Question

A random sample of 100 voters is taken to estimate the proportion of a state's electorate in favor of increasing the gasoline tax to provide additional revenue for highway repairs. Suppose that it is decided that a sample of 100 voters is too small to provide a sufficiently reliable estimate of the population proportion. It is required instead that the probability that the sample proportion differs from the population proportion (whatever its value) by more than 0.06 should not exceed 0.05. How large a sample is needed to guarantee that this requirement is met?

Please explain.

Answer 1

Given:

Margin of error, E = 0.06

Significance level, = 0.05

Confidence level = (1-0.05) = 95%

Estimate for population proportion is not known, so we take = 0.5

Therefore the sample size needs to be at least 267.