Let be the proportion of US households that own a high definition television. James is conducting the hypothesis test:H0:= 0.5Ha: <0.5 and he decides that he will reject H0 if p-hat, the observed sample proportion, is less than 0.4(otherwise he will fail to reject H0). 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 sampleX1,...,X80from Bern(= 0.4).