[Step-by-Step] "What do you think is the ideal number of children for a family to have?" A Gallup Poll asked this question of 300 randomly chosen adults.
Question: "What do you think is the ideal number of children for a family to have?" A Gallup Poll asked this question of 300 randomly chosen adults. Almost half \((49 \%)\) thought two children was ideal. Suppose that \(p=0.49\) is exactly true for the population of all adults. Gallup announced a margin of error of \(\pm 3\) percentage points for this poll. What is the probability that the sample proportion \(\hat{p}\) falls between 0.46 and 0.52? What is the probability that the sample proportion \(\hat{p}\) falls between 0.46 and 0.52 if \(n=5000\) ?
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