Question

Age and Marital Status of Women

The following two-way table describes the age and marital status of American women in 1995. The table entries are in thousands of women.

	Marital Status
Age (years)	Never married	Married	Widowed	Divorced	Total
18-24	9289	3046	19	260	12614
25-39	6948	21437	206	3408	31999
40-64	2307	26679	2219	5508	36713
>=65	768	7767	8636	1091	18262
Total	19312	58929	11080	10267	99588

1)(4 Points)Report the marginal distribution of marital status for all adult women (use percents). Draw a bar graph to display this distribution (draw either in Excel or in SPSS).

2) (4 Points)Compare the conditional distributions of marital status for women aged 18 to 24 and women aged 40 to 64. Briefly describe the most important differences between the two groups of women, and back up your description with percents.

3) (4 Points)You are planning a magazine aimed at women who have never been married. Find the conditional distribution of age among single women (those who have never been married) and display it in a bar graph (with either Excel or SPSS). What age group or groups should your magazine aim to attract?

Answer 1

1) The marginal distribution for all adult women is shown below (dividing each number by the total number of women). The numbers in bold in the last row and column show the marginal distributions.

Marital Status					P(Age Group=x)
Age (years)	Never married	Married	Widowed	Divorced	Total
18-24	9.33%	3.06%	0.02%	0.26%	12.67%
25-39	6.98%	21.53%	0.21%	3.42%	32.13%
40-64	2.32%	26.79%	2.23%	5.53%	36.86%
>=65	0.77%	7.80%	8.67%	1.10%	18.34%
P(Marital Status=y)	19.39%	59.17%	11.13%	10.31%	100.00%

2) The conditional probability of marital status given age is shown below. For age group 18-24 and 40-64, the conditional probabilities are highlighted in bold:

Marital Status
Age (years)	Never married	Married	Widowed	Divorced
18-24	48.10%	5.17%	0.17%	2.53%
25-39	35.98%	36.38%	1.86%	33.19%
40-64	11.95%	45.27%	20.03%	53.65%
>=65	3.98%	13.18%	77.94%	10.63%
Total	100.00%	100.00%	100.00%	100.00%

We can clearly see that the % of married women in the 18-24 age group is quite low compared to the % of married women in the 40-64 age groups, for the obvious reason that the earlier age group is generally too early compared to normal marriage age (late 20's or early 30's on an average).

For the same reason that 18-24 is a low age group for marriage, the % of divorced women in this age group is naturally lower too.

3) The bar graph for single women (never married) is shown below:

The magazine should naturally try to attract the 18-24 age group (followed by 25-39 if required) as the Never Married % is a relatively much higher fraction there.