A manufacturer has developed a new fishing line, which he claims has a mean breaking strength of 15 kilograms with a standard deviation of 0.5 kilogram. To test the hypothesis that, p = 15 kilograms against the alternative that p < 15 kilograms, a random sample of 50 lines will be tested. The critical region is defined to be x < 14.9.

(a) Find the probability of committing a type I error when Ha is true.

(b) Evaluate 8 for the alternatives p — 14.8 and p = 14.9 kilograms.