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 5.1 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 210 engines and the mean pressure was 5.2 pounds/square inch. Assume the standard deviation is known to be 0.6. A level of significance of 0.1 will be used. Determine the decision rule.

Enter the decision rule.

Answer 1

Given that a mean pressure of =5.1 pounds/square and the standard deviation is known to be =0.6.  The valve was tested on n=210 engines and the mean pressure was =5.2 pounds/square inch.

Since sample size n=210 is greater than 30 hence it is assumed that the sample is from a large population to assume the distribution as normal.

Based on the given information A Z test will be conducted since population standard deviation is known and the level of significance is 0.1.

Based on the belief the hypotheses are:

Based on the hypotheses it will be a right-tailed test.

Rejection region/Decision rule:

Based on the significance level and type of test the rejection region is set up and the critical value of Z is calculated using excel formula for normal distribution as =NORM.S.INV(0.9) which results as Zc=1.282

So, reject Ho if Z-calculated is greater than 1.282

Test statistic:

P-value:

P-value is calculated using an excel tool for normal distribution which =1-NORM.S.DIST(2.415,TRUE) this results in P-value=0.0079.

Decision:

Since Z>Zc =1.282 hence we reject the null hypothesis.

Conclusion:

Since we are able to reject the null hypothesis hence we conclude that at 0.10 level of significance there is enough evidence to support the claim that the valve performs above the specifications which 5 pounds/square inch.