Question

A sample survey interviews SRSs of $500$female college students and $550$male college students. Each student is asked whether he or she worked for pay last summer. In all,$410$of the women and $484$of the men say “Yes.” Take$p_M$and localid="1650271716184" $p_F$be the proportions of all college males and females who worked last summer. We conjectured before seeing the data that men are more likely to work. The hypotheses to be tested are

(a) $H_0:p_M-p_f=0$versus $H_a;p_M-p_F\ne 0$

(b) $H_0:p_M-p_F=0$versus$H_a:p_M-p_F>0$.

(c) $H_0:p_M-p_F=0$versus$H_a:p_M-p_F<0$

(d) $H_0:p_M-p_F>0$versus$H_a:p_M-p_F=0$

(e) $H_0:p_M-p_F\ne 0$versus$H_a:p_M-p_F=0$

Short answer

The tested hypothesis is option (b)$H_0:p_M-p_F=0,H_a:p_M-p_F>0.$

Step-by-step solution

Given information

Male proportions in the college$=p_M=484$

Female proportion in the college $=p_F$$=410$

To find the correct hypothesis.

Explanation

The equal sign is always used in the null hypothesis

$H_0:p_M-p_F=0$

The alternative hypothesis contradicts the null hypothesis (according to the claim)

$H_a:p_M-p_F>0$

Because of $p_M-p_F>0$

Then, $p_M>p_F$

So it is option (b)$H_0:p_M-p_F=0,H_a:p_M-p_F>0.$