Question

an engineer has designed a valve that will regulate water pressure on an automobile engine. the valve was tested on 110 engines and the mean pressure was 7.1 lbs/square inch. assume the variance is known to be 0.81. if the valve was designed to produce a mean pressure of 7.3 lbs/square inch, is there sufficient evidence at the 0.02 level that the valve performs below the specifications? state the null and alternative hypotheses for the above scenario.

Explanation:

Step1: Define null hypothesis

The null hypothesis $H_0$ is usually a statement of no - effect or equality. Here, it is that the mean pressure $\mu$ is equal to the designed mean pressure.
$H_0:\mu = 7.3$

Step2: Define alternative hypothesis

We want to test if the valve performs below the specifications. So the alternative hypothesis $H_a$ is that the mean pressure $\mu$ is less than the designed mean pressure.
$H_a:\mu<7.3$

Answer:

$H_0:\mu = 7.3$
$H_a:\mu<7.3$