Question

an engineer has designed a valve that will regulate water pressure on an automobile engine. the valve was tested on 130 engines and the mean pressure was 4.9 lbs/square inch. assume the standard deviation is known to be 0.9. if the valve was designed to produce a mean pressure of 4.7 lbs/square inch, is there sufficient evidence at the 0.1 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 that the valve performs at or below the specifications. So, $H_0:\mu\leq4.7$

Step2: Define alternative hypothesis

The alternative hypothesis ($H_a$) is that the valve performs above the specifications. So, $H_a:\mu > 4.7$

Answer:

$H_0:\mu\leq4.7$
$H_a:\mu > 4.7$