Does education really make a difference in how much money you will earn? Researchers randomly selected 100 people from each of three income categories-"marginally rich," "comfortably rich," and "superrich"-and recorded their education levels. The data is summarized in the table that follows.
|
Highest Education Latl
|
Marginally
Rich
|
Comfortably
Rich
|
Super Rich
|
|
No college
|
32
|
20
|
23
|
|
Some college
|
13
|
16
|
1
|
|
Undergraduate degree
|
43
|
51
|
60
|
|
Postgraduate study
|
12
|
13
|
16
|
|
Total
|
100
|
100
|
100
|
a. Describe the independent multinomial populations whose proportions are compared in the χ2 analysis.
b. Do the data indicate that the proportions in the various education levels differ for the three income categories? Test at the α =.01 level.
c. Construct a 95% confidence interval for the difference in proportions with at least an undergraduate degree for individuals who are marginally and super rich. Interpret the interval.