Question

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 190 engines and the mean pressure was 7.3lbs/square inch. Assume the variance is known to be 1. If the valve was designed to produce a mean pressure of 7.2 lbs/square inch, is there sufficient evidence at the 0.05 level that the valve does not perform to the specifications? State the null and alternative hypotheses for the above scenario.

Answer 1

This is a two tailed test.

The null and alternative hypothesis is,

Ho: 7.2

Ha: 7.2

The test statistics,

Z =( - )/ (/n)

= ( 7.3 - 7.2 ) / ( 1 / 190 )

= 1.38

P-value = 2 * P(Z > 1.38 )

= 2 * ( 1 - P( Z < 1.38 ))

= 2 * 0.0838

= 0.1676

The p-value is p = 0.1676, and since p = 0.1676 > 0.05, it is concluded that the null hypothesis is fail to rejected.