A simple random sample of 3,500 people age 18 or over is taken in a large town t

Question

A simple random sample of 3,500 people age 18 or over is taken in a large town to estimate the percentage of people (age 18 and over in that town) who read newspapers. It turns out that 2,487 people in the sample are newspaper readers. The population percentage is estimated as

2,487/3500 x 100 = about 71%

The standard error is estimated as 0.8 of 1%, because root 3500 x root 0.71 x2.9 = about 27, 27/3500 x 100% = about 0.8 of 1%

(a) Is 0.8 of 1% the right SE Answer yes or no, and explain

(b) 71% +- 1.6% is a ______ for the ______. Fill in the blanks and explain

Explanation / Answer

a) sample size, n= 3500
p = (2487/3500) = 0.71
q = 1-p=1-0.71 = 0.29
SE = (npq) = (3500 * 0.71 * 0.29) = 26.845

b) 71% +- 1.6% is a confidence interval for the confidence level of 97.26%.

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