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Homework 5 Solutions

# Homework 5 Solutions - Homework 5 solution 1 Since n = 12...

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Homework 5 – solution 1. Since n = 12, we should use no more than 4 bins. Let the bins correspond to the four seasons (with the first bin corresponding to winter). Then we have E i = 3 for i = 1 , . . . , 4. O 1 = 3, O 2 = 6, O 3 = 2, and O 4 = 1. The value of the test statistic is χ 2 = 1 3 (0 + 9 + 1 + 4) = 4 . 67 The corresponding critical value is χ 2 0 . 05 , 4 - 0 - 1 = χ 2 0 . 05 , 3 = 7 . 81. Since χ 2 < χ 2 0 . 05 , 3 , we cannot reject the null hypothesis, and conclude that the data is consistent with the uniform birthday hypothesis. 2. Let x be the number of female smokers in the sample. Then the table of observed values looks like smoking nonsmoking men 40 - x 60 + x women x 100 - x and the table of expected values is smoking nonsmoking men 20 80 women 20 80 Computing the value of the test statistic, we obtain χ 2 = (20 - x ) 2 1 20 + 1 80 + 1 20 + 1 80 = (20 - x ) 2 8 . Equating it to the critical value, we obtain (20 - x ) 2 8 = χ 2 0 . 05 , 1 = 3 . 84 . Solving the latter for x , we get x = 20 - 8 · 3 . 84 = 14 . 46 . 1

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Therefore, the smallest number of female smokers for which the independence hypothesis would not be rejected is 15. 3. Using Minitab we obtain that the test statistic value is χ 2 = 14 . 19 and the corresponding P-value is 0.116 meaning that there is only a moderate
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Homework 5 Solutions - Homework 5 solution 1 Since n = 12...

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