Question

An engineer has 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 6.9 pounds/square inch. The valve was tested on 24 engines and the mean pressure was 7.1 pounds/square inch with a variance of 1.00. Is there evidence at the 0.1 level that the valve does not perform to the specifications? Assume the population distribution is approximately normal.

Find the value of the test statistic. Round your answer to three decimal places.

Make the decision to reject or fail to reject the null hypothesis.

Answer 1

The test hypothesis is

This is a two-sided test because the alternative hypothesis is formulated to detect differences from the hypothesized mean value of 30 on either side.

Now, the value of test static can be found out by following formula:

Since t0 = 0.9798 < -1.7139 = -t{0.05}, we fail to reject the null hypothesis

there is insufficient evidence to claim that the valve does not perform to the specifications