uppose now that that Y denotes the annual salaries (in thousands of dollars) for US citizens who are in their 40s and 50; and X is an indicator (dummy) variable: X = 1 if that worker graduated from college and X=0 otherwise. Suppose the average annual salary for this age group is $45,000 and the estimate for β is β~ = 15 with s.e. = 5. a. What is the t-statistic and associated p-value for the null hypothesis that attending college has no impact on subsequent salary? b. What is the upper and lower bound of a 95-percent confidence interval for β~ ? c. In a credible research design attending college would be randomly assigned to a large sample of potential students. Propose such a research design. What are the potential ethical issues?
Suppose now that that Y denotes the annual salaries (in thousands of dollars) for US citizens
who are in their 40s and 50; and X is an indicator (dummy) variable: X = 1 if that worker
graduated from college and X=0 otherwise. Suppose the average annual salary for this age group
is $45,000 and the estimate for β is β~ = 15 with s.e. = 5.
a. What is the t-statistic and associated p-value for the null hypothesis that attending college
has no impact on subsequent salary?
b. What is the upper and lower bound of a 95-percent confidence interval for β~ ?
c. In a credible research design attending college would be randomly assigned to a large
sample of potential students. Propose such a research design. What are the potential ethical
issues?
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