The manufacturer of “Ice Melt” claims its product will melt snow and ice at temperatures as low as 0° Fahrenheit. Arepresentative for a large chain of hardware stores is interested in testing this claim. The chain purchases a large shipment of 5-pound bag

Question 8.75 

The manufacturer of “Ice Melt” claims its product will

melt snow and ice at temperatures as low as 0° Fahrenheit.

Arepresentative 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 ±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, and 42 of

them 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?