean 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: There is insufficient evidence to conclude that the mean lap times are different.
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Examine practice laps 3 and 4. Determine whether or not the variance in lap time is statistically the same for those practice laps.

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

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Source:  OpenStax, Collaborative statistics. OpenStax CNX. Jul 03, 2012 Download for free at http://cnx.org/content/col10522/1.40
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