Chapter 8, Problem 63PS

The manufacturer of Ice Melt claims that its products will melt snow and ice at temperatures as low as $0°$ Fahrenheit. A representative for a large chain of hardware stores is interested in testing this claim. The chain purchases a large shipment of 5-pound bags for distribution. The representative wants to know, with $95\%$ confidence and within $\pm 0.05,$ what proportion of bags of Ice Melt perform the job as claimed by the manufacturer.

a. How many bags does the representative need to test? What assumption should be made concerning the population proportion? (This is called destructive testing: i. e., the product being tested is destroyed by the test and is then unavailable to be sold.)

b. Suppose that the representative tests 50 bags, 42 of then do the job as claimed. Construct a 95% confidence interval estimate for the population proportion that will do the job as claimed.

c. How can the representative use the results of (b) to determine whether to sell the Ice Melt Product?