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Exam3_practice_solutions

Exam3_practice_solutions - 5E Exam 3 practice Formulas at...

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5E Exam 3 practice Formulas at end are as they will be on exam. For any hypothesis test, clearly state null and alternative hypotheses. 1. Let μ 1 =the mean for ΣΘΞ and μ 2 =the mean for ΛΔΞ. H 0 : μ 1 - μ 2 0 or μ 2 - μ 1 0 (I’ll use the first in my calculations.) H a : μ 1 - μ 2 > 0 or μ 2 - μ 1 < 0 To find the standard error and degrees of freedom I’ll first calculate s 2 1 /n 1 and s 2 2 /n 2 . These are 20 2 / 70 = 5 . 714 and 23 2 / 70 = 7 . 557. So the standard error is p ( s 2 1 n 1 + s 2 2 n 2 = 5 . 714 + 7 . 557 = 3 . 643. The t statistic for the data is then t = (160 - 152) - 0 3 . 643 = 2 . 196. At this point we need to compare that t value with one from the table. To do so we need the degrees of freedom. According to the formula it is df = (5 . 714+7 . 557) 2 1 69 5 . 714 2 + 1 69 7 . 557 2 = 135 . 4. We don’t find this exact df in the table, but comparison with df = 120 and df = 140 indicates a P value of just under 2%. So reject H 0 in favor of H a : The data does provide evidence that ΣΘΞ members drink more.

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