Suppose we have taken independent, random samples of sizes n1 = 8 and n2 = 8 from two normally distributed populations having means µ1 and µ2, and suppose we obtain x¯1 = 227, x¯2 = 190, s1 = 6, s2 = 6. Use critical values to test the null hypothesis H0: µ1 − µ2 < 27 versus the alternative hypothesis Ha: µ1 − µ2 > 27 by setting α equal to .10, .05, .01 and .001. Using the equal variance procedure, how much evidence is there that the difference between µ1 and µ2 exceeds 27? (Round your answer to 3 decimal places.) t = H0 at α = 0.1, 0.05, and, 0.01, evidence.
B.Suppose a sample of 49 paired differences that have been randomly selected from a normally distributed population of paired differences yields a sample mean d¯ =4.6 of and a sample standard deviation of sd = 7.6. (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 ? equal to evidence that µ1 differs from µ2. (c) The p-value for testing H0: µd < 3 versus Ha: µd > 3 equals .0735. 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 ? equal to , evidence that µ1 and µ2 differ by more than 3