sample207_1

sample207_1 - Sample problems 2 1 Consider the following...

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Sample problems 2 1. Consider the following random sample: - 2 . 5, 0 . 3, 1 . 5, - 1 . 2, - 1 . 4, - 2 . 0, - 1 . 7, 1 . 5, 1 . 2, 2 . 0, - 0 . 5, 1 . 1. Test the hypothesis that this comes from a t-distribution with 1 degree of freedom. Use α = 0 . 05 Solution: Since n = 12, we should use no more than 4 bins. Let’s set up the bins in such a way that the expected frequency in each bin is equal to 3. Since t 0 . 25 , 1 = 1 . 000, the bins should be x < - 1, - 1 < x < 0, 0 < x < 1, and x > 1, respectively. So the observed frequencies become: O 1 = 5, O 2 = 1, O 3 = 1 and O 4 = 5. The value of the test statistic is χ 2 0 = 1 3 2 2 + 2 2 + 2 2 + 2 2 · = 5 . 33 . Since χ 2 0 . 05 ,k - p - 1 = χ 2 0 . 05 , 4 - 0 - 1 = χ 2 0 . 05 , 3 = 7 . 81, we can’t reject the null hypothesis and conclude that it is plausible. 2. Out of 70 Lehigh students 50 like Heineken more than Beck’s, and out of 60 Lafayette students, 35 prefer Heineken to Beck’s. Is it reasonable to believe that the beer preference is independent of the place of study? Solution: Let’s compute the expected frequencies.

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