Question

A random sample of size n will be selected from a population, and the proportion p^$\frac{305}{1526}=0.200=20.0\%\hat{p}$ of those in the sample who have a Facebook page will be calculated. How would the margin of error for a $95\%$ confidence interval be affected if the sample size were increased from $50to200$ and the sample proportion of people who have a Facebook page is unchanged?

a. It remains the same.

b. It is multiplied by $2$.

c. It is multiplied by $4$.

d. It is divided by $2$.

e. It is divided by $4$.

Short answer

The correct answer is:

d. It is divided by$2$

Step-by-step solution

 Step 1: Given information 

We have to tell about confidence interval would be affected if the sample size were increased.

Explanation 

• The term that comes to me while thinking about this issue is proportion. What should be considered is the proportional margin of error.
• It's critical to comprehend the link between 'n' and the margin of error. When 'n' is in the denominator, the margin of error reduces at a square root rate as n rises.
• The number four can be found in the square root of four, which is two. The new margin of error is half that of the previous one.