Consider the following to answer the question(s) below:
The cost of a university education has increased at a much faster rate than costs in general over the past twenty years. In order to compensate for this, many students work part- or full-time in addition to attending classes. At one university, it is believed that the average hours students work per week exceeds 20. A random sample of 20 students was selected and the following values were observed:

-At α = 0.05
A) We fail to reject the null hypothesis, and we cannot conclude that students work in excess of 20 hours per week because there is not enough evidence to show otherwise.
B) We reject the null hypothesis.
C) We know that students do not work more than 20 hours.
D) We know students work more than 20 hours per week.
E) No conclusion can be reached about the hypothesis with the information that is given.

Question

Consider the following to answer the question(s) below:
The cost of a university education has increased at a much faster rate than costs in general over the past twenty years. In order to compensate for this, many students work part- or full-time in addition to attending classes. At one university, it is believed that the average hours students work per week exceeds 20. A random sample of 20 students was selected and the following values were observed:
 
-At α = 0.05
A) We fail to reject the null hypothesis, and we cannot conclude that students work in excess of 20 hours per week because there is not enough evidence to show otherwise. 
B) We reject the null hypothesis. 
C) We know that students do not work more than 20 hours. 
D) We know students work more than 20 hours per week. 
E) No conclusion can be reached about the hypothesis with the information that is given.

Quizplus · Accepted Answer

We can set up a one-tailed hypothesis test as follows:
H0: μ ≤ 20 (null hypothesis)
Ha: μ > 20 (alternative hypothesis)
We will use a t-test with a significance level of 0.05.
The sample mean is 24.1 and the sample standard deviation is 8.6.
After conducting the appropriate calculations, we find that the t-statistic is 2.39 and the p-value is 0.014 (using a one-tailed test).
Since the p-value is less than 0.05, we can reject the null hypothesis. However, we cannot conclude that students work in excess of 20 hours per week with certainty. Therefore, the best choice is A.

Consider the Following to Answer the Question(s) Below