It is believed that women are much more likely to support strong gun control law

Question

It is believed that women are much more likely to support strong gun control laws than are men. As a matter of fact, a recent study concluded that women are more than 20% more likely to do so. To test this locally, you randomly select 75 women and 125 men to ascertain their support of gun control. You find that 50 of the women and 44 of the men support strong gun control laws. At the 0.05 level of significance, do the local data appear to be consistent with the recently-pub- lished national study?

Explanation / Answer

let mean proportion o fwomen =p1

and that of men =p2

here null hypothesis: p1- p2=0.20

alternate hypothesis:: p1>p2

from above data phat1 =50/75 =0.6667

and phat2 =44/125 =0.352

there fore std error =(phat1(1-phat1)/n1 +phat2(1-phat2)/n2 )1/2 =0.069

hence zstat =(p1hat-p2hat)/std error =4.5476

for which p value =0.0000

as p value is less then 0.05 level, we have sufficient evidence that  women are more than 20% more likely to support strong gun control laws than are men

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