Question

An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 4.2 pounds/square inch. The valve was tested on 150 engines and the mean pressure was 4.1 pounds/square inch. Assume the standard deviation is known to be 0.8. Is there evidence at the 0.05 level that the valve performs below the specifications? Enter the decision rule.

Answer 1

To determine if the valve performs below specifications, we can conduct a hypothesis test. Set up the null and alternative hypotheses, use a one-sample t-test, and find the critical t-value to make a decision.

Step-by-step explanation:

To determine if the valve performs below the specifications, we can conduct a hypothesis test. Let's set up the null and alternative hypotheses:

Null Hypothesis (H0): The mean pressure of the valve is equal to 4.2 pounds/square inch.

Alternative Hypothesis (Ha): The mean pressure of the valve is less than 4.2 pounds/square inch.

We can use a one-sample t-test since we know the standard deviation of the population. With a sample size of 150, the degree of freedom is 149. Using a significance level of 0.05, we find the critical t-value. If the calculated t-value is less than the critical t-value, we reject the null hypothesis and conclude that there is evidence the valve performs below the specifications.