School of Economics
ASSIGNMENT
Semester 1 - 2024
ECMT1010 Introduction to Economic Statistics
Due: 11.59PM Friday 17 May 2024
Instructions
i. Review the entries for ‘Late submission’, ‘Special consideration’, and ‘Academic integrity’ in the ECMT1010 unit of study outline.
ii. Enter your answers using the Word template available at the ECMT1010 Canvas module ‘Assignment’ .
iii. Save your answers as a .PDF file named 123456789.pdf where 123456789 is your 9-digit University of Sydney SID. Do not put your name on your answers. Do not include a cover sheet.
iv. Submit a .PDF of your answers at the ECMT1010 Canvas module ‘Assignment’. Work sub- mitted after 11.59PM Friday 17 May 2024 is subject to a penalty of 1 mark (5% ) per calendar day late. Work submitted after 11.59PM Monday 27 May 2024 will receive a mark of 0.
v. Your assigned data set (see below) is available at the ECMT1010 Canvas module ‘Assign- ment’. Enter your data set number (#) using the box provided in the Word template. Use of the wrong data set is automatically reported to the Educational Integrity Coordinator, Faculty of Arts and Social Sciences.
vi. There are 10 questions worth 2 marks each for a maximum of 20 marks. Answer all ques-tions. The assignment is anonymously graded (provided you don’t put your name on it).
vii. Show numerical answers to 3 decimal places. Carry out all tests at a 5% level of significance.
viii. When communicating statistical results, it is important to be accurate and concise. Keep your comments, conclusions, comparisons, etc., to one or two sentences. Excessively long responses indicate a lack of understanding and will be penalised accordingly.
Aim: The assignment uses Excel and StatKey to analyze economic data.
Data description: Your assigned data set contains 100 randomly-selected workers from the May 1978 current population survey conducted by the U.S. Department of Commerce. The data con- tain information on wage, gender, and years of education.
• Your assigned data set is available at the Canvas module ‘Assignment’ in the Excel file Wages#.csv (where # is the last digit of your SID).
• The first row contains the variable names; the remaining rows contain the data. 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 each worker’s gender (0 = male, 1 = female), and EDUC is years of education (i.e., total years of schooling).
QUESTIONS
1. Use Statkey to produce two separate histograms for the wage rates of males and females, respectively. Use an appropriate number of bins for your histogram and remember to label the axes. Describe and compare the shape of the histograms, including the central location, dispersion and skewness. [2 marks]
2. Use Excel to produce a scatterplot of wage rates against years of education, remembering to label the axes. Compute the sample correlation and comment on the degree of association between years of education and wages. [2 marks]
3. Carry out a t-test for linear association between wage rates and years of education. List your notation, the null and alternative hypotheses, the test statistic, decision rule, and conclusion to the test. [2 marks]
Amy believes that wage rates are a linear function of years of education. She sets up a regression model to investigate her belief formally.
4. Write down Amy’s regression model taking care to define the notation clearly. [2 marks]
5. Use Excel to estimate the regression model. Report your regression results. Give a one- sentence interpretation of the slope estimate. [2 marks]
6. Test the effectiveness of your estimated regression model, using a t-test. List your notation, the null and alternative hypotheses, the test statistic, decision rule, and conclusion to the test. [2 marks]
Amy is certain that men were paid more than women, on average, in 1978. To investigate this claim, follow the steps below.
7. Set up Amy’s null and alternative hypotheses taking care to define your notation clearly. [2 marks]
8. Using Statkey, produce a dotplot of the randomization distribution of the appropriate sample statistic (with at least 5,000 randomization samples). Comment on its shape (e.g., central location, degree of symmetry, etc.). [2 marks]
9. Now carry out the hypothesis test two ways: one using the randomization distribution, and another using the approximation supported by a Central Limit Theorem. Explain whether the test results support the claim that men were paid more than women, on average, in 1978. [2 marks]
10. Elaborate on your conclusion to the hypothesis test results. In particular, do you think men and women are paid differently due to the gender difference? Explain. [2 marks]