Question

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 110 engines and the mean pressure was 4.6 pounds/square inch (psi). Assume the population standard deviation is 0.8. If the valve was designed to produce a mean pressure of 4.5 psi, is there sufficient evidence at the 0.02 level that the valve does not perform to the specifications?

Answer 1

To determine if the valve performs to the specifications, we can conduct a hypothesis test using the Z-test. If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that there is sufficient evidence that the valve does not perform to the specifications.

Step-by-step explanation:

To determine if the valve performs to the specifications, we can conduct a hypothesis test.

Null hypothesis: The valve performs to the specifications, i.e., the mean pressure is 4.5 psi.

Alternative hypothesis: The valve does not perform to the specifications, i.e., the mean pressure is not 4.5 psi.

Since we have a sample size of 110, we can use the Z-test. We calculate the test statistic (Z) using the formula Z = (sample mean - population mean) / (population standard deviation / sqrt(sample size)).

With the given values, the Z-test statistic is Z = (4.6 - 4.5) / (0.8 / sqrt(110)).

We can then compare the test statistic to the critical value for the given significance level (0.02). If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that there is sufficient evidence that the valve does not perform to the specifications.

If the test statistic is less than or equal to the critical value, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the valve does not perform to the specifications.