A recent poll of 700 people who work indoors found that 278 smoke. If the researchers want to be 98% confident of their results to within 3.5 percentage points, how large a sample is necessary?
A) 751
B) 1062
C) 33
D) 532

Question

Quizplus · Accepted Answer

To determine the sample size, we need to use the formula:
n = (Z^2 * p * q) / E^2
where:
Z = Z-value for the desired level of confidence (2.33 for 98% confidence)
p = proportion of smokers in the sample (278/700 ≈ 0.397)
q = proportion of non-smokers in the sample (1 - p ≈ 0.603)
E = maximum error margin (0.035)

Plugging in the values, we get:
n = (2.33^2 * 0.397 * 0.603) / 0.035^2
n ≈ 1061.96

Rounding up to the nearest whole number, we get a sample size of 1062. Therefore, the best choice is B.

A Recent Poll of 700 People Who Work Indoors Found