Question: Leaky gas tanks. Nationwide, it is estimated that 40% of service stations have gas tanks that leak to some extent. A new program in California is designed to lessen the prevalence of these leaks. We want to assess the effectiveness of the program by seeing if the percentage of service stations whose tanks leak has decreased. To do this, we randomly sample 27 service stations in California and determine whether there is any evidence of leakage. In our sample, only 7 of the stations exhibit any leakage. Is there evidence that the new program is effective?

a) What are the null and alternative hypotheses?

b) Check the assumptions necessary for inference.

c) Test the null hypothesis.

d) What do you conclude (in plain English)?

e) If the program actually works, have you made an error? What kind?

f) What two things could you do to decrease the probability of making this kind of error?

g) What are the advantages and disadvantages of taking those two courses of action?