Question

2. What is meant by the margin of error of 3.5 percentage points?

Answer 1

Answer:

On this case a margin of error of $\pm 3.5 \%$ means that the true population proportion is 3.5% above or below the estimated proportion calculated from the sample. And this value helps in order to find the limits for a confidence interval with a confidence given.  

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

The margin of error for the proportion interval is given by this formula:  

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$    (a)  

On this case a margin of error of $\pm 3.5 \%$ means that the true population proportion is 3.5% above or below the estimated proportion calculated from the sample. And this value helps in order to find the limits for a confidence interval with a confidence given.