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?