Question

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 290 engines and the mean pressure was 6.1 pounds/square inch (psi). Assume the population variance is 0.36. If the valve was designed to produce a mean pressure of 6.0 psi, is there sufficient evidence at the 0.02 level that the valve performs above the specifications?

Identify the level of significance for the hypothesis test.

Answer 1

Solution :

= 6.0

= 6.1

= 0.36 = 0.60

n = 290

This is the right tailed test .

The null and alternative hypothesis is

H₀ :   = 6.0

H_a : > 6.0

Test statistic = z

= ( - ) / / n

= (6.1- 6.0) / 0.60 / 290

= 2.838

p(Z >2.838 ) = 1-P (Z < 2.838) = 0.0023

P-value = 0.0023

= 0.02

0.0023 < 0.02

Reject the null hypothesis .

There is sufficient evidence to suggest that