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

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.

A microbiologist believes that a majority (i.e. more than 50%) of women wash their hands after using the bathroom.

I.e P= Proportion of women wash their hands after using the bathroom.

We want to test that the P is greater than 50%

Null Hypothesis:- Majority of women do not wash their hands after using the bathroom.

vs

Alternative Hypothesis:- Majority of women wash their hands after using the bathroom.

i.e

Ho:-P=0.50

vs

Ha:- P > 0.50

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

Type II error: - we do not reject Ho when it is false.

I.e Accept Ho when Ha is true.

We may conclude that the majority of women do not wash their hands after using the bathroom but actually the majority of women wash their hands after using the bathroom.