Just before a city referendum on a school budget, a local newspaper polls 480 vo

Question

Just before a city referendum on a school budget, a local newspaper polls 480 voters in an attempt to predict whether the budget will pass. Suppose that, unknown to everyone, the budget actually has the support of 53% of the voters.

Question. What is the probability the newspaper's sample will lead the newspaper to predict defeat of the referendum, that is, what is the probability that the newspaper's sample results in a sample proportion p less than 0.50 in favor of the referendum? (calculate the standard deviation of p to 4 decimal places, round your final answer to 4 decimal places).

Explanation / Answer

here p=0.53 and n=480

therefore std error =(p(1-p)/n)1/2 =0.0228

hence  probability the newspaper's sample will lead the newspaper to predict defeat of the referendum

=P(phat<0.5)=P(Z<(0.5-0.53)/0.0228)=P(Z<-1.3169)=0.0939

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