an engineer has designed a valve that will regulate water pressure on an automobile engine. the valve was…

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.

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.

Answer

Explanation:

Step1: Define null hypothesis

The null hypothesis ($H_0$) is a statement of no - effect or no - difference. Here, it assumes the valve performs at or above the specifications. So, $H_0:\mu\geq4.9$.

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:

$H_0:\mu\geq4.9$ $H_a:\mu < 4.9$