Question

Barron's reported that the average number of weeks an individual is unemployed is 13 weeks. Assume that for the population of all unemployed individuals, the population mean length of unemployment is 13 weeks, and that the population standard deviation is 3 weeks. Suppose you would like to select a random sample of 80 unemployed individuals for a follow-up study. Using the z-table.

A) True
B) False

Answer 1

Suppose you would like to select a random sample of 80 unemployed individuals for a follow-up study. Using the z-table it is A) True

Barron's reported the average number of weeks as 13. This implies that we are dealing with the population mean of unemployment duration.

The population standard deviation is given as 3 weeks. This implies that σ = 3 weeks. We need to select a random sample of 80 unemployed individuals. This sample size (n = 80) is considered large enough to apply the central limit theorem.

Therefore, we can use the z-table to analyze the distribution of the sample mean because it will be approximately normal with a mean of μ = 13 weeks and a standard deviation of σ/√n = 3/√80 ≈ 0.35 weeks.