The director of housekeeping at Elegante, a luxury resort hotel with two locations (Seaside and Oceanfront), wants to evaluate housekeeping performance at those two locations. Random samples of 100 rooms were inspected at each location for defects (e.g., missing towels, missing soap, dirty floors or showers, dusty tables) after being cleaned. It was found that 21 of the rooms at Seaside had some housekeeping defect(s), and 28 rooms at Oceanfront had some housekeeping defect(s).

a. Develop the hypotheses to test whether the proportion of housekeeping defects differs between the two hotel locations.

b. What is the value of the test statistic and the associated p-value?

c. Do the results suggest that the proportion of housekeeping defects differs between the two hotel locations at the 5% significance level?

d. Construct the 95% confidence interval for the difference between the population housekeeping defect rates between the two hotel locations. How can this confidence interval be used to reach the same conclusion as in part (c)?