Answer to Question #277125 in Statistics and Probability for NRL

Question

Researchers want to investigate whether frequent use of acetaminophen-based painkillers can lead to resistance. 500 men and women between the ages of 20 and 50 will be recruited as participants who have frequent headaches. Regardless of gender, it is randomly divided into two groups. One group consistently takes painkillers daily and the other only once a week. Each group has been on painkillers for two years, but they don’t know what cycle each other takes. At the end of the study, researchers count the number of people in each group who are drug resistant and no longer effective.

1) What are the hypotheses?

2) What hypothesis test would you be doing?

3) What would you set the significance level at?

4) What would it mean if you reject the null hypothesis? What would it mean if you fail to reject it?

Answer 1

1)

$H_0:p_1=p_2$ , in two groups proportions of people who are drug resistant are equal

$H_a:p_1> p_2$ , in daily drug using group proportion of people who are drug resistant is more than this proportion in weekly drug using group

2)

Test for Two-Sample Proportions:

$z=\frac{p_1-p_2}{\sqrt{p(1-p)(1/n_1+1/n_2)}}$

$p=\frac{x_1+x_2}{p_1+p_2}$

3)

The significance level $\alpha$ is the probability of rejecting the null hypothesis when it is true.

We can set the significance level at $\alpha=0.05=5\%$

4)

Rejecting the null hypothesis means that frequent use of acetaminophen-based painkillers can lead to drug resistance.

Failing to reject the null hypothesis means that frequent use of acetaminophen-based painkillers cannot lead to drug resistance.