Question

Some states allow voters to pass laws through ballot initiatives. In most states that allow ballot initiatives, a simple majority is all that’s needed. Before backing a ballot initiative, a political organization wants to know whether the majority of a state’s voters would be in favor of it. The organization wants to know what size random sample is required to estimate the percentage of voters who favor the initiative with different margins of error. Find the sample size needed to estimate support for the initiative with 5, 3, 1, and 0 percent margins of error. If any of these sample sizes can’t be calculated, explain why.

Answer 1

We can assume the sample proportion of state’s voters who would be in favor to be 0.5 This will provides the conservative estimate of the sample size (largest sample size) to achieve the give margin of error at a confidence level.

We cannot calculate these sample sizes as the confidence level to achieve the margin of errors is not given.

Let us assume 95% confidence level. Z score for 95% confidence level is 1.96

Sample size n =

For Margin of error E = 5% = 0.05

Sample size n =

For Margin of error E = 3% = 0.03

Sample size n =

For Margin of error E = 1% = 0.01

Sample size n =

For Margin of error E = 0% = 0.00

Sample size n =

Thus for 0 percent margins of error, we cannot calculate the sample size for any given confidence level. The sample will contain almost entire population.