A recent survey suggests that Americans anticipate a reduction in living standar
ID: 1886610 • Letter: A
Question
A recent survey suggests that Americans anticipate a reduction in living standards and that a steadily increasing level of consumption no longer may be as important as it was in the past. Suppose that a poll of 2000 people indicated 1373 in favor of forcing a reduction in the size of American automobiles by legislative means. Would you expect to observe as many as 1373 in favor of this proposition if, in fact, the general public was split 50-50 on the issue? Why?Explanation / Answer
if p=1/2, the distribution is binomial and has mean p and variance pq/n=1/2*1/2*1/2000=1/8000 we can use normal approximation to binomial without correction P(X>1373/2000)=P(Z>(1373/2000-1/2)/sqrt(1/8000))=P(Z>16) which is less than .0001 So the p value is very small. We therefore conclude that we do not expect to obtain 1373 votes in favor.