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Suppose grade point averages are normally distributed. We are interested in whether smokers have different gpa’s...

Suppose grade point averages are normally distributed. We are interested in whether smokers have different gpa’s than non-smokers. We know that non-smokers have a mean gpa of 3.1. You take a sample of 16 smokers and find they have a mean gpa of 3.38 with standard deviation of .021.

a. Suppose you wanted to test whether the gpas of the two groups different. • write down the null and alternative hypotheses • Construct the test statistic. What is the distribution of the test statistic? • Is there evidence that the two groups differ ? (assume α = .1)

b. Suppose you wanted to test the hypothesis that smoker have higher gpa’s • write down the null and alternative hypotheses • Construct the test statistic. What is the distribution of the test statistic? • Is there evidence that smokers have higher gpa’s (assume α = .05)

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