Question

A criminology professor wants to know the impact of the type of course delivery. Their current class is a hybrid, consisting of 22 students. The average this semester was 84.1 with an SS of 158.76. The past semester’s class, taught in a traditional face to face format, had an n = 17 and an average performance in the class was a 78.2 with an SS of 160.35. Test the hypothesis that the current class has a higher average than the previous class. What do you conclude? Use an alpha level of 0.01. Make sure to show all four (or five) steps in order.

Answer 1

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μ1​ = μ2​

Ha: μ1​ > μ2​

This corresponds to a right-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=0.01, and the degrees of freedom are df=37. In fact, the degrees of freedom are computed, assuming that the population variances are equal.

Hence, it is found that the critical value for this right-tailed test is tc​=2.431, for α=0.01 and df=37.

The rejection region for this right-tailed test is R={t:t>2.431}.

(3) Test Statistics

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

(4) The decision about the null hypothesis

Since it is observed that t=1.447≤tc​=2.431, it is then concluded that the null hypothesis is not rejected.

Using the P-value approach: The p-value is p=0.0782, and since p=0.0782≥0.01, 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 greater than μ2​, at the 0.01 significance level.

Graphically

The t-test run in excel provides the following output: