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 4.7 lbs/square inch. assume the standard deviation is known to be 0.8. if the valve was designed to produce a mean pressure of 4.9 lbs/square inch, is there sufficient evidence at the 0.05 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 a statement of no - effect or equality. Here, it is that the valve performs as per the specifications. So, $H_0:\mu = 4.9$.

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 below the specifications, $H_a:\mu<4.9$.

Answer:

$H_0:\mu = 4.9$
$H_a:\mu<4.9$