Question

A sample of 900 computer chips revealed that 58% of the chips fail in the first 1000 hours of their use. The company's promotional literature claimed that 62% fail in the first 1000 hours of their use. Is there sufficient evidence at the 0.01 level to dispute the company's claim? State the null and alternative hypotheses for the above scenario.

Answer 1

Answer with explanation:

We are given Sample proportion :
`\hat{p}=0.58`

And Population proportion : p=0.62

By considering company's claim, we have

`H_0:p=0.62\\\\H_a:p\\eq0.62`

Since alternative hypothesis is two-tailed , so the test is two-tailed test.

Test statistic :
`z=\frac{\hat{p}-p}{\sqrt{(p(1-p))/(n)}}`

i.e.
`z=\frac{0.58-0.62}{\sqrt{(0.62(1-0.62))/(900)}}\approx-2.47`

P-value (two-tailed test)=
`2P(z>|-2.47|)=2P(z>2.47)`

`=0.0135113\approx0.013`

Since, the p-value is greater than the significance level (0.01), so we accept the null hypothesis.

We conclude that we have enough evidence to support company's claim.