4. The body weight for the population of male diabetics between the ages of 30 and 34 follows a normal distribution with an unknown mean ,u and stande deviation 0 = 9.2 kg. It may be useful to know whether the mean of this population is equal to 74 kg, the mean body weight of the general population of males in this age group. {a} What are the appropriate null and alternative hypotheses for the issue. {b} If a sample of 10 diabetic men is selected to test the hypotheses aboye at signif icance level a = .05, what is the appropriate test? Print your test statistics and report your test rejection region. (c) What is the power of the test in (b) if the true mean body weight for this popula tion of diabetic men is 80 kg? Explain the meaning of the power that you obtained in the context of this study. (d) How large a sample size do we need for the test above to have a 80% power to detecting a true mean body weight of 80 kg? (e) A sample of 10 diabetic men is selected and their body weight in kg are 69.6 86.1 86.0 76.4 82.8 76.8 87.2 74.8 57.8 88.1 Conduct a statistical test in {b} and report your conclusion