A Subsample from the Current Population Survey Is Taken, on Weekly

question 51

Essay

A subsample from the Current Population Survey is taken, on weekly earnings of individuals, their age, and their gender. You have read in the news that women make 70 cents to the $1 that men earn. To test this hypothesis, you first regress earnings on a constant and a binary variable, which takes on a value of 1 for females and is 0 otherwise. The results were: $\widehat{ E a m }$ = 570.70 - 170.72 × Female, R²=0.084, SER = 282.12.
(9.44)(13.52)
(a)Perform a difference in means test and indicate whether or not the difference in the mean salaries is significantly different. Justify your choice of a one-sided or two-sided alternative test. Are these results evidence enough to argue that there is discrimination against females? Why or why not? Is it likely that the errors are normally distributed in this case? If not, does that present a problem to your test?
(b)Test for the significance of the age and gender coefficients. Why do you think that age plays a role in earnings determination?

Learn how to calculate the sum of squares for error in regression analysis.

Identify the different names and interpretations of the residual term in a regression equation.

Understand the interpretation of slope and y-intercept in the context of regression lines.

Distinguish between direct and inverse relationships in regression models.

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Definitions:

Binomial Distribution

A probability distribution that summarizes the likelihood that a value will take one of two independent states and is based on a fixed number of trials.

P(X = 1)

The probability that a random variable X takes the value 1, a specific outcome in a probability distribution.

Sports Fans

Individuals who exhibit enthusiasm and support for sports teams or athletes, often through attendance at games, viewership, and merchandise purchase.

College Students

Individuals enrolled in an institution of higher education with the aim of achieving a degree, certificate, or course completion.