Question

An engineer has designed a valve that will regulate water pressure on automobile engine. The valve was tested on 180 engines and the mean pressure was 4.6 pounds/square inch (psi). Assume the population standard deviation is 0.5. If the valve was designed to produce a mean pressure of 4.5 psi, is there sufficient evidence at the 0.01 level of significance that the valve performs above the specifications?

Answer 1

Solution :

= 4.5

= 4.6

= 0.5

n = 180

This is the right tailed test .

The null and alternative hypothesis is

H0 :   = 4.5

Ha : > 4.5

Test statistic = z

= ( - ) / / n

= (4.6 - 4.5) / 0.5 / 180

= 2.683

p(Z >2.683 ) = 1-P (Z <2.683 ) = 0.0036

P-value = 0.0036

= 0.01

0.0036 < 0.01

Reject the null hypothesis .

There is sufficient evidence to suggest that