# Three Statistics Multiple Choice Questions in Mean

Suppose you are doing research on the differences in wages earned by men and women in the U.S. workforce. You gain access to a data set that contains information on a random sample of 534 U.S. workers surveyed in 1985. The data set contains information about the hourly wage (in U.S. dollars) and the sex of each of the workers surveyed, as well as information about each worker's age (years), union membership (yes/no), and type of occupation (collapsed into 8 different categories). You decide to use multiple linear regression to estimate unadjusted differences in the mean hourly wage for female workers as compared to males, as well as adjusted gender-wage differences, adjusted for various other worker characteristics. Below find the estimated coefficient for sex, along with its standard error from 4 different linear regression models, all which include sex as a predictor. The sample is 45% female, 18% union members, the age range is 18 - 62 years and the years of education ranges from 2 years to 18 years (college + at least some graduate school).

Predictor Regression Coefficient Standard Error

Sex -2.10 0.44

Sex, Age -2.20 0.43

Sex, Age, Union Membership -2.10 0.43

Sex, Age, Union Membership, Job Type -2.20 0.43

6. Which of the following statements best describes the unadjusted mean difference (and 95% CI) in hourly wages for females as compared to males?

a. Females make an estimated $2.10 per hour less, on average, than males (95% CI $1.22 to 2.98 per hour less)

b. Females make an estimated $2.10 per hour more, on average, than males (95% CI $1.22 to 2.98 per hour more)

c. Cannot estimate unadjusted mean difference in wages (and corresponding 95% confidence interval) without more information.

7. The regression coefficient for sex does not change much when additional covariates are added to a model estimating the association between hourly wages and sex amongst U.S. workers in 1985. The best explanation for this, among the following, is:

a. There is a statistical interaction between gender and union membership.

b. The wage/gender association is not confounded by other worker characteristics (union membership, age, and job type)

c. Union membership is a confounder in the association between wages and age.

d. Gender modifies the relationship between hourly wages and worker age.

8. The overall R2 for the regression model with hourly wage as the outcome, and gender, age, union membership, and occupation type as predictors is 25%. What would happen to this R2 value if age was instead entered in months, not years, and gender were coded 1 for males and 0 for females?

a. R2 would increase.

b. R2 would decrease.

c. R2 would remain the same.

d. Cannot answer from the information given.

See attached file for full problem description.

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#### Solution Preview

Please see the attached file.

The following information is referenced in questions 6-8.

Suppose you are doing research on the differences in wages earned by men and women in the U.S. workforce. You gain access to a data set that contains information on a random sample of 534 U.S. workers surveyed in 1985. The data set contains information about the hourly wage (in U.S. dollars) and the sex of each of the workers surveyed, as well as information about each worker's age (years), union membership (yes/no), and type of occupation (collapsed into 8 different categories). You decide to use multiple linear regression to estimate unadjusted differences in the mean hourly wage for female workers as compared to males, as well as adjusted gender-wage differences, adjusted for various other worker characteristics. Below find the estimated coefficient for sex, along with its standard ...