Question

A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n = 1010 and x= 515 who said "yes" . Use a 99% confidence level. Identify the value of the margin of error E.

Answer 1

Answer: The margin of error is 0.041.

Step-by-step explanation:

Since we have given that

n = 1010

x = 515

So, it becomes $\hat{p}=\dfrac{x}{n}=\dfrac{515}{1010}=0.51$

At 99% level of confidence ,

z = 2.58

So, Margin of error would be

$z\sqrt{\dfrac{\hat{p}(1-\hat{p}}{n}}\\\\=2.58\sqrt{\dfrac{0.51\times (1-0.51)}{1010}}\\\\=2.58\times \sqrt{\dfrac{0.51\times 0.49}{1010}}\\\\=2.58\times 0.0157\\\\=0.041$

Hence, the margin of error is 0.041.