\"What do you think is the ideal number of children for a family to have?\" A Ga
ID: 3207966 • Letter: #
Question
"What do you think is the ideal number of children for a family to have?" A Gallup Poll asked this question of 1016 randomly chosen adults. Almost half (49%) thought two children was ideal.† We are supposing that the proportion of all adults who think that two children is ideal is p = 0.49.
(a) What is the probability that a sample proportion p falls between 0.46 and 0.52 (that is, within ±3 percentage points of the true p) if the sample is an SRS of size n = 300? (Round your answer to four decimal places.)
(b) What is the probability that a sample proportion p falls between 0.46 and 0.52 if the sample is an SRS of size n = 5000? (Round your answer to four decimal places.)
Combine these results to make a general statement about the effect of larger samples in a sample survey.
___ Larger samples give a smaller probability that p will be close to the true proportion p.
___ Larger samples give a larger probability that p will be close to the true proportion p.
___ Larger samples have no effect on the probability that p will be close to the true proportion p.
Explanation / Answer
a. P(0.46<x<0.52)=P(0.46-0.49/sqrt(p(1-p)/n)<z<0.52-0.49/sqrt(p(1-p)/n))=P(-1.04<z<1.04)=0.7017
b. P(0.46<x<0.52) for n=5000, P(-4.2<z<4.2)=1
___ Larger samples give a larger probability that p will be close to the true proportion p.
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