An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 280 engines and the mean pressure was 6.6 $\mathrm{lbs} / \mathrm{square}$ inch. Assume the standard deviation is known to be 1 . If the valve was designed to produce a mean pressure of $6.5 \mathrm{lbs} / \mathrm{square}$ inch, is there sufficient evidence at the 0.05 level that the valve does not perform to the specifications?
State the null and alternative hypotheses for the above scenario.
Answer

Step 1 ：State the null and alternative hypotheses for the above scenario.

Step 2 ：The null hypothesis (H0) is the statement that we want to test. In this case, the null hypothesis is that the mean pressure produced by the valve is 6.5 lbs/square inch, which is the designed specification.

Step 3 ：The alternative hypothesis (H1) is the statement that we will accept if the null hypothesis is rejected. In this case, the alternative hypothesis is that the mean pressure produced by the valve is not 6.5 lbs/square inch, which means the valve does not perform to the specifications.

Step 4 ：Final Answer: The null hypothesis, H0: μ = 6.5

Step 5 ：The alternative hypothesis, H1: μ ≠ 6.5