A certain supplier manufactures a type of rubber mat that is sold to automotive companies. The material used to produce the mats 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 mats, so an experiment was conducted in which 400 mats were 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 intervals from (a) and (b) and comment on the claim made by the supplier.