Fasteners are manufactured for an application involving aircraft. Each fastener is categorized either as conforming (suitable for its intended use), downgraded (unsuitable for its intended use but useable for another purpose), and scrap (not useable). It is thought that 85% of fasteners are conforming, while 10% are downgraded and 5% are scrap. In a sample of 500 fasteners, 405 were conforming, 55 were downgraded, and 40 were scrap. Can you concluded that the true percentages differ from 85%, 10%, and 5%?

(a) State the appropriate null hypothesis.

(b) Compute the expected values under the null hypothesis.

(c) Compute the value of the chi-square statistic.

(d) What can you conclude at a = 0.05 level of significance?