\"What do you think is the ideal number of children for a family to have?\" A po

Question

"What do you think is the ideal number of children for a family to have?" A poll asked this question of 1030 randomly chosen adults. Slightly less than half (48%) thought that a total of two children was ideal. Suppose that

p = 0.48

is exactly true for the population of all adults. The polling company announced a margin of error of

±4 percentage

points for this poll. What is the probability that the sample proportion p for an SRS of size

n = 1030

falls between 0.44 and 0.52? You see that it is likely, but not certain, that polls like this give results that are correct within their margin of error. (Round your answer to four decimal places.)

Explanation / Answer

Ans:

sampling distribution of sample proportions:

mean=p=0.48

standard deviation=sqrt(0.48*(1-0.48)/1030)=0.0156

z(0.44)=(0.44-0.48)/0.0156=-2.56

z(0.52)=(0.52-0.48)/0.0156=2.56

P(-2.56<z<2.56)=P(z<2.56)-P(z<-2.56)

=0.9948-0.0052=0.9896

(it is high probability,so it is likely to be within 4%,but not certain)

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