Question

According to the Center for Disease Control (CDC),76 million people in the US get diarrhea and upset stomachs each year. Most of these infections can be prevented by regularly washing one’s hands. A microbiologist believes that a majority (i.e. more than 50%) of women wash their hands after using the bathroom. She collects a sample of 40 women, calculates p, and performs a hypothesis test at alpha = 0.05.

(a) Give the hypotheses which the microbiologist wants to test.

(b) Describe a Type II error in terms of this problem.

Answer 1

a) Let P be the population proportion of women in the US who wash their hands after using the bathroom

The microbiologist wants to test the following hypothesis

Null Hypothesis:- P=0.5

Alternate Hypothesis:- P>0.5

b) Type II error is the probability of accepting the Null Hypothesis when the Alternate Hypothesis is true. In this problem, type II error is the probability that microbiologist fails to reject the null hypothesis ( accepting H0) when actually the proportion of women in the US who wash their hands after using the bathroom is more than 50%