Question

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 280 engines and the mean pressure was 5.2 pounds/square inch (psi). Assume the population standard deviation is 0.8. If the valve was designed to produce a mean pressure of 5.3 psi, is there sufficient evidence at the 0.01 level that the valve performs below the specifications? Step 2 of 6 : Find the value of the test statistic. Round your answer to two decimal places.

Answer 1

Solution :

Given that,

Population mean = = 5.3

Sample mean = = 5.2

Population standard deviation = = 0.8

Sample size = n = 280

Level of significance = = 0.01

This is a two tailed test.

The null and alternative hypothesis is,

Ho: 5.3

Ha: 5.3

The test statistics,

Z =( - )/ (/n)

= ( 5.2 - 5.3 ) / ( 0.8 / 280 )

= -2.09

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

= 2 * P(Z < -2.09 )

= 0.0366

The p-value is p = 0.0366, and since p = 0.0366 > 0.01, it is concluded that the null hypothesis is fail to reject.