A) Here we use the z test for two proportions
A) Here we use the z test for two proportions.
The null hypothesis is Ho: p1 = p2
The alternative hypotheisis is H1: p1 ≠ p2
B) The test statistic is given by,
[pic] , where [pic]
Here, n1 = 800, n2 = 600, x1 = 440, x2 = 360.
Thus, p1^ = 440/800 = 0.55, p2^ = 360/600 = 0.6 and
p^ = (440+360)/(800+600) = 0.5714
Therefore,
z = (0.55 – 0.6)/Sqrt[0.5714*(1-0.5714)(1/800 + 1/600)] = -1.8708
The p-value of the test is given by,
p-value = P[|Z| > 1.8708] = P[Z < -1.8708] + P[Z > 1.8708]
= 2*P[Z < -1.8708] = 2*0.0307 = 0.0614
C) At a 5% level of significance, the critical values are -1.96 and 1.96.
That is we reject Ho if either z < -1.96 or z > 1.96.
Here z = -1.8708 lies between -1.96 and 1.96. So we fail to reject Ho.
(Since the p-value = 0.0614 > 0.05, we fail to reject the null hypothesis Ho.)
Thus we can conclude that the voters favor the Democratic candidate equally in both states.
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