An economist is interested in studying the incomes of consumers in a particular country. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in a
Mean 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. For a 95% confidence interval, Z is approximately 1.96. Given σ = $1,000 and E = $50 (half the width), n = (1.96*1000/50)^2 = 1536.64, rounded to 1537.

An Economist Is Interested in Studying the Incomes of Consumers