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12.6 Homework  (Page 2/2)

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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 mean 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} } } {}
  • Alternate Hypothesis: At least one pair of means 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: There is sufficient evidence to conclude that the mean lengths are different.

Eliminate one magazine type that you now feel has a mean length different than 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?

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?

A researcher wants to know if the mean time (in minutes) that people watch their favorite news station are the same. Suppose that the table below shows the results of a study.

CNN FOX Local
45 15 72
12 43 37
18 68 56
38 50 60
23 31 51
35 22
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.

  • df(n) = 2; df(d) = 14
  • F 2,14 size 12{H rSub { size 8{o} } } {}
  • 4.08
  • 0.0401
  • Reject the null hypothesis
  • There is sufficient evidence to conclude that the mean times are different.

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.

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

Are the mean number of times a month a person eats out same for whites, blacks, Hispanics and Asians? Suppose that the table below shows the results of a study.

White Black Hispanic Asian
6 4 7 8
8 1 3 3
2 5 5 5
4 2 4 1
6 6 7
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.

  • df(n) = 3; df(d) = 15
  • F 3,15 size 12{H rSub { size 8{o} } } {}
  • 0.8853
  • 0.4711
  • Do not reject the null hypothesis
  • There is insufficient evidence to conclude that the mean number of times are different.

Are the mean number 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.

Powder Machine Made Hard Packed
1210 2107 2846
1080 1149 1638
1537 862 2019
941 1870 1178
1528 2233
1382
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.

Is the variance for the amount of money, in dollars, that shoppers spend on Saturdays at the mall the same as the variance for the amount of money that shoppers spend on Sundays at the mall? Suppose that the table below shows the results of a study.

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
Assume that both distributions are normal. Use a level of significance of 0.05.

  • df(n) = 11; df(d) = 12
  • F 11,12 size 12{H rSub { size 8{o} } } {}
  • 1.35
  • 0.6090
  • Do not reject the null hypothesis
  • There is insufficient evidence to conclude that the variances are different.

Are the variances for incomes on the East Coast and the West Coast the same? Suppose that the table below shows the results of a study. Income is shown in thousands of dollars.

East West
38 71
47 126
30 42
82 51
75 44
52 90
115 88
67
Assume that both distributions are normal. Use a level of significance of 0.05.

**Exercises 11 - 16 were contributed by Dr. Larry Green
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Source:  OpenStax, Collaborative statistics for mt230. OpenStax CNX. Aug 18, 2011 Download for free at http://legacy.cnx.org/content/col11345/1.2
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