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 $30,000.What 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 = 20
D) n = 40

Question

Quizplus · Accepted Answer

To find the sample size needed for a specific confidence interval width, use the formula for the margin of error: E = Z * (σ/√n). For a 95% confidence interval, Z is approximately 1.96. Set E to 50 (half of the total width of 100), and solve for n: 50 = 1.96 * (1000/√n). Solving this gives n ≈ 1537.

An Economist Is Interested in Studying the Incomes of Consumers