Question

You want to conduct a survey to determine the proportion of people who favor a proposed tax policy. How does increasing the sample size affect the size of the margin of error?

Answer 1

Margin of error will decrease

Explanation:

Given that you want to conduct a survey to determine the proportion of people who favor a proposed tax policy.

Margin of error is the quantity allowed for the mean to deviate on either side

Margin of error is calculated as

Critical value for the required confidence level * std deviation of sample/population/square root of sample size

Here for 95% for eg z critical value is 1.96

We find that margin of error is inversely proportional to square root of sample size n.

So when n increases margin of error decreases proportional to square root of sample size

If margin of error is 2% say and if sample size is made 4 times then margin of error reduced to half of original i.e. 1%