Question

Data broken down by generation (Group 1: Millennials; Group 2: Not Millennials) are shown below based on their agree or disagreement of the statement below:

“You shouldn’t worry too much about other people.”

Find the 90% confidence interval for the true difference in the proportions agreeing with the statement.

Agree Disagree    Total

Group 1 139    112    251

Group 2 278    484    417

Total:    417    596 668

A. 0.130 to 0.248

B. -40.9 to -37.1

C. 0.097 to 0.282

D. -0.245 to -0.144

E. -0.189 to 0.249

Answer 1

Solution:

Given:

	Agree	Disagree	Total
Group 1	139	112	251
Group 2	278	484	762
Total	417	596	1013

(Note that: total of group 2 is incorrect in given table, correct totals are in above table)

We have to find 90% confidence interval for the true difference in the proportions agreeing with the statement.

Formula:

where

and

Z_c is z critical value for c = 90% confidence level.

Find Area = ( 1 + c ) / 2 = ( 1 + 0.90) / 2 = 1.90 / 2 = 0.9500

Look in z table for Area = 0.9500 or its closest area and find corresponding z value.

Area 0.9500 is in between 0.9495 and 0.9505 and both the area are at same distance from 0.9500

Thus we look for both area and find both z values

Thus Area 0.9495 corresponds to 1.64 and 0.9505 corresponds to 1.65

Thus average of both z values is : ( 1.64+1.65) / 2 = 1.645

Thus Z_c = 1.645

Thus

Thus correct answer is: A. 0.130 to 0.248