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?