Question

a survey was given to a random sample of voters in the united states to ask about their preference for a presidential candidate. the survey reported a confidence interval that between 21% and 29% of the population preferred candidate a. what is the margin of error on the survey? do not write ± on the margin of error.

Explanation:

Step1: Find the mid - point

The mid - point of the confidence interval gives the sample proportion $\hat{p}$. The formula for the mid - point of an interval $[a,b]$ is $\hat{p}=\frac{a + b}{2}$, where $a = 21\%=0.21$ and $b = 29\%=0.29$. So, $\hat{p}=\frac{0.21 + 0.29}{2}=\frac{0.5}{2}=0.25$.

Step2: Calculate margin of error

The margin of error $E$ is the difference between the upper limit of the confidence interval and the sample proportion (or the sample proportion and the lower limit). Using the upper limit, $E=b-\hat{p}$. Substituting $b = 0.29$ and $\hat{p}=0.25$, we get $E=0.29 - 0.25=0.04$ or $4\%$.

Answer:

$4\%$