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.

Explanation:

Since we have given that

n = 1010

x = 515

So, it becomes
`\hat{p}=(x)/(n)=(515)/(1010)=0.51`

At 99% level of confidence ,

z = 2.58

So, Margin of error would be

`z\sqrt{\frac{\hat{p}(1-\hat{p}}{n}}\\\\=2.58\sqrt{(0.51* (1-0.51))/(1010)}\\\\=2.58* \sqrt{(0.51* 0.49)/(1010)}\\\\=2.58* 0.0157\\\\=0.041`

Hence, the margin of error is 0.041.