A pilot study of a new antihypertensive agent is performed for the purpose of planning a larger study. Five patients who have a mean DBP of at least 95 mm Hg are recruited for the study and are kept on the agent for 1 month. After 1 month the observed mean decline in DBP in these five patients is 4.8 mm Hg with a standard deviation of 9 mm Hg. 1. (17 points) If pa = true mean difference in DBP between baseline and 1 month, then how many patients would be needed to have a 90% chance of detecting a significant change in DBP over 1 month using a two-tailed test with a significance level of 5%? Assume that the true mean and standard deviation of the DBP difference were the same as observed in the pilot study. 2. (11 points) Suppose we conduct a study of the preceding hypothesis based on 20 participants. What is the probability we will be able to reject Ho using a two-sided test at the 5% level if the true mean and standard deviation of the DBP difference are the same as in the pilot study