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⎯⎯=5.9 and a sample standard deviation of sd = 7.4. (a) Calculate a 95 percent confidence interval for µd = µ1 – µ2. Can we be 95 percent confident that the difference between µ1 and µ2 is greater than 0? (Round your answers to 2 decimal places.) Confidence interval = [ , ] ; (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? (Round your answer to 3 decimal places.) t = Reject H0 at α equal to evidence that µ1 differs from µ2. (c) The p-value for testing H0: µd < 3 versus Ha: µd > 3 equals .0043. Use the p-value to test these hypotheses with α 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? (Round your answer to 3 decimal places.) t = ; p-value Reject H0 at α equal to , evidence that µ1 and µ2 differ by more than 3.

Answer 1

a)

95 percent confidence interval =3.77 , 8.03

b)

t =5.581

Reject H0 at all levels ........

c)

t=2.743

p value =0.0043

Reject H0 at .10, .05, .01 level , very strong evidence,,,,,,,,,,,