Final answer:
The null hypothesis is that the mean pressure is 7.3 lbs/square inch, while the alternative hypothesis is that it is greater than 7.3 lbs/square inch. To test at the 0.1 level, a one-sample Z-test is used, comparing the test statistic against the critical value.
Step-by-step explanation:
The student is asking about hypothesis testing in the context of a valve designed by an engineer to regulate water pressure in an automobile engine. The null hypothesis (H0) in this scenario would be that the mean pressure is equal to 7.3 lbs/square inch, as specified (H0: μ = 7.3 lbs/in²). The alternative hypothesis (Ha) is that the valve produces a mean pressure greater than 7.3 lbs/square inch (Ha: μ > 7.3 lbs/in²). To test the hypothesis at the 0.1 significance level, one would use a one-sample Z-test due to the known variance. Based on the mean pressure of 7.5 lbs/square inch observed during testing on 120 engines and the known variance of 0.81, the test statistic can be calculated and compared against the critical value corresponding to the 0.1 significance level to determine whether there is sufficient evidence to support the alternative hypothesis that the valve performs above specifications.