Covercraft manufactures covers to protect automobile interiors and finishes. Its Block-It 200 Series fabric has a limited two-year warranty. Periodic testing is done to determine if the warranty policy should be changed. One such study may have examined those covers that became unserviceable while still under warranty. Data that could be produced by such a study are contained in the file titled Covers. The data represent the number of months a cover was used until it became unserviceable. Covercraft might want to examine more carefully the covers that became unserviceable while still under warranty. Specifically, it wants to examine those that became unserviceable before they had been in use one year.
a. Covercraft has begun to think that it should lower its warranty period to perhaps 20 months. It believes that in doing this, 20% of the covers that now fail before the warranty is up will have surpassed the 20-month warranty rate. Calculate the proportion of the sample that became unserviceable after 20 months of service.
b. Determine the probability of obtaining a sample proportion at least as large as that calculated in part a if the true proportion was equal to 0.20.c. Based on your calculation in part b, should Covercraft lower its warranty period to 20 months? Support your answer.