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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: $H_a:p_1鈮�p_2$

$p_1$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.