Question

1. After teaching multiple sections of a statistics course for many years, a professor decides to add an online quiz component to help students review throughout the semester for their final exam. The professor specifically wants to know if adding the online quiz component improves student exam scores. This semester the professor teaches 2 sections of the class with a total of 38 students. The average final exam score for this semester's students is 82.

Over the past many years the professor has taught the course, the average exam score is 75; (σx = 13.5)

Answer 1

$H_0: \mu=83 \\ H_1: \mu> 82$

Test-statistic

$Z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}} \\ Z = \frac{75-82}{13.5 / \sqrt{38}} = -3.196 \\ α=0.05 \\ Z_{crit} = 1.645$

If $Z > Z_{crit}$ reject H₀.

-3.196 < 1.645

Accept H₀.

There is no evidence to claim that the online quiz component improve student exam scores at 0.05 level of significance.