Question

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 140 engines and the mean pressure was 7.7 lbs/square inch. Assume the variance is known to be 0.64. If the valve was designed to produce a mean pressure of 7.9lbs/square inch, is there sufficient evidence at the 0.1 level that the valve does not perform to the specifications?

State the null and alternative hypotheses for the above scenario.

Answer 1

Solution :

Given that,

Population mean = = 7.9

Sample mean = = 7.7

Population standard deviation = = 0.8

Sample size = n = 140

Level of significance = = 0.1

This is a two tailed test.

The null and alternative hypothesis is,

Ho: 7.9

Ha: 7.9

The test statistics,

Z =( - )/ (/n)

= ( 7.7 - 7.9 ) /( 0.8 / 140 )

= -2.96

P-value = 2 * P( Z < z )

= 2 * P(Z < -2.96 )

= 2 * 0.0015

= 0.0030

The p-value is p =0.0030, and since p = 0.0030 < 0.1, it is concluded that the null hypothesis is rejected.

There sufficient evidence at the 0.1 level that the valve does not perform to the specifications.