Question

A February 2016 Gallup Poll of 1,021 US adults found that 73% believe that cyberterrorism is a critical threat to US vital interests in the next 10 years. The reported margin of error is ±4 percentage points. The reported confidence level is 95%.

The same poll of 1,021 US adults showed that 75% believe that development of nuclear weapons by Iran is also a critical threat to US vital interests in the next 10 years. The margin of error for this estimate is also ±4 percentage points. A member of the US House Committee on Appropriations is satisfied with 95% confidence, but she wants a smaller margin of error than ±4 percentage points to be able to distinguish which threat is more concerning to Americans.

Which of the following modifications will achieve the smaller margin of error at 95% confidence?

	change the sampling method
	decrease in sample size
	increase in sample size

Answer 1

We know that the formula for margin of error is given as

ME =

where z is critical value corresponding to confidence level

sigma is population standard deviation

n is the sample size

we can see that margin of error is inversely proportional to the sample size n

This means that increase in sample size n will decrease the margin of error or decrease in sample size n will increase the margin of error

So, to decrease the margin of error, we must increase the sample size n

option C

Increase in sample size