Question

An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 6.9 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 13 engines and the mean pressure was 7.1 pounds/square inch with a variance of 0.49. A level of significance of 0.1 will be used. Assume the population distribution is approximately normal. Is there sufficient evidence to support the claim that the valve performs above the specifications?

A. There is sufficient evidence to support the claim that the valve performs above the specifications.

B. There is not sufficient evidence to support the claim that the valve performs above the specifications.

Answer 1

Solution :

= 6.9

= 7.1

= 0.49

= 0.7

n = 13

This is the right tailed test .

The null and alternative hypothesis is ,

H0 :    = 6.9

Ha : >6.9

Test statistic = z

= ( - ) / / n

= (7.1- 6.9) / 0.7 / 13

= 1.03

Test statistic = z = 1.03

P(z > 1.03 ) = 1 - P(z < 1.03 ) = 1 - 0.8485

P-value =0.1515

= 0.10

P-value >

0.1515 > 0.10

Fail to reject the null hypothesis .

There is insufficient evidence to suggest that