You Have Collected Weekly Earnings and Age Data from a Sub-Sample

Essay

You have collected weekly earnings and age data from a sub-sample of 1,744 individuals using the Current Population Survey in a given year.
(a)Given the overall mean of $434.49 and a standard deviation of $294.67, construct a 99% confidence interval for average earnings in the entire population. State the meaning of this interval in words, rather than just in numbers. If you constructed a 90% confidence interval instead, would it be smaller or larger? What is the intuition?
(b)When dividing your sample into people 45 years and older, and younger than 45, the information shown in the table is found. $\begin{array} { | c | c | c | c | } \hline \text { Age Category } & \text { Average Earnings } \bar { Y } & \text { Standard Deviation } S _ { Y } & N \\\hline \text { Age } \geq 45 & \$ 488.87 & \$ 328.64 & 507 \\\hline \text { Age } < 45 & \$ 412.20 & \$ 276.63 & 1237 \\\hline\end{array}$ Test whether or not the difference in average earnings is statistically significant. Given your knowledge of age-earning profiles, does this result make sense?