# Question

Suppose a sample of 49 paired differences that have been randomly selected from a normally distributed population of paired differences yields a sample mean of d-bar = 5 and a sample standard deviation of sd = 7.

a. Calculate a 95 percent confidence interval for μd = μ1 – μ2. Can we be 95 percent confident that the difference between m1 and m2 is not equal to 0?

b. Test the null hypothesis H0: μd = 0 versus the alternative hypothesis Ha: μd ≠ 0 by setting α equal to .10, .05, .01, and .001. How much evidence is there that μd differs from 0? What does this say about how μ1 and μ2 compare?

c. The p-value for testing H0: μd ≤ 3 versus Ha: μd > 3 equals .0256. Use the p-value to test these hypotheses with a equal to .10, .05, .01, and .001. How much evidence is there that μd exceeds 3? What does this say about the size of the difference between μ1 and μ2?

a. Calculate a 95 percent confidence interval for μd = μ1 – μ2. Can we be 95 percent confident that the difference between m1 and m2 is not equal to 0?

b. Test the null hypothesis H0: μd = 0 versus the alternative hypothesis Ha: μd ≠ 0 by setting α equal to .10, .05, .01, and .001. How much evidence is there that μd differs from 0? What does this say about how μ1 and μ2 compare?

c. The p-value for testing H0: μd ≤ 3 versus Ha: μd > 3 equals .0256. Use the p-value to test these hypotheses with a equal to .10, .05, .01, and .001. How much evidence is there that μd exceeds 3? What does this say about the size of the difference between μ1 and μ2?

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