Question

7. A maker of microwave ovens advertises that no more than 10% of its microwaves need repair during the first five years of use. In a random sample of 57 microwaves five years old or less, 13% needed repairs. At , can you reject the maker’s claim that no more than 10% of its microwaves need repair during the first five years of use? Use mathematics to justify your answer.

Answer 1

There is insufficient evidence to support the claim.

Explanation:

What we need to do is calculate the z factor and see whether or not we can refute the manufacturer's claim.

We have to:

z = (p - pm) / [pm * (1-pm) / n] ^ (1/2)

where p is the probability of the random sample, 13% or 0.13 and pm the probability per microwave maker, that is, 10% or 0.1. n sample size which is 57.

When replacing, we are left with:

z = (0.13 - 0.1) / [0.1 * (1-0.1) / 57] ^ (1/2)

z = 0.75

This value corresponds in the normal distribution to 0.7734 (attached image), this value is very large to refute the above, it must give a value less than 0.05 to be able to be refutable.

Therefore there is insufficient evidence to support the claim.