Question

An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 4.1 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 120 engines and the mean pressure was 4.3 pounds/square inch. Assume the variance is known to be 0.64. A level of significance of 0.05 will be used. Make a decision to reject or fail to reject the null hypothesis. Make a decision.

Answer 1

We reject the null hypothesis at the significance level of 0.05.

Explanation:

`H_(0): \mu = 4.1` vs
`H_(1): \mu > 4.1` (upper-tail alternative)

We have
`\bar{x} = 4.3`,
`\sigma^(2) = 0.64` and n = 120. We have a large sample and our test statistic is

`Z = \frac{\bar{X}-4.1}{\sigma/√(n)}` which is normal standard approximately. We have observed

`z = (4.3-4.1)/(0.8/√(120)) = 2.7386`.

We should use the significance level
`\alpha = 0.05`. The 95th quantile of the standard normal distribution is
`z_(0.95) = 1.6449` and the rejection region is given by {z > 1.6449}. Because the observed value 2.7386 is greater than 1.6449, we reject the null hypothesis at the significance level of 0.05.