Question

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 240 engines and the mean pressure was 5.1 pounds/square inch (psi). Assume the population standard deviation is 1.0. If the valve was designed to produce a mean pressure of 5.2 psi, is there sufficient evidence at the 0.05 level that the valve performs below the specifications?

Step 1 of 6 :  

State the null and alternative hypotheses.

Answer 1

Solution :

=  5.1

=5.2

=1.0

n = 240

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :    =  5.1

Ha :      5.1

Test statistic = z

= ( - ) / / n

= (5.2- 5.1) / 1.0 / 240

= 1.55

Test statistic = z = 1.55

P(z > 1.55 ) = 1 - P(z < 1.55 ) = 1 -0.9383

P-value =2 *0.0617 =0.1234

= 0.05  

P-value <

0.1234 < 0.05

Reject the null hypothesis .

There is sufficient evidence to suggest that