To determine the decision rule for rejecting the null hypothesis, we calculate the critical value for the hypothesis test using the z-test.
To determine the decision rule for rejecting the null hypothesis, we need to calculate the critical value for the hypothesis test. In this case, we are comparing the mean pressure of the tested valve to the designed mean pressure.
Since the population distribution is approximately normal and the sample size is large (n = 24), we can use the z-test. The critical value for a one-tailed test at a significance level of 0.1 is found by calculating the z-score corresponding to a cumulative probability of 0.9. Using a standard normal distribution table or calculator, we find that the z-score is approximately 1.282.
Therefore, the decision rule for rejecting the null hypothesis is to reject it if the sample mean pressure is greater than 7.9 + 1.282 * (standard deviation of the sample mean pressure).
The probable question may be:
an engineer designed a valve that will regulate water pressure on an automobile. the engineer designed the valve such that it would produce a mean pressure of 7.9 lb / square inch. it is believed that the valve performs above the specifications. the valve was tested on 24 engines and the mean pressure was 8.1 lb / square inch with a variance of 0.25. 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