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 7.7 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 24 engines and the mean pressure was 7.9 pounds/square inch with a variance of 0.49. A level of significance of 0.025 will be used. Assume the population distribution is approximately normal. Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places. ​

Answer 1

The decision rule for rejecting the null hypothesis is to reject it if the test statistic (calculated t-value) is greater than 2.069 or less than -2.069.

To determine the decision rule for rejecting the null hypothesis, we need to calculate the critical value for a level of significance of 0.025.

Since we are testing the mean pressure of the valve, we will use a one-sample t-test.

Using a t-distribution table, the critical value for a level of significance of 0.025 with 23 degrees of freedom (24 - 1) is approximately 2.069.

Therefore, the decision rule is to reject the null hypothesis if the test statistic (calculated t-value) is greater than 2.069 or less than -2.069.