(100 marks) The STATA dataset on Canvas called ps_cps2017.dta contains the data needed to complete this question. These

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100 Marks The Stata Dataset On Canvas Called Ps Cps2017 Dta Contains The Data Needed To Complete This Question These 1 (116.7 KiB) Viewed 32 times

(100 marks) The STATA dataset on Canvas called ps_cps2017.dta contains the data needed to complete this question. These data are representing a random sample of 1,000 individuals drawn from the 2017 United States Current Population Survey for the following study population: individuals in 2017 between the ages of 25 and 30, in the labor force, and not enrolled in school. Treat the hourly wage (W) and education (S) as random variables. Let Hy and Ov? denote the population mean and variance of the hourly wage, respectively; and, likewise, let us and os 2 denote the population mean and variance of education. 1. (3 marks) What is the estimate of the population mean of education (in years)? 2. (3 marks) What is the estimate of the population variance of education? 3. (3 marks) What is the estimate of the population standard deviation of education? 4. (3 marks) What is the sample size? 5. (3 marks) What is the standard error the estimate of the mean in #1 above? 6. Test the null hypothesis that the population mean education is 14 years of schooling versus the alternative hypothesis that mean education is not 14 years. a. (5 marks) Write down the null and alternative hypotheses mathematically. b. (5 marks) What is the formula for and the value of the test statistic? c. (5 marks) What are the number of degrees of freedom? d. (5 marks) Is this test one or two-tailed? e. (5 marks) What is (are) the critical value(s) for the test? f. (5 marks) Do you reject or not reject the null? Briefly explain your reasoning.
7. (3 marks) What is the estimate of the population mean of the hourly wage (in dollars per hour)? 8. (3 marks) What is the estimate of the population variance of the hourly wage? 9. (3 marks) What is the estimate of the population standard deviation of the hourly wage? 10. (3 marks) What is the standard error the estimate of the mean in #7 above? 11. Test the null hypothesis that the population mean wage is $25 per hour versus the alternative hypothesis that the mean wage is less than $25 per hour. a. (5 marks) Write down the null and alternative hypotheses mathematically. b. (5 marks) What is the formula for and the value of the test statistic? c. (5 marks) What are the number of degrees of freedom? d. (5 marks) Is this test one or two-tailed? e. (5 marks) What is (are) the critical value(s) for the test? f. (5 marks) Do you reject or not reject the null? Briefly explain your reasoning. 12. (3 marks) What is the estimate of the population correlation coefficient between the hourly wage and education? 13. (5 marks) What is the estimate of the population covariance between the hourly wage and education? 14. (5 marks) What is unbiasedness? Your answer can be mathematical or in plain English. Explain briefly why it is a desirable property of an estimator (Note: do not use STATA to answer this.)