A scientist performs a one tailed t test at 5% significance to distinguish between healthy mice with a mean Protein Y concentration of 21 and sick mice with a mean Protein Y concentration of 13.59 and a standard deviation in both distributions of 5.1.

(a) What number of mice would she need to test in each sample to get a power of 0.9?

(b) Write code to perform 2000 experiments in which that sample size of mice are generated from each distribution and the test performed.

(c) Comment on how many of the tests are significant at a 5% significance and how this compares to what you expect.