Question

A newspaper reports that the​ governor's approval rating stands at 47​%. The article adds that the poll is based on a random sample of 1063 adults and has a margin of error of 3 %. What level of confidence did the pollsters​ use?

options are:

90, 95, 98, or 99%

Answer 1

Solution :

Given that,

= 47% = 0.47

1 - = 1 - 0.47 = 0.53

margin of error = E = 3% = 0.03

n = 1063

sample size = n = (Z _{/ 2} / E )² * * (1 - )

Z² _{/ 2} = (n * E²) / * (1 - )

= (1063 * 0.03²) / (0.47 * 0.53)

= 0.9567 / 0.2491

Z² _{/ 2}  = 3.84

Z _{/ 2} = 1.96

P(-1.96 < z < 1.96) = 95%

level of confidence = 95%