According to the Center for Disease Control, approximately 76 million people

get upset stomach each year. A microbiologist believes that a majority (that

is, more than 50%) of females wash their hands after using the bathroom. This

microbiologist collected a sample of 40 females, and calculates the corresponding

sample proportion of those that regularly wash their hands after visiting the

bathroom and performs a hypothesis test at = :05.

(b) Assuming the value of the true proportion of females that regularly

wash their hands when H0 is assumed true is p0 = :5, while if it is

given that H0 is false, then the true value of this true proportion is pa = :7.

Sketch graphs of the sampling distributions of ^p and clearly indicate the

regions corresponding to (the prob. of a type I error) and (the prob.

of a type II error).

(c) Suppose that the true proportion of females that regularly wash

their hands is pa = :7 and that H0 will be rejected at the level = :05.

For this hypotheses, compute , the probability of a type II error.