A chemical manufacturer claims that its? ice-melting product 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 99?% confidence and within ±0.03?, what proportion of bags of the chemical perform the job as claimed by the manufacturer.

  1. How many bags does the representative need to? test?
  2. Suppose that the representative tests 50 bags, and 38 of them do the job as claimed. Construct a 99?% confidence interval estimate for the population proportion that will do the job as claimed.