In one state, 52% of the voters are Republicans, and 48% are Democrats. In a second...
In one state, 52% of the voters are Republicans, and 48% are Democrats. In a second state, 47% of the voters are Republicans, and 53% are Democrats. Suppose a simple random sample of 100 voters are surveyed from each state.
What is the probability that the survey will show a greater percentage of Republican voters in the second state than in the first state?
(A) 0.04
(B) 0.05
(C) 0.24
(D) 0.71
(E) 0.76
Homework Answers
p1cap = X1/N1 = 47/100 = 0.47
p1cap = X2/N2 = 52/100 = 0.52
pcap = (X1 + X2)/(N1 + N2) = (47+52)/(100+100) = 0.495
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.47-0.52)/sqrt(0.495*(1-0.495)*(1/100 + 1/100))
z = -0.71
P(z > -0.71) = 0.7611
Option E
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