Question

The following are the results of a study on exposure to a particulate and the larynx cancer in roughly 2000 people that lived in a certain city.

Disease outcome

Exposure	No cancer	Larynx cancer
Low	350	680
High	320	780

The analyst would like to run a test to see if the proportion of people that had cancer was higher for the high exposure group than the low exposure group. Use a=0.05.

1. Give the null and alternative hypothesis in this situation

2. Should the z-test be used here? Justify your answer

3. Test the hypothesis that you created in part A

4. Draw conclusions to the real-world

Answer 1

= proportion of people who had cancer in the high exposure group, = proportion of people who had cancer in the low exposure group.

(B) Yes, the z-test should be used here, because we are comparing two population proportions here and the sample sizes are much greater than 30. If it was not, then we would have used a t-test.

(D) We conclude that there is enough evidence to suggest that the proportion of people that had cancer was higher for the high exposure group than the low exposure group.