In a study of memory recall eight students from a large psyc

In a study of memory recall, eight students from a large psychology class were selected at random and given 10 minutes to memorize a list of 20 nonsense words. Each was asked to list as many words as he or she could remember both 1 hour and 24 hours later. The data as shown in the accompanying table. Is there evidence to suggest that the mean number of words recalled after 1 hour exceeds the mean recall after 24 hours by more than 3? Use a level of 0.01 test, and explain and show your work.

Subject        1        2        3        4        5        6        7        8

1 hour         14      12       18      7        11       9        16      15

24 hours      10      4       14       6         9        6       12      12

Ho:

H1:

P-Value:

Test Statistic:

Conclusion:

Solution

. In List L1, enter the differences: 4, 8, 4, 1, 2, 3, 4, 3.

Since ? is unknown, use STAT > TESTS > T-TEST to

find t = 4.9630,

P = .0008 (?₀ is 0 and we need a right-tail test to see if the number of words is less after 24 hours).

Since P is very small (P = .0008) we have very strong evidence that the mean number of words recalled after 1 hour will, in general, exceed the mean number of words recalled after 24 hours.