Question

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 4.2 4.2 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 240 240 engines and the mean pressure was 4.3 4.3 pounds/square inch. Assume the variance is known to be 0.64 0.64 . A level of significance of 0.02 0.02 will be used. Determine the decision rule. Enter the decision rule.

Answer 1

Since the sample size is 240 which us much greater than 30 hence we will use Z statistic here assuming the distribution as random and Normal. Now,

The hypotheses are:

Rejection region:

Reject Ho if Z calculated is less than Z(0.98)=2.33

Test statistic:

Z is calculated as

Z= 1.94

P value:

P value associated with Z score is calculated by table shown below as

0.0262

Conclusion:

Since the Z calculated=1.94<Z critical=2.33 at 98% level of confidence, and P value=0.026>0.02{level.of significance}, hence we fail to reject null hypothesis and conclude that we do not have enough evidence to support the claim.

Z table