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?
Accepted Solution
A:
Answer: There is 99% level of confidence that the pollsters used.Step-by-step explanation:Since we have given that Margin of error = [tex]\hat{p}-p=0.05[/tex]p= 0.66n = 597test statistic value would be [tex]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[/tex]So, for interval we will write as [tex]P(-2.57<Z<2.57)\\\\=P(Z<2.57)-P(Z<-2.57)\\\\=0.9949-0.0051\\\\=0.9898\\\\=98.98\%\\\\\approx 99\%[/tex]Hence, there is 99% level of confidence that the pollsters used.