Question

A maker of microwave ovens advertises that no more than 10% of its microwaves need repair during the first 5 years of use. In a random sample of 50 microwaves that are 5 years old, 12% needed repairs at a=.04 can you reject the makers claim that no more than 10% of its microwaves need repair during the first five years of use?

Answer 1

We conclude that no more than 10% of its microwaves need repair during the first five years of use.

Explanation:

We are given that a maker of microwave ovens advertises that no more than 10% of its microwaves need repair during the first 5 years of use.

In a random sample of 50 microwaves that are 5 years old, 12% needed repairs.

Let p = population proportion of microwaves who need repair during the first five years of use.

So, Null Hypothesis,
`H_0` : p
`\leq` 10% {means that no more than 10% of its microwaves need repair during the first five years of use}

Alternate Hypothesis,
`H_A` : p > 10% {means that more than 10% of its microwaves need repair during the first five years of use}

The test statistics that will be used here is One-sample z-test for proportions;

T.S. =
`\frac{\hat p-p}{\sqrt{(p(1-p))/(n) } }` ~ N(0,1)

where,
`\hat p` = sample proportion of microwaves who need repair during the first 5 years of use = 12%

n = sample of microwaves = 50

So, the test statistics =
`\frac{0.12-0.10}{\sqrt{(0.10(1-0.10))/(50) } }`

= 0.471

The value of z-test statistics is 0.471.

Now, at a 0.04 level of significance, the z table gives a critical value of 1.751 for the right-tailed test.

Since the value of our test statistics is less than the critical value of z as 0.471 < 1.751, so we have insufficient evidence to reject our null hypothesis as the test statistics will not fall in the rejection region.

Therefore, we conclude that no more than 10% of its microwaves need repair during the first five years of use.