A veterinarian collects data on the number of times race horses are raced during their career. The researcher finds the average number of races a horse enters is x = 15.3 with a standard deviation of s = 6.8 in a sample of n = 20 horses.

(a) A 95% confidence for , the average number of times a horses races is what?

(b) A rival researcher claims that the true population mean, , is 22. Preform a hypothesis test to test this claim.