Answer to Question #113938 in Statistics and Probability for Jack

Question

The university atheletic director is asked if soccer players are doing as well academically as other students atheletes. We know from a previous study that the average GPA for the student athletes is 3.05. After an initiative to help improve the GPA of student athletes, the athletes director randomly sample 25 soccer players and finds that the average GPA of the sample is 3.10 with a sample standard deviation of 0.34. is there a significant improvement? Use a 0.05 significance level.

Answer 1

$H_0: \mu\leq0\\ H_1:\mu > 0\\ \alpha =0.05\implies t_{(0.05,24)}=1.711,\\ T=\frac{\bar x-\mu_0}{\frac{s}{\sqrt n}}\\ T=\frac{3.10-3.05}{\frac{0.34}{\sqrt 25}}=0.735\\ \text{the rejection region} :\; t>1.711\\ \text{The decision is to accept}:\; H_0\\ \text {This mean that there is not}\\ \text{ a significant improvement}$