Question

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 280 engines and the mean pressure was 6.5
pounds/square inch (psi). Assume the population variance is 0.64. The engineer designed the valve such that it would produce a mean pressure of 6.6 psi. It is believed
that the valve does not perform to the specifications. A level of significance of 0.02 will be used. Find the value of the test statistic. Round your answer to two decimal
places

Answer 1

Answer:

The value of the test statistic is $t = -2.09$

Step-by-step explanation:

The null hypothesis is:

$H_{0} = 6.6$

The alternate hypotesis is:

$H_{1} \neq 6.6$

Our test statistic is:

$t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation(square roof of the variance) and n is the size of the sample.

In this problem, we have that:

$X = 6.5, \mu = 6.6, \sigma = \sqrt{0.64} = 0.8, n = 280$

So

$t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$t = \frac{6.5 - 6.6}{\frac{0.8}{\sqrt{280}}}$

$t = -2.09$

The value of the test statistic is $t = -2.09$