An engineer 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 8.0 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 250 engines and the mean pressure was 8.1 pounds/square inch. Assume the variance is known to be 1.00. A level of significance of 0.01 will be used. Make a decision to reject or fail to reject the null hypothesis. Make a decision

The calculated value z= 0.0063 does not  fall in the critical region  so we fail to reject the null hypothesis. And accept that the valve does not perform above the specifications.

Step-by-step explanation:

Given that

Population mean= μ = 8.0

Sample mean= x`= 8.1

Sample size= n= 250

Sample standard deviation= s= 1.00

Significance level= ∝ =0.01

The null hypothesis and alternate hypothesis are  

H0: μ < 8.0

Ha: μ ≥ 8.0  One tailed test

The claim is that the valve perform above the specifications

The critical value at 0.01 significance level for one tailed test is z > ±2.33

The test statistic z is used

z= x`- μ/ σ/√n

Z= 8.1-8.0/ 1/√250

z= 0.1/1/15.811

z= 0.0063

The calculated value z= 0.0063  does not fall in the critical region  so we fail to reject the null hypothesis.