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

The formula for the sample size needed for a confidence interval is:n = (Z^2 * s^2) / (E^2)where: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) / (100^2) = 384.16Since we cannot have a fractional sample size, we round up to the nearest whole number, which is 385.Therefore, the economist would need to use a total sample size of 385 for a 95% confidence interval with a width of not more than $100.

An Economist Is Interested in Studying the Incomes of Consumers