Answer:
B) The margin of error becomes smaller
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The width of the confidence interval is given by:
[tex]W = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
So as n increases, the width, or margin of error, becomes smaller.
As your sample size increases (let us say from 100 to 400 cases), which of the following becomes true?
The answer is:
B) The margin of error becomes smaller
