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 6.9 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 13 engines and the mean pressure was 7.1 pounds/square inch with a variance of 0.49. A level of significance of 0.1 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

Step-by-step explanation:

Calculate the t-value using the sample mean, population mean, sample variance, and sample size.

Find the critical t-value from the t-distribution table or software for the given level of significance (α) and degrees of freedom (n - 1).

Compare the calculated t-value with the critical t-value.

If the calculated t-value is greater than the critical t-value, reject the null hypothesis.

If the calculated t-value is less than or equal to the critical t-value, fail to reject the null hypothesis.

In this case, with a level of significance (α) of 0.1 and 12 degrees of freedom, the critical t-value is approximately 1.356 (rounded to three decimal places). Compare the calculated t-value with this critical value to make the decision.