In a study of memory recall, 5 people were given 10 minutes to memorize a list of 20 different words. Each was asked to list as many of the words as he or she could remember both 1 hour and 24 hours later. Does the data below suggest that the mean number of words recalled after 1 hour exceeds the mean recall after 24 hours? Assume we want to use a 0.05 significance level to test the claim.

Number of Words Recalled

Subject 1 hour later 24 hours later

1 14 12

2 18 14

3 11 8

4 13 12

5 12 12

(a) What is the appropriate hypothesis test to use for this analysis? Please identify and explain why it is appropriate.

(b) Let 1 = mean words recalled after 1 hour. Let 2 = mean words recalled after 24 hours. Which of the following statements correctly defines the null hypothesis?

(i) 1 - 2 > 0 (d > 0)

(ii) 1 - 2 = 0 (d = 0)

(iii) 1 - 2 < 0 (d < 0)

(c) Let 1 = mean words recalled after 1 hour. Let 2 = mean words recalled after 24 hours. Which of the following statements correctly defines the alternative hypothesis?

(i) 1 - 2 > 0 (d > 0)

(ii) 1 - 2 = 0 (d = 0)

(iii) 1 - 2 < 0 (d < 0)

(d) Determine the test statistic. Round your answer to three decimal places. Describe method used for obtaining the test statistic.

(e) Determine the p-value. Round your answer to three decimal places. Describe method used for obtaining the p-value.

(f) Compare p-value and significance level . What decision should be made regarding the null hypothesis (e.g., reject or fail to reject) and why?

(g) What do the results of this study tell us about the mean number of words recalled after 1 hours and after 24 hours? Justify your conclusion.