Question

an engineer has designed a valve that will regulate water pressure on an automobile engine. the valve was tested on 200 engines and the mean pressure was 4.5 lbs/square inch. assume the standard deviation is known to be 0.7. if the valve was designed to produce a mean pressure of 4.4 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.

Explanation:

Step1: Define null hypothesis

The null hypothesis $H_0$ is that the valve performs to specifications, i.e., the population mean $\mu$ is equal to the designed - mean.
$H_0:\mu = 4.4$

Step2: Define alternative hypothesis

The alternative hypothesis $H_a$ is that the valve does not perform to specifications. Since we are not given a direction (greater - than or less - than), it is a two - tailed test.
$H_a:\mu
eq4.4$

Answer:

$H_0:\mu = 4.4$
$H_a:\mu
eq4.4$