For Exercise 2.91, see page 106; for 2.92 and 2.93, see pages 106–107; for 2.94 to 2.96, see page 108; for 2.97 to 2.99, see page 109; and for 2.100 and 2.101, see pages 111–112.

Question 2.113

2.113 Demographics and new products

Companies planning to introduce a new product to the market must define the “target” for the product. Who do we hope to attract with our new product? Age and sex are two of the most important demographic variables. The following two-way table describes the age and marital status of American women.23 The table entries are in thousands of women.

agegen

Marital status
Age (years) Never
married		 Married Widowed Divorced
18 to 24 12,112 2,171 23 164
25 to 39 9,472 18,219 177 2,499
40 to 64 5,224 35,021 2,463 8,674
984 9,688 8,699 2,412
  1. Find the sum of the entries for each column.
  2. Find the marginal distributions.
  3. Find the conditional distributions.
  4. If you have the appropriate software, make a mosaic plot.
  5. Write a short description of the relationship between marital status and age for women.

2.113

(a) 27,792 never married; 65,099 married; 11,362 widowed; 13,749 divorced. (b) Marginal distributions:

Percent Never-
Married		 Married Widowed Divorced Total
18To24 10.26 1.84 0.02 0.14 12.3
25To39 8.03 15.44 0.15 2.12 25.7
40To64 4.43 29.68 2.09 7.35 43.5
65And-Over 0.83 8.21 7.37 2.04 18.5
Total 23.55 55.17 9.63 11.65 100

(c) Conditional distribution given Marital Status:

Percent Never-
Married		 Married Widowed Divorced
18To24 43.58 3.33 0.2 1.19
25To39 34.08 27.99 1.56 18.18
40To64 18.8 53.8 21.68 63.09
65AndOver 3.54 14.88 76.56 17.54
Total 100 100 100 100

Conditional distribution given Age:

Percent Never-
Married		 Married Widowed Divorced Total
18To24 83.7 15 0.16 1.13 100
25To39 31.19 60 0.58 8.23 100
40To64 10.17 68.16 4.79 16.88 100
65And-Over 4.52 44.48 39.93 11.07 100

(e) More than half of women are married; of that group, age 40 to 64 is the most common followed by 25 to 39. Almost 25% never married, but most of that group is represented by younger age groups. Widowed and Divorced have relatively small percentages across the board, though the 65 and Over group is most likely to be widowed and the 40 to 64 group is most likely to be divorced.