EXAMPLE 22 Sample size for estimating when is unknown

Suppose your state wants to take a poll on the proportion of its citizens who support a single statewide primary instead of primaries for each party. No poll on this subject has been taken before, so no prior information is available on the value of the sample proportion, . How large a sample size does the state need to estimate the proportion to within plus or minus 3 percentage points () with 95% confidence?

Solution

The 95% confidence implies that the value for is 1.96. Because no information is available about the value of the population proportion of all state citizens who support a single statewide primary, we use 0.5 as our most conservative value of :

So if the pollsters want to estimate the population proportion of all state citizens who support a single statewide primary to within 3% with 95% confidence, they will need a sample of 1068 voters (don't forget to round up!).