In a recent poll 35% of survey respondents said that if they only had one child,

Question

In a recent poll 35% of survey respondents said that if they only had one child, they would prefer the child to be a boy. Suppose you conducted a survey of 160 randomly selected students on your campus and find that74 of them prefer a boy. (a) Use the normal approximation to the binomial to approximate the probability that in a random sample of 160 students at least 74 would prefer a boy assuming the true percentage is 35%. (b) Does this result contradict the poll? Explain (a) The probability that at least 74 students would prefer a boy is (Round to four decimal places as needed)

Explanation / Answer

True proportion, p = 0.35

Population standard deviation, d = (p*(1-p))0.5 = (0.35*0.65)0.5 = 0.477

Sample proportion, p' = 74/160 = 0.463

(a)

z -score for the test conducted = 0.463/0.477 = 0.97

Using z-table, we find that:

P(z <= 0.97) = 0.833

So, required probability = P( z >= 0.97) = 1 - P(z <= 0.97) = 0.167

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