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Question

# Let's say the president of the United States wishes to estimate the percentage of the population that agrees with his present stance on changes to the healthcare system. The estimate must be within.04 of the actual proportion, according to the president. Count on a 95% level of certainty. The political advisers to the president located a comparable poll from two years prior that showed 60% of respondents were in favour of making changes to the health care system. Using this, find how large of a sample is required?

Solution

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The minimum sample size for estimating the population proportion is given by

$n=\pi(1-\pi)\cdot\left(\dfrac{z}{E}\right)^2,$

where $\pi$ is a reasonable estimate of the population proportion, the value of $z$ is found from the table of areas under the normal curve for the desired confidence level (or in the Student's $t$ distribution table for the desired confidence level in the row for infinite degrees of freedom), and $E$ is the desired margin of error.

The result is rounded up to a whole number.

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