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 $lbs / square$ inch. Assume the variance is known to be 0.81 . If the valve was designed to produce a mean pressure of $4.3 lbs / square$ 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.
Answer
$H_{0} :$
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The alternative hypothesis, $H_{1}$ , is that the mean pressure the valve produces is greater than the designed pressure, i.e., $μ > 4.3$ lbs/square inch.

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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., $μ = 4.3$ 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., $μ > 4.3$ lbs/square inch.

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