Problem
An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 120 engines and the mean pressure was 4.5 $\mathrm{lbs} / \mathrm{square}$ inch. Assume the variance is known to be 0.81 . If the valve was designed to produce a mean pressure of $4.3 \mathrm{lbs} / \mathrm{square}$ 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. Answer \[ H_{0}: \] Keyboard Shortcuts
Solution
Step 1 ：State the null and alternative hypotheses for the above scenario.
Step 2 ：The null hypothesis, $H_{0}$, is that the mean pressure the valve produces is equal to the designed pressure, i.e., $\mu = 4.3$ lbs/square inch.
Step 3 ：The alternative hypothesis, $H_{1}$, is that the mean pressure the valve produces is greater than the designed pressure, i.e., $\mu > 4.3$ lbs/square inch.
