HW02_answers_Econ_140A_2011Fall - Economics 140A Fall 2011...

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Unformatted text preview: Economics 140A Fall 2011 Professor Startz Answers to Homework 2 1. a) b) c) √ . 2. a) ∑ ̅ ∑ ̅ ̅ ̅ b) ∑ ̅ ∑ ̅ ̅ ∑ ̅∑ ̅ ̅̅̅ ∑ ̅̅̅ ∑ c) ∑ ̅ ̅ ∑ ̅∑ ̅ ̅ ∑ ̅ d) ∑ ̅ ̅ ∑ ∑ ∑ ̅̅ ∑ ̅ ̅̅ ∑ ̅ ∑ ̅̅ ̅̅ ̅̅ 3. a) The sample mean is . The sample median is the value in the middle, 2.0. The sample variance is 4. Since the data is normal, so is the mean. Since the normal is a continuous distribution, the probability of getting exactly a given value is effectively zero. 5. a) , since ̅ page 2 b) c) √ √ √ √ √ √ In general, any two variables that are linear functions of a third random variable are perfectly correlated. 6. That was fun to read. 7. a) Yes 8. Yes. This was really just practice in reading in an Excel spreadsheet. 9. 10. The output looks something like 120,000 Se r ies: WSAL_ VAL Sa mple 1 133092 O b s e r v a t io n s 1 3 3 0 9 2 100,000 Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis 60,000 40,000 20,000 29321.03 17000.00 1699999. 0.000000 47558.07 8.081066 142.1082 Jarque-Bera Probability 80,000 1.09e+08 0.000000 0 1 250001 500001 750001 1000001 1250001 1500001 The statistics were Mean= 29,321 Median = 17,000, Maximum = 1,699,999, and Minimum = 0. The first three make sense as annual income; the zero minimum is probably for people who aren’t working. page 3 11. For women the results were 60,000 Se r ie s: WSAL _ VAL Sample 1 133092 IF F E=1 O b s e r v a t io n s 6 8 7 7 8 50,000 Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis 30,000 20,000 10,000 2 1892.41 1 2000.00 1 099999. 0 .000000 3 4002.86 8 .437943 1 95.1424 Jarque-Bera Probability 40,000 1 .07e+08 0 .000000 0 1 200001 400001 600001 800001 1000001 and for men they looked like 50,000 Se r ie s: WSAL _ VAL Sample 1 133092 IF F E=0 O b s e r v a t io n s 6 4 3 1 4 40,000 Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis 30,000 20,000 3 7265.26 2 5000.00 1 699999. 0 .000000 5 7636.73 7 .272244 1 07.8389 10,000 Jarque-Bera 3 0020541 Probability 0 .000000 0 1 250001 500001 750001 1000001 1250001 1500001 Not too surprisingly, the men get paid more. (One might want to remember that the data includes people not working.) The average difference is around \$15 ,000. 11. We have ̂ ̂ ̂ ̂ ̂ (( )) page 4 12. The variance equals The standard deviation is √ . When I did it in EViews I got 0.0386, which was actually a little closer than I expected. 13. I opened the variable FE and chose Descriptive statistics/simple hypothesis tests. The results looked like this. Hypothesis Testing for FE Date: 09/26/11 Time: 16:34 Sample: 1 133092 Included observations: 133092 Test of Hypothesis: Mean = 0.500000 Sample Mean = 0.516770 Sample Std. Dev. = 0.499721 Method t-statistic Value 12.24309 Probability 0.0000 The 95 percent critical value is 1.96, but the computed test statistic is so big, 11.28, that the hypothesis would be rejected at any reason level of significance. The critical value for a 99 percent confidence interval is 2.57, so the confidence interval is . √ ...
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