Question

A study by the National Athletic Trainers Association surveyed random samples of $1679$high school freshmen and $1366$high school seniors in Illinois. Results showed that $34$of the freshmen and $24$ of the seniors had used anabolic steroids. Steroids, which are dangerous, are sometimes used to improve athletic performance. Is there a significant difference between the population proportions? State appropriate hypotheses for a significance test to answer this question. Define any parameters you use.

Short answer

$H_0:p_1-p_2=0$

$H_a:p_1-p_2\ne 0$

Step-by-step solution

Given Information

Given

$x_1=34$

$n_1=1679$

$x_1=24$

$n_2=1366$

Explanation

The null hypothesis states that the population proportions are equal or that their difference is zero:

$H_0:p_1-p_2=0$

The alternative hypothesis states the opposite of the null hypothesis (according to the claim):

$H_a:p_1-p_2\ne 0$

$p_1$is the population proportion of freshmen that used anabolic steroids.

$p_2$is the population proportion of seniors that used anabolic steroids.