Age and Marital Status of Wome
Age and Marital Status of Women
The following two-way table describes the age and marital statusof American women in 1995. The table entries are in thousands ofwomen.
|
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 marginaldistribution of marital status for all adult women (use percents).Draw a bar graph to display this distribution (draw either in Excelor in SPSS).
2) (4 Points)Compare the conditionaldistributions of marital status for women aged 18 to 24 and womenaged 40 to 64. Briefly describe the most important differencesbetween the two groups of women, and back up your description withpercents.
3) (4 Points)You are planning amagazine aimed at women who have never been married. Find theconditional distribution of age among single women (those who havenever been married) and display it in a bar graph (with eitherExcel or SPSS). What age group or groups should your magazine aimto attract?
Answer:
1) The marginal distribution for all adult women is shown below(dividing each number by the total number of women). The numbers inbold in the last row and column show the marginaldistributions.
| 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 isshown below. For age group 18-24 and 40-64, the conditionalprobabilities are highlighted in bold:
| Marital Status | ||||
| Age(years) | Nevermarried | 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 agegroup is quite low compared to the % of married women in the 40-64age groups, for the obvious reason that the earlier age group isgenerally too early compared to normal marriage age (late 20’s orearly 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 lowertoo.
3) The bar graph for single women (never married) is shownbelow:
The magazine should naturally try to attract the 18-24 age group(followed by 25-39 if required) as the Never Married % is arelatively much higher fraction there.
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