In a study of memory recall, 5 people were given 10 minutes to memorize a list of 20 words. Each was asked to list as many of the words as he or she could remember both 1 hour and 24 hours later. The result is shown in the following table.

Number of Words Recalled

Subject 1 hour later 24 hours later

1 14 12

2 18 15

3 11 9

4 13 12

5 12 12

Is there evidence to 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.

(a) What is the appropriate hypothesis test to use for this analysis: z-test for two proportions, t-test for two proportions, t-test for two dependent samples (matched pairs), or t-test for two independent samples? Please identify and explain why it is appropriate.

(b) Let 1 = mean number of words recalled 1 hour later. Let 2 = mean number of words recalled 24 hours later. 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 number of words recalled 1 hour later. Let 2 = mean number of words recalled 24 hours later. 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. Show all work; writing the correct test statistic, without supporting work, will receive no credit.

(e) Determine the p-value. Round your answer to three decimal places. Show all work; writing the correct critical value, without supporting work, will receive no credit.

(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) Is there sufficient evidence to support the claim that the mean number of words recalled after 1 hour exceeds the mean recall after 24 hours? Justify your conclusion