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 5.3 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 300 engines and the mean pressure was 5.4 pounds/square inch. Assume the variance is known to be 1.00. A level of significance of 0.1 will be used. Make a decision to reject or fail to reject the null hypothesis.

Make a decision.

Answer 1

Solution:
Given in the question
Claim is that it is believed that the value performs above the specification i.e. 5.3
So null and alternative hypothesis can be written as
Null hypothesis H0: = 5.3
Alternative hypothesis Ha: > 5.3
No. of sample = 300
Sample mean (Xbar) = 5.4
Population variance (^2) = 1
Population standard deviation() = sqrt(Variance) = sqrt(1) = 1
Here we will Z test as sample size is large enough and population standard deviation is known
Test statistic value can be calculated as
Test statistic = (Xbar - )//sqrt(n) = (5.4-5.3)/1/sqrt(300) = 1.73
This is right tailed test so from Z table we found p-value = 0.0418
At alpha =0.1, we can reject the null hypothesis as p-value is less than alpha value (0.0418<0.1)
So we have significant evidence to support the claim that the valve performs above the specification.