Question

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 170 engines and the mean pressure was 4.7 pounds/square inch (psi). Assume the population variance is 1.00. If the valve was designed to produce a mean pressure of 4.5 psi, is there sufficient evidence at the 0.05 level that the valve does not perform to the specifications?

A. There is sufficient evidence to support the claim that the valve does not perform to the specifications.

B. There is not sufficient evidence to support the claim that the valve does not perform to the specifications.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 4.5
Alternative Hypothesis, Ha: μ ≠ 4.5

Rejection Region
This is two tailed test, for α = 0.05
Critical value of z are -1.96 and 1.96.
Hence reject H0 if z < -1.96 or z > 1.96

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (4.7 - 4.5)/(1/sqrt(170))
z = 2.608

P-value Approach
P-value = 0.0091
As P-value < 0.05, reject the null hypothesis.

A. There is sufficient evidence to support the claim that the valve does not perform to the specifications.