statistics ss

ANONYMOUSLY MARKED

Economics

ASSIGNMENT

Semester 1 - 2018

ECMT1010 Introduction to Economic Statistics

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Further information on academic honesty, academic dishonesty, and the re- sources available to all students can be found on the academic integrity pages on the current students website: https://sydney.edu.au/students/academic-integrity.html.

You are required to submit Compliance statement for all work submitted to the University for assessment.

INSTRUCTIONS

Due: 1.00pm Friday 8 June 2018

1. Enter your answers using the Word template available under the Canvas module ‘Assignment’.

2. The assignment is anonymously marked. Make sure you fill in your University of Sydney SID (student number) using the box in the top-right corner of the template. Do not put your name on your answers.

3. Use your assigned data set (available under the Canvas module ‘Assignment’). See under Specific instructions on the next page. Make sure you fill in your data set number (#) using the box provided in the template. Use of the wrong data set will be subject to a 50% penalty.

4. Submit the electronic copy of your answers through Turnitin by following the instructions under the Canvas module ‘Assignment’. Late submissions will be penalized according to Faculty of Arts and Social Sciences rules.

5. The assignment has a maximum of 20 marks and accounts for 10% of your final grade. Maxi- mum marks are indicated for each question.

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Aim: This assignment illustrates the use of various statistical techniques in an economic applica- tion. You will use software (e.g., Excel, StatKey) to analyze real data on wage rates for 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.

Specific instructions:

• 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).

• Answer all questions. Show all numerical answers to 3 decimal places. Carry out all tests using a 1% level of significance.

Hint: If you convert your Excel data file into csv format, you can upload it to StatKey using ‘Upload File’.

QUESTIONS

1. Produce two separate histograms: one for the wage rates of males, the other for the wage rates of females. Use an appropriate number of bins for your histogram and label the axes. [2 marks]

2. Compare the shapes of the histograms for male and female wage rates by commenting on location, dispersion and skewness of the two histograms. [2 marks]

It is well-known that, on average, men are paid more than women. To investigate this claim statistically, you will use a hypothesis test.

3. Set up the null and alternative hypotheses. Make sure to define your notation clearly. [2 marks]

4. Using the ‘Shift Groups’ randomization method in Statkey, produce a dotplot of the random- ization distribution (with 5,000 randomization samples) of the appropriate sample statistic. Carry out the hypothesis test using the randomization distribution and state your conclusion. [2 marks]

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5. Verify that the Central Limit Theorem applies. Carry out the same hypothesis test using the appropriate approximation and state your conclusion. [2 marks]

6. Would you be comfortable concluding from the hypothesis tests that men are paid more than women purely as a consequence of their gender? Explain. [2 marks]

It is also interesting to investigate the effect of years of education on wage rates. Suppose we want to estimate separate regression equations for males and females.

7. Write down the population regression model for females, taking care to define your notation clearly. [2 marks]

8. Using appropriate software, estimate one regression for males and one regression for females. Use the table provided in the template to report your regression results. [2 marks]

9. Give a one-sentence interpretation of the regression slope estimate for females. Compare the regression slope estimates for females and males. [2 marks]

10. Test whether years of education is an effective predictor of female wage rates in the regres- sion model you have estimated in question 8. Make sure to report your null and alternative hypotheses, the test statistic, decision rule, and conclusion to the test. [2 marks]

Due: 1.00pm Friday 8 June 2018

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