Question

A newspaper reports that the​ governor's approval rating stands at 66​%. The article adds that the poll is based on a random sample of 597 adults and has a margin of error of 5 %. What level of confidence did the pollsters​ use?

Answer 1

Answer: There is 99% level of confidence that the pollsters used.

Explanation:

Since we have given that

Margin of error =
`\hat{p}-p=0.05`

p= 0.66

n = 597

test statistic value would be

`z=\frac{\hat{p}-p}{\sqrt{(p(1-p))/(n)}}\\\\z=\frac{0.05}{\sqrt{(0.66(1-0.66))/(597)}}\\\\z=(0.05)/(0.01939)\\\\z=2.57`

So, for interval we will write as

`P(-2.57<Z<2.57)\\\\=P(Z<2.57)-P(Z<-2.57)\\\\=0.9949-0.0051\\\\=0.9898\\\\=98.98\%\\\\\approx 99\%`

Hence, there is 99% level of confidence that the pollsters used.