MUST SHOW WORK.

A researcher wished to estimate the difference between the proportion of users of two shampoos who are satisfied with the prodcut. In a sample of 400 users of Shampoo A taken by this researcher, 78 said they are satisifed. In another sample of 500 users of Shampoo B taken by the same researcher, 92 said they were satisfied.

a) Construct a 90% confidence interval for the true difference between the two population proportions.

b) Based on your answer in (a), what would be your response at cx=0.1 to the claim that there is no difference in customer satisfaction between the two shampoos?