An economist is interested in studying the incomes of consumers in a 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

The formula for the sample size needed for a confidence interval is:n = (Z^2 * s^2) / E^2where:Z is the z-score for the desired confidence levels is the population standard deviationE is the margin of errorIn this case, we have:Z = 1.96 (for a 95% confidence level)s = $1,000E = $100Plugging these values into the formula, we get:n = (1.96^2 * 1,000^2) / 100^2n = 1537.6Therefore, the economist would need to use a total sample size of 1537 individuals to achieve a 95% confidence interval with a width of no more than $100.

An Economist Is Interested in Studying the Incomes of Consumers