Prob SolvingData Analysis I
Prob SolvingData Analysis I PUAD 611
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Date Created: 09/28/15
PUAD 611GOVT 711 Fall 08 Here are three sample questions on twosample ttests from previous exams The questions are given without solutions on the first page The questions include links to the required datasets and readings I give suggested solutions on the pages that follow QUESTIONS WITHOUT SOLUTIONS General instructions Each question on this part requires you to conduct a statistical test In answering each question please follow these steps 1 identify the unit of analysis the null hypothesis the dependent variable and the independent variable 2 present separate descriptive statistics in both tabular and graphical form for each variable that you include in the test 3 conduct the appropriate test 4 identify and interpret means and pvalues 5 tell whether you reject or fail to reject H0 and 6 brie y summarize your findings in plain language 1 For this question use the mortfirmsav dataset For all people included in the dataset do men on average earn significantly more than women If so how does the gap compare to the general average difference reported in the first clause of the first sentence of the Associated Press article Also do your results demonstrate that this firm discriminates against women in determining salaries 2 For this question use the murdersav dataset Is there a relationship between a state s murder rate and whether state law allows the death penalty 3 For this question use the renalsav dataset Does the number of preoperative risk factors for cardiac surgery patients differ by gender QUESTIONS WITH SUGGESTED SOLUTIONS For this question use the mortfirmsav dataset For all people included in the dataset do men on average earn significantly more than women If so how does the gap compare to the general average difference reported in the first clause of the first sentence of the Associated Press article Also do your results demonstrate that this firm discriminates against women in determining salaries Unit of analysis employees H0 No difference in average salaries between men and women Dependent variable salary Independent variable gender Descriptive statistics are presented in tabular and graphical form below mean standard deviation minimum and maximum with a histogram for salary a continuous variable and percentages and a bar chart for gender a categorical variable Descriptive Statistics N Minimum Maximum Mean Std Deviation Current salary 474 28250 145000 4550607 16511006 Valid N Iistwise 474 14D 12n mn Frequency a Mean 455ua am an Dev 1B511EIEIEEI N 474 I I I I I I zuuuu 4n nu EDUEIEI EDUEIEI munun 12EIEIEIEI MEIEIEIEI Current salary Gender Cumulative Freque Percent Valid Percent Percent Valid Female 2 498 498 498 Male 238 502 502 1000 Total 474 1000 1000 000 500 400 Percent 300 39 200 100 I Female Male Gender Because we are comparing means for the same variable salary in two groups males and females an independent samples t test is appropriate Group Statistics Std Error nder N Mean Std Deviation Current salary Female 236 3997915 11427836 743889 Male 238 5098653 18814963 1219593 Independent Samples Test Levene39s Test for Equality ofVariances me u 0 39 95 Con dence Interval ofthe Mean Std Error Dine ence F Sig t df Sig 2tailed Difference Difference Lower Upper Current salary assumed 62834 000 7690 472 000 11007381 1431 345 138200 8194784 Equal quot3 7705 391500 000 11007381 1428 558 138160 8198777 Of the employees in this dataset men on average earn 51000 while women on average earn 40000 This difference is statistically signi cant p0 so we reject H0 We are 95 con dent that for whatever population this sample represents women on average earn between 8200 and 13800 less than men In this sample the gender gap is 399791550986530784 So these women earn on average about 784 of what men earn This is pretty close to the estimate of 80 reported in the alticle although we haven t done a test for the statistical significance of the difference This analysis does not conclusively demonstrate gender bias in pay because it does not control for other variables that may explain the difference 2 For this question use the murdersav dataset Is there a relationship between a state s murder rate and whether state law allows the death penalty Unit of analysis State H0 No relationship between a state s murder rate and whether state law allows the death penalty Dependent variable Murder rate Independent variable Death penalty allowed yesno Descriptive statistics Percentages and bar chart for the categorical variable mean standard deviation minimum maximum and histogram for the continuous variable Death penalty permitted under the law Cumulative Frequency Percent Valid Percent Percent Valid No 13 260 260 260 Yes 37 740 740 1000 Total 50 1000 1000 US States Slam penalty permitted under the IS About three quarters of US states permit the death penalty Statistics ample 2n 6 yam 5n Missing a Mean 4 77m 5m Dewatmn 2 57 Minimum 1 u Maximum 12 4 Nurder rate by state Frequency Mean 0 77m Std Dev 2 577m N5EI 239n t39n e39n a39n win Murders per100000 people 2006 The average murder rate is about 5 murders per year per 100000 people there is one outlier on high side Louisiana The appropriate test is an independent samples t test Group Statistics Death penany permmed ndert e1aw 0 Std Error u n N Mean Std Dewauon Mean 11an 1 p 1 WWW N 13 3123 17451 4840 peopte 2006 Yes 37 5 349 2 5879 4254 Independent Samples Test Mean 5m Errur 137 V2 87D 48 EIEIE e2 2256 7754 73 7846 e BEBE 73 454 3145B EIEI2 e2 2256 B444 73 5391 e 9121 The average murder rate for states with the death penalty is 53 murders per 100000 people for states with no death penalty the rate is 31 Reading the top row because the p value on the F test gt 005 we f39md that the difference is statistically signi cant p0006 lt005 Reject H0 But in a surprising result states with the death penalty actually have higher murder rates Note that this does not imply that the death penalty leads to higher murder rates The test does not account for many possible confounding variables 3 For this question use the renalsav dataset Does the number of preoperative risk factors for cardiac surgery patients differ by gender Unit of analysis Cardiac surgery patients H0 No difference in average number of preoperative risk factors for males and females Dependent variable Preoperative risk factors Independent variable Gender gender Descriptive statistics Gender is a categorical variable so a bar chart is appropriate Preoperative risk factors is a continuous variable so a histogram is appropriate gender Percmt s gender