An economist is interested in studying the incomes of consumers in a particular region. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in an average income of $15,000. What total sample size would the economist need to use for a 95% confidence interval if the width of the interval should not be more than $100?
A) n = 1537
B) n = 385
C) n = 40
D) n = 20

Question

Quizplus · Accepted Answer

To find the sample size for a desired confidence interval width, use the formula: n = (Z * σ / E)^2, where Z is the Z-score for the confidence level (1.96 for 95%), σ is the population standard deviation ($1,000), and E is the desired margin of error ($50, since the total width is $100). Calculating gives n ≈ 1537.

An Economist Is Interested in Studying the Incomes of Consumers