Question

Show your work. Carry out all calculations to at least 3 significant digits.

1. 1.1 AmanufacturerofTVsetsclaimsthatatleast98%ofitsTVsetscanlastmorethan10years without needing a single repair. In order to verify and challenge this claim, a consumer group randomly selected 800 consumers who had owned a TV set made by this manufacturer for 10 years. Of these 800 consumers, 60 said that their TV sets needed some repair at least once.

   a. Is there significant evidence showing that the manufacturer’s claim is false? Test using ? = 0.01.

   b. Do the data support that the manufacturer’s actual no-repair rate does not even reach 94%? Use ? = 0.01.

Answer 1

Answer a)

We have used z test for one proportion for testing hypothesis.

At 0.01 significance level, there is enough evidence to claim that the manufacturer’s claim is false. In other words, there is enough evidence to claim that the manufacturer’s actual no-repair rate is less than 98%.

Answer b)

At 0.01 significance level, there is not enough evidence to claim that the manufacturer’s actual no-repair rate does not even reach 94%.