Question: To try to understand the reason for returned goods, the manager of a store examines the records on 40 products that were returned in the last year. Reasons were coded by 1 for "defective," 2 for "unsatisfactory," and 0 for all other reasons, with the results shown in the table.
a. Give a point estimate of the proportion of all returns that are because of something wrong with the product, that is, either defective or performed unsatisfactorily.
b. Assuming that the sample is sufficiently large, construct an 80% confidence interval for the proportion of all returns that are because of something wrong with the product.