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 793 Millennials was taken, and each was asked to report the highest level of completed education. It was found that 264 of those surveyed had completed a Bachelor's degree or higher.

• With 95% 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 727 Gen Xers (those born between 1965 & 1980) was taken and they were asked the same question. Of this sample, 180 individuals had completed a Bachelor's degree or highter.

• With 95% 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 entire interval for this group exceeds the interval for the 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 upper limit of the confidence interval for this group is greater than the upper limit of the confidence interval for Gen Xers.

Answer 1

1)

With 95% confidence, we estimate between 30% and 36% of all Millennials have completed a Bachelor's degree or higher.

2)

With 95% confidence, we estimate between 22% and 28% of all Gen Xers have completed a Bachelor's degree or higher.

3)

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.