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) 532
B) 751
C) 33
D) 1062

Question

Quizplus · Accepted Answer

To determine the necessary sample size for a given confidence level and margin of error, the formula is used: $n = \frac{Z^2 \cdot p \cdot (1-p)}{E^2}$, where $Z$ is the Z-score corresponding to the desired confidence level, $p$ is the proportion of the population that has the characteristic of interest (in this case, the proportion of people who smoke), and $E$ is the margin of error. For a 98% confidence level, the Z-score is approximately 2.33. The proportion $p$ is 278/700, but since we're looking for a general sample size for a population, we use a conservative estimate where $p = 0.5$ for maximum variability. The margin of error $E$ is 0.035 (3.5%). Plugging these values into the formula gives a sample size that rounds to the nearest whole number, which is 1062.

A Recent Poll of 700 People Who Work Indoors Found