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In a survey, 52% of the respondents said that they prefer sports drink X and 48%...

In a survey, 52% of the respondents said that they prefer sports drink X and 48% said they prefer sports drink Y. How many people would have to be surveyed for you to be confident that sports drink X is truly preferred by more than half the population?

Math   Statistics-And-Probability   
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Answer #1

Proportion of people who prefer sports drink X, p = 0.52

To be confident that X is truly preferred, the margin of error must be less than 0.52-0.50 = 0.02

Margin of Error, E = Z*

We assume 95% confidence level. Therefore, Z* = 1.96

0.02 = 1.96 x

= 48.96

n = 2398 (rounded up)

Number of people to be surveyed for you to be confident that sports drink X is truly preferred by more than half the population = 2398

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