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.

a. 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?

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