GEN&SEX 50B Chapter 22: Section 22- Women, Work and Immigration

A hypothetical observational breast cancer study enrolled 10,000 women age 50 and older during 1990 and followed each woman for 10 years. All women received a free medical exam, including a mammogram, at baseline and each year thereafter. All deaths were full investigated and there was no loss to follow-up. At the baseline examination, 80 women were diagnosed with having early breast cancer. Twenty of these women died during the 10 year follow-up. By the end of follow-up, 240 other women had developed breast cancer, including 30 who died from their disease. Two hundred other women (who did not develop breast cancer) died from other causes.

a. What was the prevalence of diagnosed early breast cancer in the study population at baseline?

b. What was the 10-year case-fatality “rate” in women with early breast cancer at baseline?

c. What was the cumulative incidence of breast cancer during the 10 year follow-up?

d. What was the incidence rate (incidence density) of breast cancer in the study population during the 10 year follow-up?

e. What was the breast cancer mortality rate in the study population during the 10 years?

f. What was the all-cause mortality rate in the study population during the 10 years?

g. What was the proportionate mortality for breast cancer?

h. What was the prevalence of (diagnosed) breast cancer in 2000?

3. Over the past 35 years, an increasing number of mothers have gone back to work relatively quickly after giving birth. Consider a labor market where a worker’s wage is a function of his or her years of education past the compulsory level (E), work experience (X), and years of tenure with their current employer (T). Suppose the relationships between wages, education, experience, and tenure for males (M) and females (F) can be represented by the equations

W_M = 3 + 0.5E + 0.4X + 0.2T

and

W_F = 3 + 0.4E + 0.3X + 0.3T.

On average, E = 4, X =20, and T = 8 for men, while for women the averages are E = 4, X = 14, and T = 4.

A) Find the average wage of men and women. What is the ratio of female to male wages? What is the gap between women and men’s wages in percentage terms?

B) What wage would women earn if they had the same pre-market characteristics as men on average? What would be the ratio of women’s to men’s wages?

C) Express the amount of current wage discrimination in percentage terms.

Suppose in the analysis that years of tenure are either unmeasurable or unobservable to the researcher. As a result, the analysis produces the following wage equations.

W_M = 4.6 + 0.5E + 0.4X

and

W_F = 4.2 + 0.4E + 0.3X.

D) Find the average wage of men and women. What is the ratio of female to male wages? What is the gap between women and men’s wages in percentage terms?

E) What wage would women earn if they had the same pre-market characteristics as men on average? What would be the ratio of women’s to men’s wages?

F) Express the amount of current wage discrimination in percentage terms.

G) Does this (failing to include tenure in the model) overstate or understate the effects of gender discrimination?

(1)Agri-Beef Inc. operates cattle feedlots in several midwestern states. The company wishes to estimate the average daily weight gain of cattle on their lots. To do this a simple random sample of cattle is taken and the daily weight gain is recorded. The data below, in pounds, represent the results of the sample.

8.7

6.1

6.1

9.8

6.5

8.3

6.3

5.8

8.0

8.7

5.1

7.0

6.0

7.9

6.1

a. Construct a 95% confidence interval estimate for the true daily weight gain.
b. Construct a 99% confidence interval estimate for the true daily weight gain.
c. Discuss the differences between the two estimates found in parts a and b
and indicate the advantages and disadvantages of each.

(2)A survey of 400 women for the American Orthopedic Foot and Ankle Society revealed that 38% wear flats to work.

a. Use this sample information to develop a 99% confidence interval for the population proportion of women who wear flats to work.

b. Suppose the society wished to estimate the proportion of women who wear athletic shoes to work and the proportion of women who wear flats to work within a margin of error of 0.01 (one percentage point) with 95% confidence. Determine the sample size required.