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 5.8 lbs/square inch. Assume the variance is known to be 0.36. If the valve was designed to produce a mean pressure of 5.9 lbs/square inch, is there sufficient evidence at the 0.01 level that the valve does not perform to the specifications? State the null and alternative hypotheses for the above scenario.

Answer 1

H0: = 5.9

Ha: 5.9

Test statistics

z = ( - ) / sqrt [ / n ]

= (5.8 - 5.9) / sqrt ( 0.36 / 290)

= -2.84

This is test statistics value.

Critical values at 0.01 level = -2.576 , 2.576

Since test statistics falls in rejection region, reject H0.

We conclude at 0.01 level that we have sufficient evidence to support the claim that the valve does

not perform to the specifications.