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 7.9 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 16 engines and the mean pressure was 8.2 pounds/square inch with a standard deviation of 0.5. A level of significance of 0.01 will be used. Assume the population distribution is approximately normal. Make the decision to reject or fail to reject the null hypothesis.

Answer 1

Solution :

Given that ,

= 7.9

= 8.2

= 0.5

n = 16

The null and alternative hypothesis is ,

H₀ :   = 7.9

H_a : > 7.9

This is the right tailed test .

Test statistic = z

= ( - ) / / n

= ( 8.2 - 7.9) / 0.5 / 16

= 2.4

The test statistic = 2.4

P - value = P(Z > 2.4 ) = 1- P (Z < 2.4 )

= 1 - 0.9918

= 0.0082

P-value = 0.0082

= 0.01

0.0082 < 0.01

P-value <

Reject the null hypothesis .