Could you help me answer question (d). I'm not sure how to know how many people are needed for the survey.

4. A new post-surgical treatment is being compared with a standard treatment with respect to the recovery times (in days) after the procedures. nJlr subjects receive the new treatment, while u, others (the controls) receive the standard treatment. Assume we are going to design that n, = y. We have not yet collected the data but we want to make some power computations before going out and collecting the data. Suppose we are conducting a test at the 2% signicance level. (a) Write down the appropriate hypotheses assuming we are only testing whether the recovery times are different for treatment and control groups. (b) Suppose the difference between the two groups has to be at least 3 days for it to be considered signif- icant. Assume that the population standard deviation for the control group is 6 days and we assume that the variances of the two groups are the same. What is the effect size that we are considering in our problem? (c) Suppose we want a statistical power of 80%. What is the sample size we require. i.e., how many controls and treatment group people do we need to collect data from? (d) Suppose we start a sign-up sheet for the data collection but we know that 10% of the people who sign up will actually not turn up. How many people should we plan to sign up for the experiment knowing this attrition rate, so that we still have sufcient statistical power