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.

Step-by-step explanation:

Since we have given that

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

p= 0.66

n = 597

test statistic value would be

$z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}\\\\z=\dfrac{0.05}{\sqrt{\dfrac{0.66(1-0.66)}{597}}}\\\\z=\dfrac{0.05}{0.01939}\\\\z=2.57$

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.