16. In a study of memory recall, 5 people were given 10 minutes to memorize a li
ID: 3330923 • Letter: 1
Question
16. 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.
1 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) Identify the null hypothesis and the alternative hypothesis. (b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit. (c) Determine the P-value. Show all work; writing the correct P-value, without supporting work, will receive no credit. (d) 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.
Numbers of Words Recall Subject 1 hour 24hours 1 13 12 2 18 16 3 10 9 4 15 1 5 11 11 67 49Explanation / Answer
H0: D 0
H1: D > 0
Numbers of Words Recall
Subject
1 hour
24hours
Di
(Di-D)
(Di-D)^2
1
13
12
-1
2.6
6.76
2
18
16
-2
1.6
2.56
3
10
9
-1
2.6
6.76
4
15
1
-14
-10.4
108.16
5
11
11
0
3.6
12.96
Sum
67
49
-18
137.2
Average
-3.6
D=ED/n=-18/5=-3.6
S.D=(E(Di-D)2/n-1)=137.2/4=5.8566
tSTAT=D-µ /S.D/n
Where tSTAT has n - 1 d.f
tSTAT=-3.6-0/5.8566/5
=-1.37
The P-Value is .121275.
Do not reject the null hypothesis. Hence, there is no sufficient evidence to support the claim that the mean number of words recalled after 1 hour exceeds the mean recall after 24 hours.
Numbers of Words Recall
Subject
1 hour
24hours
Di
(Di-D)
(Di-D)^2
1
13
12
-1
2.6
6.76
2
18
16
-2
1.6
2.56
3
10
9
-1
2.6
6.76
4
15
1
-14
-10.4
108.16
5
11
11
0
3.6
12.96
Sum
67
49
-18
137.2
Average
-3.6
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