Question

A random sample of size $n$will be selected from a population, and the proportion 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 $50$to $200$?

(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

Step 1: Given information

Step-by-step solution

Given information

We are given that in random sample of size n ,confidence interval of $95\%$

From given information we need to find that what will be change in margin of error if sample is increased from $50$to $200$.

Explanation

Confidence level is a range of values so defined that there is a specified probability that the value of a parameter lies within it.

Formula of confidence level is

$\overline{X}\pm Z\alpha \sigma /2\sqrt{n}$

Where

$\overline{X}$= Mean

= Confidence coefficient

= Confidence level

= Standard deviation

= sample space

The value after the symbol is known as the margin of error.

We need to find change in margin of error(Let it be )

For confidence intervalwe have