Question

A sample of 900 computer chips revealed that 75% of the chips do not fail in the first 1000 hours of their use. The company's promotional literature claimed that above 72% do not fail in the first 1000 hours of their use. Is there sufficient evidence at the 0.05 level to support the company's claim

Answer 1

No the evidence is not sufficient

Explanation:

From the question we are told that

The sample size is
`n = 900`

The sample proportion is
`\r p = 0.75`

The population proportion is
`p = 0.72`

The Null hypothesis is

`H_o : p = 0.72`

The Alternative hypothesis is

`H_a : p > 0.72`

The level of significance is given as
`\alpha = 0.05`

The critical value for the level of significance is
`t_(\alpha ) = 1.645`

Now the test statistic is mathematically evaluated as

`t = \frac{\r p - p }{ \sqrt{(p(1-p))/(√(n) ) } }`

substituting values

`t = \frac{ 0.75 - 0.72 }{ \sqrt{(0.72 (1-0.72))/(√(900) ) } }`

`t = 0.366`

Since the critical value is greater than the test statistics then the Null hypothesis is rejected which there is no sufficient evidence to support the claim