Question

A recent article in Time magazine argued that people belonging to the so-called Millennial Generation (defined as those individuals born between 1980 and the early 2000s) are more self-centered than their counterparts in previous generations. The General Social Survey asked a sample of American Adults whether they agreed or disagreed with the following statement:

“People do not need to be overly concerned with others.”

Data by age group (18-30 “Millennials”, and 31 and over: “Older”) are shown below:

Age Group	Agree	Disagree	Total
18-30 (Group 1; Millennials)	139	112	251
31 & Over (Group 2; Older)	278	484	762
Total	417	596	1013

Find and interpret the 95% confidence interval for the true difference in the proportion of people in each group who would agree with the statement.

		We are 95% confident that the true difference in the proportions of individuals agreeing with the statement is between 0.28 and 0.40. Millennials tend to agree with the statement proportionally more than the previous generation.
		We are 95% confident that the true difference in the proportions of individuals agreeing with the statement is between 0.12 and 0.26. Millennials tend to agree with the statement proportionally more than the older generation.
		We are confident that 95% of the time, the true difference in the proportions of individuals agreeing with the statement will be between -0.19 and 0.26. We cannot conclude that there is a difference between Millennials and the older generation in the proportion who would agree with the statement.
		We are confident that 95% of Millennials believe that between 12% and 26% of the previous generation agree with the statement.
		We are 95% confident that the true difference in the proportions of individuals agreeing with the statement is between -0.19 and -0.14. The previous generation tends to agree with the statement proportionally more than Millennials.

Answer 1

The statistical software output for this problem is:

Hence,

We are 95% confident that the true difference in the proportions of individuals agreeing with the statement is between 0.12 and 0.26. Millennials tend to agree with the statement proportionally more than the older generation.

Option B is correct.