Only answer Question 2, answers for 1 are provided

Question 1. You decide to carry out a trial on 12 goats to collect coefficients of digestibility of dry matter. Suppose you know thats=3 and that you would be able to consider that as known in a subsequent study (admitted not too likely in "real life"). You wish to test H_o:m = 54 versus H₁:m 54; (i.e. 54 being, say, the known mean parameter for sheep but you didn't know whether the mean for goats would be larger or smaller and so are interested in testing this) Before approving your research protocol, the Animal Use and Care Committee wishes to know if you have sufficient power of test to make sure you don't unnecessarily inconvenience 12 goats.

1. If you suspect the true mean digestibility for goats is in the neighborhood of 57, how much power of test did you have fora = 0.05? Should you proceed with the trial as planned then? = 0.9337

b. To assure a statistical power no less than 90%, how many goats should you have in your trial? = 10.49 = 11

Question 2. Refer to Question 1 of the previous homework; i.e., you are thinking about conducting such an experiment yourself.

1. What would be the power of the hypothesis test conducted in part b) of that question if the true mean calcium intake for individuals below the poverty level is 700 mg.

1. How large of a sample size should be considered for the hypothesis test in part b) of that question in the previous homework if the desired power was 90% and the true mean calcium intake for individuals below the poverty level is 700 mg.

1. Suppose that you wouldn't be able to assume that the variance as known in a subsequent experiment. Demonstrate how this changes, if at all, your answers to part a) and b) above.