Checking for survey errors. One way of checking the effect of undercoverage, non

Question

Checking for survey errors. One way of checking the effect of undercoverage, nonresponse, and other sources of error in a sample survey is to compare the sample with known facts about the population. About 24% of the Canadian population over 15 years of age are first-generation; that is, they were horn outside Canada. The number X of first-generation Canadians in random samples of 1000 persons over 15 should therefore vary with the binomial (n = 1000, p = 0.24) distribution. What are the mean and standard deviation of X? Use the Normal approximation to find the probability that the sample will contain between 210 and 270 first-generation Canadians. Be sure to check that you can safely use the approximation.

Explanation / Answer

n=1000 and p = 0.24
Mean of binomial = np = 240
Variance =npq = 240(0.76)
std dev = 13.51
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X is N(240, 13.51)
P(210<x<270) =
P(|z|<30/13.51)
= P(|z|<2.22)
= 0.4868(2)
= 0.9936

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