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 5.5 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 19 engines and the mean pressure was 5.7 pounds/square inch with a variance of 0.64. A level of significance of 0.1 will be used. Assume the population distribution is approximately normal. Make the decision to reject or fail to reject the null hypothesis.

Answer 1

Sample size = n = 19

Sample mean = = 5.5

Variance = 0.64

Standard deviation = s = 0.8

Claim: The valve performs above the specifications.

The null and alternative hypothesis is

Level of significance = 0.1

Here population standard deviation is unknown so we have to use t-test statistic.
Test statistic is

Degrees of freedom = n - 1 = 19 - 1 = 18

Critical value = 1.330    ( Using t table)

Test statistic < critical vaue we fail to reject null hypothesis.

Conclusion:

The valve NOT performs above the specifications.