Question

an engineer has designed a valve that will regulate water pressure on an automobile engine. the valve was tested on 120 engines and the mean pressure was 5.8 lbs/square inch. assume the variance is known to be 0.64. if the valve was designed to produce a mean pressure of 5.6 lbs/square inch, is there sufficient evidence at the 0.01 level that the valve performs above the specifications? state the null and alternative hypotheses for the above scenario.

Explanation:

Step1: Define null hypothesis

The null hypothesis $H_0$ is a statement of no - effect or equality. Here, it is that the mean pressure $\mu$ is equal to the designed mean pressure.
$H_0:\mu = 5.6$

Step2: Define alternative hypothesis

The alternative hypothesis $H_a$ is what we are trying to find evidence for. Since we want to test if the valve performs above the specifications, it is a one - tailed test.
$H_a:\mu>5.6$

Answer:

$H_0:\mu = 5.6$
$H_a:\mu>5.6$