Arecent poll of 500 residents in a large town found that only​ 36% were in favor of a proposed referendum to build a new high school. find the margin of error for this poll if we want​ 95% confidence in our estimate of the percentage of residents in favor of this proposed referendum.

The margin of error is 0.0421 = 4.21 percentage points

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.

In which

z is the zscore that has a pvalue of .

The margin of error is:

95% confidence level

So , z is the value of Z that has a pvalue of , so .

In this problem, we have that:

So

The margin of error is 0.0421 = 4.21 percentage points