(Solved): A college professor believes that students achieve a higher grade point average (GPA) in the fall ...

A college professor believes that students achieve a higher grade point average (GPA) in the fall semester than in the spring semester. To test his theory, he samples 37 of his fall semester students and 34 of his spring semester students. The fall semester students had an average semester GPA of \( 3.44 \) with a standard deviation of \( 0.33 \); the spring semester students had an average semester GPA of \( 3.29 \) with a standard deviation of \( 0.41 \). If the GPAs in both student populations are normally distributed, conduct a hypothesis test using a \( 9 \% \) level of significance to test the professor's theory. Step 1: State the null and alternative hypotheses. Let \( \mu_{F} \) indicate the mean GPA of fall semester students and \( \mu_{S} \) indicate the mean GPA of spring semester students. \[ \begin{array}{l} H_{0}: \mu_{F}-\mu_{S} \\ H_{a}: \mu_{F}-\mu_{S} \end{array} \] (So we will be performing a \( \quad \checkmark \) test.) Part 2 of 4 Step 2: Assuming the null hypothesis is true, determine the features of the distribution of the differences of sample means. The differences of sample means are with distribution mean and distribution standard deviation Question Help: D Post to forum