Question

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 290 engines and the mean pressure was 6.1 pounds/square inch (psi). Assume the population variance is 0.36. If the valve was designed to produce a mean pressure of 6.0 psi, is there sufficient evidence at the 0.02 level that the valve performs above the specifications?

Find the P-value of the test statistic. Round your answer to four decimal places

Answer 1

This is the right tailed test .

The null and alternative hypothesis is

H₀ : = 6.0

H_a : > 6.0

Test statistic = z

= ( - ) /    / n

= (6.1 - 6) / 0.6 / 290

Test statistic = 2.838

P-value = 0.0023

P-value <

Reject the null hypothesis .

There is sufficient evidence at the 0.02 level that the valve performs above the specifications .