Question 1052861: I need help with this:
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 24 hours are less
than the mean recall after 1 hour?
Assume we want to use a 0.05 significance level to test the claim. Please show all work.
(a) Identify the null hypothesis and the alternative hypothesis.
(b) Determine the test statistic.
(c) Determine the P-value for this test.
(d) Is there sufficient evidence to support the claim that the mean number of words recalled after 24 hours is less than the mean recall after 1 hour? Justify your conclusion.
Thank you very much for any help!
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Ho: the number of words recalled is unchanged or greater
Ha: the number of words recalled is less.
alpha=0.05, one way test
Paired t-test
4 degrees of freedom
Critical value is -2.132
difference defined here as number after 24 hours-number after 12 hours.
average d/[s/sqrt(n)]
This is -1.6/(1.14/sqrt(5))
That is t=-3.14
This has a p-value of 0.0175, and we can conclude that there is a significant difference (reject Ho).
The important part of this problem is to use each person as their own control. The df are less, but the variability is much less.
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