Question

Does the use of examples improve memory for the concepts being taught? Joe Researcher tested this possibility by teaching 10 subjects 20 concepts each. For each subject, examples were provided to help explain 10 of the new concepts, no examples were provided for the other 10. Joe then tested his subjects memory for the concepts and recorded how many concepts, out of 10, that the subject could remember. Here are his data: Test the above hypothesis at ( alpha=0.05) level?

Subject No.	Without Example	With Example
1	6	8
2	8	8
3	5	6
4	4	6
5	7	7
6	8	7
7	2	5
8	5	7
9	6	7

Answer 1

NULL HYPOTHESIS H0:

ALTERNATIVE HYPOTHESIS HA:

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μD​ = 0

Ha: μD​ > 0

This corresponds to a right-tailed test, for which a t-test for two paired samples be used.

(2) Rejection Region

Based on the information provided, the significance level is α=0.05, and the degrees of freedom are df = 8df=8.

Hence, it is found that the critical value for this right-tailed test is tc​=1.86, for α=0.05 and df=8.

The rejection region for this right-tailed test is R=t:t>1.86.

(3) Test Statistics

The t-statistic is computed as shown in the following formula:

(4) Decision about the null hypothesis

Since it is observed that t = 2.626 > t_c = 1.86t=2.626>tc​=1.86, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p=0.0152, and since p=0.0152<0.05, it is concluded that the null hypothesis is rejected.

(5) ConclusionIt is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the use of examples improve memory for the concepts being taught ​, at the 0.05 significance level.