9.6 An art store receives their glass (for framing pictures) from an overseas supplier. The supplier sends sheets of glass in quantities of 1,000 pieces. Because the quality of the glass is so important, the art store must discard any sheets of glass that are scratched. Because of this, the art store won't accept any shipments where more than 20% of the sheets are scratched. Because inspecting all 1,000 sheets is impractical, the store randomly chooses 50 sheets of glass for inspection. If 15 of the 50 sheets are scratched, should the art store reject the shipment of glass? In your answer, let p denote the population proportion of scratched sheets in a shipment (of 1,000 sheets).

(a) (4 pts) To answer this question, we must perform a one-sided hypothesis test. How should H0 and Ha be specified?

(b) (6 pts) Perform the test in 9.6(a) at the = 0.10 significance level using the score test. Find the test statistic and critical value, plot the rejection region, and state your decision and final conclusion.

(c) (2 pts) Based upon your answer in 9.6(b), should the store reject the shipment of glass? Why?

(d) (4 pts) Find the pvalue for the test in 9.6(a).

(e) (2 pts) Based upon your answer in 9.6(d), is there evidence that the proportion

of scratched sheets in the shipment is higher than 0.20? Why?

(f) (2 pts) If the significance level = 0.01 (instead of 0.10), should the shipment be rejected? Why?