Steroids in high school 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 in an attempt to improve athletic performance. Researchers want to know if there is a difference in the proportion of all Illinois high school freshmen and seniors who have used anabolic steroids.

a. State appropriate hypotheses for performing a significance test. Be sure to define the parameters of interest.

b. Check if the conditions for performing the test are met.

It is given that researchers want to know if there is difference in proportion of all Illinois high school and seniors using steroids or not.

$x_1=34$

$x_2=24$

$n_1=1679$

$n_2=1366$

Claim is difference between the proportions.

Appropriate hypothesis are:

Null: $H_0:p_1=p_2$

Alternative hypothesis: $H_a:p_1\ne p_2$

$p_1$isrole="math" localid="1654706370645" $\text{proportionfreshmen in Illinois that used anabolic steroids.}$

$p_2$is$\text{proportion ofseniors in Illinois that used anabolic steroids.}$

Conditions are:

Random: Samples are independent random samples from separate populations.

Independent: $1679<10\%$of high school freshmen and $1366<10\%$of high school seniors.

Normal: There are $34$success and $1679-34=1645$failures in first sample and $24$success and $1366-24=1342$failures in second sample, all are less than ten.

All conditions are satisfied, we can use hypothesis test.