Question

During the 90's, the average GPA of graduating psychology majors was normally distributed with a mean of 2.50 and a standard deviation of 0.5. Since 2000, the number of psychology majors almost tripled. A faculty member wonders if the GPA of the most recent graduates is different from what it had been in the 90's. She randomly selects a sample of 64 psychology majors graduating in May 2014 and finds that their mean GPA is 2.40. Assuming that the standard deviation hasn't changed since the 90's, use hypothesis testing to decide whether the average GPA of psychology majors now is different from the average GPA of psychology majors in the 1990s. State the null and alternate hypotheses, calculate the appropriate test statistic (z), find the critical value(s) for the test statistic (using alpha=0.05), make a sketch of the distribution for your null hypothesis while labeling the critical region(s) and test statistics, and state what decision you would make about the hypothesis test.

Answer 1

Here claim is that the GPA of the most recent graduates is different from what it had been in the 90's.

So hypothesis is vs

As n=64 and population standard deviation is known, we will use z distribution to find test statistics

The z-critical values for a two-tailed test, for a significance level of α=0.05

zc​=−1.96 and zc​=1.96

Graphically

As test statistics in not in the rejection region, we fail to reject the null hypothesis

Hence we do not have sufficient evidence to suppor the claim that the GPA of the most recent graduates is different from what it had been in the 90's.