Suppose that .06 of each of two populations possess a given characteristic.Samples of size 400 are randomly drawn from each population.The probability that the difference between the first sample proportion which possess the given characteristic and the second sample proportion which possess the given characteristic being more than +.03 is _______.
A)0.4943
B)0.9943
C)0.0367
D)0.5057
E)0.5700

Question

Quizplus · Accepted Answer

The difference between two independent sample proportions follows a normal distribution with mean 0 and standard deviation sqrt[(p(1-p)/n1) + (p(1-p)/n2)]. Here, p = 0.06 and n1 = n2 = 400. The standard deviation is approximately 0.034. Using the normal distribution, the probability of the difference being more than +0.03 is approximately 0.0367.

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