# Question: Suppose a sample of 49 paired differences that have been

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?

## Answer to relevant Questions

In the book Essentials of Marketing Research, William R. Dillon, Thomas J. Madden, and Neil H. Firtle (1993) present preexposure and postexposure attitude scores from an advertising study involving 10 respondents. The data ...What assumptions must be satisfied in order to use the methods presented in this section? On January 7, 2000, the Gallup Organization released the results of a poll comparing the lifestyles of today with yesteryear. The survey results were based on telephone interviews with a randomly selected national sample of ...A marketing manager wishes to compare the mean prices charged for two brands of CD players. The manager conducts a random survey of retail outlets and obtains independent random samples of prices. The six retail outlets at ...An article in Fortune magazine reported on the rapid rise of fees and expenses charged by mutual funds. Assuming that stock fund expenses and municipal bond fund expenses are each approximately normally distributed, suppose ...Post your question