A researcher proposes a study to investigate a quantitative variable for which the population standard deviation is known to be 4. She wants a margin of error of 2.5 with 95% confidence. Which sample size should she use?

Question

Quizplus · Accepted Answer

The formula for sample size with a known population standard deviation is n = [Z*(sigma/E)]^2, where Z is the Z-score corresponding to the desired confidence level (in this case, 1.96 for 95% confidence), sigma is the population standard deviation (4 in this case), and E is the desired margin of error (2.5 in this case). Plugging in these values gives n = [(1.96*4)/2.5]^2 ≈ 9.64. Since sample size must be a whole number, the researcher should round up and use a sample size of 10 to achieve the desired margin of error with 95% confidence.

A Researcher Proposes a Study to Investigate a Quantitative Variable