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 4.7 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 24 engines and the mean pressure was 5.0 pounds/square inch with a standard deviation of 0.7. A level of significance of 0.01 will be used. Assume the population distribution is approximately normal. Make the decision to reject or fail to reject the null hypothesis.

Answer 1

Solution:

This a right (One) tailed test.

The null and alternative hypothesis is,  

Ho: 4.7

Ha: 4.7

The test statistics,

t =( - )/ (s /n)

= ( 5 - 4.7 ) / ( 0.7 / 24 )

= 2.100

P-value = 0.023

The p-value is p = 0.023 > 0.01, it is concluded that the null hypothesis is fail to rejected.

fail to reject the null hypothesis.