illustrates the use of various statistical techniques in an economic application

Order Description
Aim: This assignment illustrates the use of various statistical techniques in an economic application. You will use software (e.g., Excel, StatKey) to analyze real
data to investigate the relationship between wage rates and level of education as well as differences between males and females.
Data description: The monthly current population survey by the U.S. Department of Commerce covers over 50,000 households and serves as the basis for U.S. employment
and unemployment statistics. Data are collected on a number of individual characteristics as well as employment status. You are assigned a data set containing 100
randomly-selected employed workers from the May 1978 survey. Your data extract contains information on wage, gender, and years of education for 100 employed workers
randomly extracted from the main sample.
Your data set is available in the Excel spreadsheet Wages#.xlsx (where # is the last digit of your SID). It contains 4 columns and 101 rows. The first row contains the
variable names; the remaining 100 rows contain the information for each of the 100 workers in your sample. The Obs column identifies each worker (and can be ignored),
WAGE is each worker’s hourly wage rate (in 1978 U.S. dollars), FEM is gender (0 = male, 1 = female), and EDUC is years of education (including primary, secondary and
tertiary education, as applicable).
Hint: You can import the Excel file into StatKey using the ‘Upload File’ facility after first con- verting the file into csv format.
Specific instructions: Answer all 9 questions below. Show all numerical answers to 3 decimal places. Carry out all tests using a 1% level of significance.

QUESTIONS
1. Using appropriate software, produce a scatterplot of wage rates against years of education using your sample. Compute the sample correlation and comment on whether
you agree with Amy. [2 marks]

2. Test whether there is a statistically significant linear association between wages and years of education, showing all your steps and clearly stating your
conclusion. [4 marks]

Amy sets up a regression model to investigate whether wage rates depend positively on years of education.
3. Write down Amy’s regression model taking care to define your notation clearly. Using appropriate software, estimate the regression model and report your results. [2
marks]

4. Use your regression results to give a one-sentence interpretation of the regression slope estimate. [2 marks]

5. Test whether years of education is an effective predictor of wage rates in the regression model you have estimated in question 3. Make sure to report your null and
alternative hypotheses, the test statistic, decision rule, and conclusion to the test. [2 marks]
Amy suspects that men are paid more than women, on average. To investigate this claim statistically, you will use a hypothesis test.

6. Set up the null and alternative hypotheses taking care to define your notation clearly. [2 marks]

7. Using the ‘ShiftGroups’ randomization method in Statkey, produce a dot plot of the randomization distribution (with at least 2,000 samples) of the appropriate
sample statistic. Carry out the hypothesis test using the randomization distribution and state your conclusion. [2 marks]

8. Verify that the Central Limit Theorem applies in this case, carry out the same hypothesis test using the appropriate approximation and state your conclusion.
Briefly compare these results to your findings in question 7. [2 marks]

9. Does the evidence suggest that men are paid more than women as a consequence of their gender? Explain. [2 marks]