Recall the Cholesterol Example from class where we were interested in the mean serum cholesterol level for the hypertensive male smokers sub-population (). We obtained a random sample of 36 hypertensive male smokers, calculated the sample mean (x), and assumed the standard deviation of this sub population was known to be= 46 mg/100 ml. The following were the hypotheses of interest.

H₀:= 211

H_A: = 211

Previously, our decision rule was to reject the null hypothesis if x <196 or x >226. This decision rule was obtained such that our Type I error was= 0.05. This_{means that under the null hypothesis distribution ofXn},/2 of the probability was to the left of 196 and/2 of the probability was to the right of 226. Using this decision rule, the Type I error rate was approximately 5% and the Type II error rate was 81.8%.

Suppose having a 5% probability of committing a Type I error is too high for you and, instead, you prefer to conduct your hypothesis tests at a Type I error rate of 1% ( = 0.01). What would the decision rule to reject the null hypothesis be for hypothesis tests conducted at a Type I error rate of 1%?