Question

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 120 120 engines and the mean pressure was 4.7 4.7 pounds/square inch (psi). Assume the population variance is 0.81 0.81 . If the valve was designed to produce a mean pressure of 4.9 4.9 psi, is there sufficient evidence at the 0.02 0.02 level that the valve performs below the specifications? Step 4 of 6 : Find the P-value of the test statistic. Round your answer to four decimal places.

Answer 1

Solution :

Given that,

Population mean = = 4.9

Sample mean = = 4.7

Population standard deviation = = 0.9

Sample size = n = 120

Level of significance = = 0.02

Step - 1

This is a left (One) tailed test,

The null and alternative hypothesis is,  

Ho: 4.9

Ha: 4.9

Step - 2

The test statistics,

Z =( - )/ (/n)

= ( 4.7 - 4.9 ) / ( 0.9 / 120 )

= -2.43

Step - 3

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

= 2 * P(Z < -2.43 )

= 2 * 0.0075

= 0.0150

Step - 4

The p-value is p = 0.0150 , and since p = 0.0150 < 0.02, it is concluded that the null hypothesis is rejected.