A certain supplier manufactures a type of rubber at that is sold to automotive companies. In the application, the pieces of material must have certain hardness characteristics. Defective mats are occasionally discovered and rejected. The supplier claims that the proportion defective is 0.05. A challenge was made by one of the clients who purchased the product. Thus an experiment was conducted in which 400 mats are tested and 17 were found defective.

(a) Compute a 95% two-sided confidence interval on the proportion defective.

(b) Compute an appropriate 95% one-sided confidence interval on the proportion defective.

(c) Interpret both of these in (a) and (b) and comment on the claim made by the supplier.