A teacher hypothesizes that the students at her school are sleep deprived--specifically, that they on average get less than 8 hours of sleep daily. The teacher decides to test her hypothesis by collecting data on a random sample of 50 students from the school. Suppose she prespecifies a significance level of 0.075 for the hypothesis test and obtains a test statistic with a p-value of 0.08.

(A) (5 pts) What is the null hypothesis and what is the alternative hypothesis? Be specific.

(B) (5 pts) If the teacher rejects the null hypothesis, what is the probability of her making a mistake? How do you know?

(D) (5 pts) What maximum probability of making a mistake is the teacher willing to tolerate if she were to reject the null hypothesis? How do you know?

(D) (5 pts) At which conventional significance level(s) if any can the teacher reject the null hypothesis? Why?