Question

In a study of memory recall, ten students from a large statistics and data analysis class were
selected at random and given 15 minutes to memorize a list of 20 nonsense 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 data are as shown in Table 1. Is there evidence to suggest the mean number of words recalled
after 1 hour exceeds the mean recall after 24 hours by more than 3? Use a significance level of
0.05.

students	1	2	3	4	5	6	7	8	9	10
1 hours later (words)	14	12	18	7	11	9	16	15	13	17
24 hours later(words)	10	4	14	5	8	5	11	12	9	10

Answer 1

Solution :

Null and alternative hypotheses :

The null and alternative hypotheses would be as follows :

Test statistic :

To test the hypothesis the most appropriate test is paired t-test. The test statistic is given as follows :

Where, is sample mean of the differences, is hypothesized mean difference under H_{​​​​​​0}, s is sample standard deviation of differences and n is sample size.

From the above table we have,

The value of the test statistic is 1.4.

P-value :

Since, our test is right-tailed test, therefore we shall obtain the right-tailed p-value for the test statistic. The right-tailed p-value is given as follows :

P-value = P(T > t)

P-value = P(T > 1.4)

P-value = 0.1102

The p-value is 0.1102.

Decision :

Significance level = 0.05

(0.1102 > 0.05)

Since, p-value is greater than the significance level of 0.05, therefore we shall be fail to reject the null hypothesis (H_{​​​​​​0}) at 0.05 significance level.

Conclusion :

At 0.05 significance level, there is not sufficient evidence to suggest the mean number of words recalled after 1 hour exceeds the mean recall after 24 hours by more than 3.

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