4. Hypothesis testing (25%)

A population of patients with high cholesterol has a true cholesterol level mean mu = 250 milligrams per deciliter (mg/dL). A sample of 50 of those patients receive a new drug. After taking the drug, we find that the sample average cholesterol level is 240 mg/dL with a sample standard deviation of 10 mg/dL. Is the new drug effective to reduce the cholesterol level? Perform a one-sided t-test with a significance level of alpha = 5%.

Report clearly 1) the null and alternative hypothesis, 2) the test statistic, 3) the critical values / rejection region and your conclusion.