ECMT1010 Written Assignment (2015, Semester 2) Lecturers: Tim Fisher General instructions All students are required to submit an authorized statement of compliance with all work submitted to the University for assessment, presentation or publication. A statement of compliance certifies that no part of the Work constitutes a breach of Academic Dishonesty and Plagiarism Policy. The University is opposed to and will not tolerate academic dishonesty or plagiarism, and will treat all allegations of academic dishonesty or plagiarism seriously. This assignment is worth a total of 20 marks and counts towards 10% of your final grade. Maximum marks are indicated for each question. The assignment must be submitted in BOTH hard copy AND electronic copy by 1.00pm Friday 30 October 2015. Deposit your hard copy in the box marked \"ECMT1010\" on level 2, Merewether Building. Submit the electronic copy through Blackboard using Turnitin by following the instructions under \"Assignment submission\". Late submissions will be penalized at the rate of 2% per day. Complete and attach the individual assessment cover sheets as the front page of BOTH the hard copy and electronic copy submissions. The cover sheet is available on Blackboard (under \"Assignments\"). Each student will use one of 10 different data set available for download under \"Assignment Data\" on Blackboard. Use the data set with the number equal to the last digit of your SID. Use of the wrong data set will be penalized. Keep your answers concise and confine your submission to no more than 5 pages (including cover sheet) using at least a 12pt font and clearly legible graphs. Anything over the 5-page limit will not be marked. Messy work or unclear images will be penalized. Where written explanations are required, you should provide no more than 40 words. Excessive verbosity will be penalized. 1 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 education levels and wages as well as male-female differences in wages. Data description: You are each assigned a data set consisting of 100 randomly-selected employed workers from the May 1978 current population survey conducted by the U.S. Department of Commerce. The monthly survey covers over 50,000 households and it 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. 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 column heading Obs 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 (i.e., total years of schooling). Hint: You can import the data into StatKey by copy-and-paste. To do this, copy any required columns in the data set to a new spreadsheet. Now with all the required columns side-by-side, copy and paste them all at once to the text-input region in the \"Edit Data\" pop-up window. Specific instructions: Answer all 10 questions. Show all numerical answers to 3 decimal places. Carry out all tests using a 1% level of significance. Questions 1. Using appropriate software, produce two separate histograms for the wage rates of males and females. Use an appropriate number of bins for your histogram and remember to label the axes. Describe and compare the shape of the histograms, including a discussion of central location, dispersion, and skewness. [2 marks] 2. Using appropriate software, produce a scatterplot of wage rates against years of education using your sample. Compute the sample correlation and comment on the degree of association. No need to show your computational steps. [2 marks] 3. Carry out a t-test for linear association between wage rates and years of education. Make sure you report your null and alternative hypotheses, the test statistic, decision rule, and conclusion to the test. [2 marks] 2 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 your notation clearly. [2 marks] 5. Using appropriate software, estimate the regression model and report your results. Give a one-sentence interpretation of the slope estimate. [2 marks] 6. Test the effectiveness of the regression model you have estimated in question 5, using a t-test. Make sure you 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, carry out a hypothesis test by constructing a randomization distribution as follows. 7. Set up the null and alternative hypotheses taking care to define your notation clearly. [2 marks] 8. Using Statkey with the \"shift groups\" randomization method, produce a dotplot of the randomization distribution (with at least 10,000 samples) of the appropriate sample statistic. Comment on its shape (e.g., central location, symmetry). [2 marks] 9. With reference to the randomization distribution in question 8, carry out the hypothesis test two ways, one using the randomization distribution and another using the appropriate approximation supported by a Central Limit Theorem. What do you conclude about Amy's claim? [2 marks] 10. Elaborate on your conclusion in question 9. In particular, do you think men and women are paid differently due to their gender difference? Explain. [2 marks] Remember to submit the assignment along with a completed cover sheet in front. Please submit BOTH a hard copy and an electronic copy. DUE: 1.00pm Friday 30 October 20151 3 Obs WAGE FEM 9 1.43 19 3.5 33 5.25 36 8.63 40 3.5 42 5.14 48 4.75 60 8.23 64 3.75 68 3.31 77 3.25 81 8 89 3.65 91 3.75 95 1.96 97 8.5 114 12.5 117 3.65 121 2.85 131 3.38 133 5.83 140 6.72 146 4 158 9 162 3.75 169 4.24 170 4.25 187 6.88 188 7.25 189 4.75 190 8.75 191 7.5 196 6.4 197 0.92 199 5 203 3.12 211 9.54 215 8.82 217 11.11 221 8 223 3.5 232 5.61 233 4.6 234 3 239 3.6 242 3.85 246 7.25 EDUC 1 0 1 1 1 0 0 0 0 0 1 0 1 1 1 0 0 1 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 1 0 1 1 0 16 6 8 12 16 12 14 18 8 12 12 10 16 12 18 8 14 7 12 12 16 17 10 12 16 13 12 14 16 12 12 11 8 9 10 12 16 16 12 11 14 14 12 13 15 12 16 258 264 281 282 287 288 295 297 321 324 328 335 336 343 348 352 361 362 363 365 372 377 378 381 383 385 387 391 401 402 416 425 436 438 441 444 450 453 457 463 471 499 502 508 509 510 511 514 5 2.8 5.25 5.62 2.85 4.56 15 8.33 5 6.25 5.71 3.2 5.07 9 12.09 5 5 5.75 5.1 5 5.62 4.63 4 6.5 5.65 4.25 3.54 4 5.2 7 5 7.7 3.15 12.5 4.2 2.65 7.9 4.75 6 2.8 4.5 8 11.08 7.75 5 7.5 2.64 10 1 1 1 0 1 0 0 0 0 0 1 1 0 0 0 0 1 1 0 1 1 1 0 1 0 1 1 0 0 1 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 12 16 12 12 8 7 18 16 12 11 14 10 12 16 18 7 12 13 12 12 12 12 12 17 10 12 12 12 8 14 18 12 4 11 12 11 18 12 11 9 13 12 14 12 10 17 13 18 518 524 525 529 543 2.75 5 13.25 5.75 2.5 1 1 0 1 1 12 12 17 17 13