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 7.9 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 16 engines and the mean pressure was 8.2 pounds/square inch with a standard deviation of 0.5. A level of significance of 0.01 will be used. Assume the population distribution is approximately normal. Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.

Answer 1

Solution :

Given that,

Population mean = = 7.9

Sample mean = = 8.2

Sample standard deviation = s = 0.5

Sample size = n = 16

Level of significance = = 0.01

This a right (One) tailed test.

The null and alternative hypothesis is,  

Ho: 7.9

Ha: 7.9

The test statistics,

t = ( - )/ (s/)

= ( 8.2 - 7.9 ) / ( 0.5 / 16 )

= 2.400

Critical value of  the significance level is α = 0.01, and the critical value for a right-tailed test is

= 2.602

Rejection region : t > 2.602

Since it is observed that t = 2.4 < = 2.602, it is then concluded that the null hypothesis is fail to rejected.