A recent post-presidential election survey in a state which voted for the Obama-

Question

A recent post-presidential election survey in a state which voted for the Obama-Biden ticket investigated the difference between men and women voters. A sample of 1000 women found that 580 voted for Obama-Biden, whereas a sample of 1000 men found that 520 voted for Obama-Biden. At a level of significance alpha = .01, can we say that the population proportion of women who voted for Obama-Biden is greater than that of men? (i. e. can the null hypothesis H_0: P_women = P_men be rejected in favor of the alternate hypothesis H_1: P_women > P_men wit a probability of error alpha of at most .01?)

Explanation / Answer

Proportion for women=580/1000=0.58

Proportion for men=520/1000=0.52

P=580+520/1000+1000=1100/2000=0.55

ZSTAT=(p1-p2)-(1 – 2)/p(1-p)(1/n1+1/n2)

         =(0.58-0.52)-0/0.55*0.45*(1/1000+1/1000)

         =0.06-0/0.022

         =2.6967

ZCRIT is 1.645

Since, 2.6967>1.645, reject the null hypothesis. We can conclude that women voted more in favour of Obama-Biden.

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