To assess if the valve performs above specifications, the null hypothesis states the mean pressure is 4.1 lbs/square inch, while the alternative hypothesis suggests it's higher. A one-sample z-test at a 0.1 significance level is used to compare the sample mean of 4.2 lbs/square inch against the design specification.
To determine if there is sufficient evidence that the valve performs above the specifications, we conduct a hypothesis test. The null hypothesis (H0) is that the valve does not perform above the specified mean pressure of 4.1 lbs/square inch, i.e., H0: μ = 4.1 lbs/square inch.
The alternative hypothesis (H1) is that the valve does perform above the specification, i.e., H1: μ > 4.1 lbs/square inch.
Given a sample mean of 4.2 lbs/square inch and a known standard deviation of 0.6 with a sample size of 170 engines, we would perform a one-sample z-test since the standard deviation is known. The evidence level chosen, also known as the alpha level, is 0.1, meaning we are testing at the 10% significance level.
If the calculated p-value from the z-test is less than 0.1, we reject the null hypothesis in favor of the alternative, concluding that there is sufficient evidence the valve regulates the pressure above the designed specifications. However, if the p-value is larger than 0.1, we do not reject the null hypothesis, which means there is not sufficient evidence to claim the valve performs above the set mean pressure.