4. You have collected weekly earnings and age data froma sub-sample of 1,744 individuals using the Current PopulationSurvey in a given year.
(a) Given the overall mean of $434.49 and a standarddeviation of $294.67, construct a 99% confidence interval foraverage earnings in the entire population. State the meaning ofthis interval in words, rather than just in numbers. If youconstructed a 90% confidence interval instead, would it be smalleror larger? What is the intuition?
(b) When dividing your sample into people 45 years andolder, and younger than 45, the information shown in the table isfound.
Age Category | Average Earnings | Standard Deviation | N |
Age ≥ 45 | $468.87 | $308.64 | 507 |
Age < 45 | $412.20 | $276.63 | 1237 |
Test whether or not the difference in average earningsis statistically significant. Given your knowledge of age-earningprofiles, does this result make sense?
