Sociology 674 – Elementary Demographic Techniques
Test 2
11/15/05
Page 1
Name __________________________
Please answer all questions in a blue exam book. There are a total of 100 points on the exam.
For me to provide any partial credit for incomplete answers, it is essential that you show your
work. Please give answers to the fourth decimal point (e.g., 0.1234).
1) Answer the following four questions about reproduction rates (20 points).
a. Provide a brief interpretation of the Gross Reproduction Rate.
b. Does a GRR of 1.0 correspond to replacement level fertility? Why or why not?
c. Under what circumstances would the Gross Reproduction Rate be equal to the Net
Reproduction Rate?
d. Consider two countries with identical Net Reproduction Rates. The mean age of
childbearing is 21.5 in Country X and 26.4 in Country Y. Which country’s population
has a higher growth rate? Why?
2) The following information is for men in the Philippines in 1980. Answer the three
questions below. (20 points)
Age group
15-19
20-24
25-29
30-34
35-39
40-45
45-49
50-54
Total
Number of
marriages
36,000
149,000
103,000
33,000
12,000
6,900
3,800
Percent never
married
91
54
24
12
8
6
5
5
343,700
a. What is the mean age at marriage for Philippine men in 1980?
b. What is the median age at marriage?
c. What is the singulate mean age at marriage?
Sociology 674 – Elementary Demographic Techniques
Test 2
11/15/05
Page 2
3) Use this 1985 life table for women in Ireland to answer the five questions below. (20
points)
1985 life table for women in Ireland
x
qx
dx
0
0.0079
790
1-5
0.0017
167
5-10
0.0008
78
10-15
0.0009
90
15-20
0.0013
128
20-25
0.0018
174
25-30
0.0014
134
30-35
0.0032
316
35-40
0.0042
409
40-45
0.0076
744
45-50
0.0117
1,131
50-55
0.0214
2,047
55-60
0.0366
3,437
60-65
0.0629
5,684
65-70
0.0943
7,980
70-75
0.1622
12,442
75-80
0.2494
16,021
80-85
0.4143
19,981
85+
1.0000
28,247
lx
100,000
99,210
99,043
98,965
98,875
98,747
98,573
98,439
98,123
97,714
96,970
95,838
93,792
90,355
84,671
76,690
64,248
48,228
28,247
Lx
99,337
396,440
495,020
494,601
494,056
493,300
492,530
491,405
489,592
486,708
482,020
474,076
460,367
437,564
403,403
352,347
281,190
191,186
134,245
Tx
7,649,387
7,550,050
7,153,610
6,658,590
6,163,989
5,669,933
5,176,633
4,684,103
4,192,698
3,703,106
3,216,398
2,734,378
2,260,302
1,799,935
1,362,371
958,968
606,621
325,431
134,245
ex
76.49
76.10
72.23
67.28
62.34
57.42
52.52
47.58
42.73
37.90
33.17
28.53
24.10
19.92
16.09
12.50
9.44
6.75
4.75
a. What is life expectancy at birth?
b. For a woman who survives until age 55, how many more years can she expect to
live?
c. What is the probability of dying between exact age 20 and exact age 50?
d. What is the probability of surviving from exact age 60 to exact age 80?
e. If these death rates (probabilities) were to continue indefinitely and if 100,000
baby girls were born in Ireland every year for the foreseeable future, what would
the total female population of Ireland be in 100 years?
f. In the scenario described in (e), how many women would there be between exact
ages 20 and 25?
Sociology 674 – Elementary Demographic Techniques
Test 2
11/15/05
Page 3
4) Based on the following hypothetical data, answer the four questions below. (20 points)
Country 1
Age
15-19
20-24
25-29
30-34
35-39
40-45
45-49
Total
# women at
mid-year
# births
2,000
100
2,200
400
2,500
350
2,700
200
3,000
100
3,500
50
3,700
25
19,600
1,225
Country 2
ASFR
(per 1,000)
50.00
181.82
140.00
74.07
33.33
14.29
6.76
# women at
mid-year
3,200
3,000
3,000
2,900
2,700
2,500
2,300
19,600
# births
128
480
345
189
68
38
12
1,260
ASFR
(per 1,000)
40.00
160.00
115.00
65.00
25.00
15.00
5.00
a. What is the General Fertility Rate for each country?
b. Why is the GFR for country 2 greater than that of country 1?
c. What is the Total Fertility Rate for each country?
d. Which country has higher fertility?
5. A mysterious disease affects some children born to an indigenous tribe living in a tropical rain
forest. Among children born with this disease, 70% die in the first year of life. Among those who
survive the first year of life 60% die before reaching age two. 50% of survivors to age 2 die
before age 3 and 50% of survivors to age 3 die before age 4. No child born with this disease has
ever reached his/her fifth birthday. Based on this information, answer the following questions:
(20 points)
a. What is the average life expectancy of a child born with this disease?
b. How long can a child with this disease expect to live if he/she survives the first year
of life?
c. Assume that the population of this indigenous tribe is stationary. If 100 children are
born with this disease every year, how many children are there in the population
suffering from this disease in any given year?