Question

A survey was undertaken to compare the educational background of several different generation. One generation of interest was the Millennials (those born after 1980). A sample of 646 Millennials was taken, and each was asked to report the highest level of completed education. It was found that 218 of those surveyed had completed a Bachelor's degree or higher.

• With 99% confidence, we estimate between % and % of all Millennials have completed a Bachelor's degree or higher. (After converting to percentages, round the limits of your interval to two decimal places.)

A sample of 531 Gen Xers (those born between 1965 & 1980) was taken and they were asked the same question. Of this sample, 130 individuals had completed a Bachelor's degree or highter.

• With 99% confidence, we estimate between % and % of all Gen Xers have completed a Bachelor's degree or highter. (After converting to percentages, round the limits of your interval to two decimal places.)

Based on the two intervals calculated, can we conclude there is a difference in the percentage of individuals in these two generations who have completed a Bachelor's degree or higher?

• A larger percentage of Millennials have completed a Bachelor's degree or higher because the upper limit of the confidence interval for this group is greater than the upper limit of the confidence interval for Gen Xers.
• A larger percentage of Millennials have completed a Bachelor's degree or higher because most of the interval for this group exceeds the interval for the Gen Xers.
• The data collected is inconclusive because the intervals estimating the proportion who have completed a Bachelor's degree or higher for the two generations overlap.
• A larger percentage of Millennials have completed a Bachelor's degree or higher because the entire interval for this group exceeds the interval for the Gen Xers.

Answer 1

SOLUTION 1:

Z critical value of 99% confidence interval is 2.58

(0.29, 0.39) is 99% confidence interval

SOLUTION B: WITH THE SAME PROCEDURE THE 99% CONFIDENCE INTERVAL IS

0.197<p<0.293.

(0.20, 0.29) is 99% confidence interval

SOLUTION C: A larger percentage of Millennials have completed a Bachelor's degree or higher because the entire interval for this group exceeds the interval for the Gen Xers.