The Marriott Hotel marketing team wants to estimate ρ, the proportion of the hotel guests who were return visitors in the past three years. They select a simple random sample of 150 guests from the past three year's records and finds that 27 of the sampled guests are return visitors.
a) Compute a point estimate for ρ.
b) What are the upper and lower bounds for the 90% confidence interval for ρ (4 decimals)?
c) Marriott has decided to offer a room discount for returning visitors unless the sample provides evidence (with 90% confidence) that ρ is greater than 0.15. In that case, Marriott will not offer the discount. State the null and alternative hypotheses (in symbols) that need to be tested in order to make the decision.
d) Based on the confidence interval in part b, would you conclude that the Marriott should offer the room discount? (Justify your response).