Question

A market research firm is interested in determining the proportion of households that are watching a particular

sporting event. To accomplish this task, it plans on using a telephone poll of randomly chosen households.

What is the smallest number of households to be included into a sample if the firm wants to be 97.5 % certain

that its proportion estimate is correct to within ±1.5%? Explain your answer.

Answer 1

Let p be the proportion of households that are watching a

particular sporting event.

97.5% Confidence Interval of p is,

[, ].

Given that, = 2 * 0.015

i.e. = 0.0067 i.e. = / 0.0067

Now is minimum when = 0.5.

Thus, the minimum value of n = 75. (Ans).