What do you think is the ideal number of children for a fami

\"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.

Solution

P(0.46<phat<0.52) = P((0.46-0.49)/sqrt(0.49*(1-0.49)/200)<Z<(0.52-0.49)/sqrt(0.49*(1-0.49)/200))

=P(-0.85<Z<0.85)

=0.6047 (from standard normal table)

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P(0.46<phat<0.52) = P((0.46-0.49)/sqrt(0.49*(1-0.49)/5000)<Z<(0.52-0.49)/sqrt(0.49*(1-0.49)/5000))

=P(-4.24<Z<4.24)

=1 (from standard normal table)

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Larger samples give a larger probability that phat will be close to the true proportion p