1. A firm has provided services to over 10,000 customers over the past year. As VP of Customer Service, you are interested in knowing what fraction of those customers is either "satisfied" or "very satisfied" with the service. A random sample of 400 of those customers is taken, and 360 of those surveyed report being "satisfied" or "very satisfied".

(a) Describe the population parameter of interest.

(b) What is the value of the point estimate of the population parameter?

(c) Construct a 95% confidence interval for the proportion of all of your customers who are either satisfied or very satisfied with your service. Interpret the confidence interval.

(d) Now construct a 99% confidence interval for the population proportion.

2. A hospital is concerned with the rate of "hospital-acquired infection (HAI)" that is, an infection acquired during a patient's stay. A random sample of the medical records of 480 surgical patients from 2017 revealed that 75 of those patients experienced an HAI. In early 2018, the hospital introduced a number of new sterilization guidelines designed to reduce HAI rates. A random sample of the medical records of 460 surgical patients whose hospital stays following the implementation of the new guidelines revealed that 67 of those patients experienced an HAI. Test the hypothesis that implementation of the new sterilization guidelines has reduced the proportion of patients who experience an HAI. [Use a 5% level of significance.}