1. A team of researchers has developed a new drug to treat isolated systolic hypertension, also known as high blood pressure (systolic - top number). They want to know if this new drug lowers the systolic number. The known side effects of the new drug are headaches and nausea. To address their research question, they will take a random sample of patients with isolated systolic hypertension to administer the drug over a 90-day period. Each patient will be examined by an independent physician (i.e., not a member of the research team) before and after 90 days of using the new drug. The physician will measure the change in blood pressure during the 90 days. If no change is found, the researchers will lose their funding for any further research on the new drug.

A. State the null and alternative hypothesis that the researchers should test. Use to denote the difference in blood pressure computed as the beginning systolic pressure minus the ending systolic pressure for each patient.[10 points]

B. What does a Type I error mean in this situation? What are the consequences of making a Type I error here? [15 points]

C. What does a Type II error mean in this situation? What are the consequences of making a Type II error here? [15 points]

D. In this scenario, is a Type I or Type II error more serious? Or, are they equally serious?Explain your reasoning. [10 points]

E. If you were working with this research team, what alpha level would you use? Explain your reasoning. [10 points]

Assume the researchers complete the study with a sample size of n = 199 who take the new drug and finds the mean difference is 6.100 with a standard deviation of 25.802. The p-value was .001.

F. Using the alpha level you selected in part E, are their results statistically significant? Explain why or why not. [10 points]

G. Are their results practically significant? Compute Cohen's d value and explain why or why not. [10 points]

H. The 95% confidence interval for the differences in systolic blood pressure is [2.49, 9.71]. If the alpha for the test was .05, why would this interval confirm that the drug was effective in the sample? [10 points]

I. Using this scenario, compare and contrast confidence intervals and hypothesis testing. List at least one similarity and at least one difference. [10 points]