Question

A high school language course is given in two sections, each using a different teaching method. The first section has 21 students, and the grades in that section have a mean of 82.6 and a standard deviation of 8.6. In the second section, with 43 students, the mean of the grades is 85.2, with a standard deviation of 7.9. At alpha=0.05, test the hypothesis that the method used in second section is more effective. (Assume equal variances)

Hint: We are testing for difference between two means, independent populations. Let µ1 indicate mean of the first section, µ1 indicate the mean of the second section. Here, we would like to see if the second section is better. Therefore, the null hypothesis states H0: µ1-µ2=0, where the alternative hypothesis states H1: µ1-µ2<0, indicating a left tailed test.

Answer 1

since test statistic does not falls in rejection region we fail to reject null hypothesis

we do not have have sufficient evidence to conclude that method used in second section is more effective