A campus parking lot contains 20 spaces, all reserved for faculty members. The administration decides that students may park their cars in the lot after 4:00 PM if faculty usage then drops to less than 70%. A random weekday afternoon is chosen to sample the faculty usage after 4:00 PM.

a. State the null hypothesis.

b. State a one-tailed alternative hypothesis that would lead to student usage of the lot.

c. Find the region of rejection for a as close to 0.05 as possible.

d. If there are 18 faculty cars in the lot at the time of the survey:

i. What is the P value?

ii. What decision should be made about student parking?

e. Do you see any difficulties in the design of this survey? Suggest a better design.