Question

1. An educational psychologist studies the effect of frequent testing on retention of class material. In one section of an introductory course, students are given quizzes each week. A second section of the same course receives only two tests during the semester. At the end of the semester, both sections receive the same final exam, and the scores are summarized below:

                                    Frequent Quizzes       Two Exams

                                            n = 20                    n = 20

                                           M = 73                   M = 68

1. Determine the correct t-test needed. If the first sample variance has s² = 84 and the second sample has s² = 96, do the data indicate that testing frequency has a significant effect? Again, use a two-tailed test with α = .05. Draw your distribution. (2 pts)

Answer 1

The provided sample means are shown below:

Also, the provided sample standard deviations are:

and the sample sizes are

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho:

Ha:

This corresponds to a two-tailed test, for which a t-test for two population means, with two independent samples, with unknown population standard deviations will be used.

(2) Rejection Region

Based on the information provided, the significance level is α=0.05, and the degrees of freedom are df = 38 . In fact, the degrees of freedom are computed as follows, assuming that the population variances are equal:

Hence, it is found that the critical value for this two-tailed test is t_c = 2.024 , for α=0.05 and df = 38

(3) Test Statistics

Since it is assumed that the population variances are equal, the t-statistic is computed as follows:

(4) Decision about the null hypothesis

Since it is observed that |t| = 1.667< t_c = 2.024, it is then concluded that the null hypothesis is not rejected.

Using the P-value approach: The p-value is p = 0.1038, and since p = 0.1038> 0.05 , it is concluded that the null hypothesis is not rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean μ1​ is different than μ2​, at the 0.05 significance level.

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