Let be the proportion of US households that own a high definition television. James is conducting the hypothesis test:

H0: = 0.5

Ha: <0.5

and he decides that he will reject H0 if p^ the observed sample proportion, is less than 0.4(otherwise he will fail to rejectH0). Notice that he is ignoring the sample size.

(a) Compute the approximate probability of a Type I error of James' testing method if he were to conduct it with a random sample X1,...,X80 from Bern(= 0.5).

(b) Compute the approximate probability of a Type II error of James' testing method if he were to conduct it with a random sample X1,...,X80 from Bern(= 0.4).