Question

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 200 engines and the mean pressure was 4.2 lbs/square inch. Assume the standard deviation is known to be 1. If the valve was designed to produce a mean pressure of 4.1 lbs/square inch, is there sufficient evidence at the 0.02 level that the valve performs above the specifications?

State the null and alternative hypotheses for the above scenario.

Answer 1

The null and alternate hypothesis here are given as:

As we are aware about the population standard deviation here, we perform the standard normal test to do the hypothesis testing here. The test statistic here is computed as:

Now as this is a one tailed upper sided test, the p-value here is computed from the standard normal tables as:

p = P(Z > 1.4142) = 0.079

As the p-value here is 0.079 > 0.02 which is the level of significance, therefore the test is not significant and we cannot reject the null hypothesis here. Therefore we dont have sufficient evidence here that the mean is greater than the specifications.