Sample problems for the midterm. At least 50% of the exam will be selected from these questions (possibly with minor modifications). 1. The National Opinion Research Center conducted the 1974 General Social Survey (GSS). One of the questions asked that year was, "Do you agree with this statement? -- Women should take care of running their homes and leave running the country up to men." Male interviewees answered as shown in Table 1-m, which is then entered into Stata in Table 1-s. TABLE 1-m. ------------------------------------------------------------ -- Response --- Sex of respondent Education (yrs) Agree Disagree Male 0-8 72 47 9-12 110 196 13+ 44 179 ------------------------------------------------------------ TABLE 1-s. ------------------------------------------------------------ . tabi 72 47\110 196\44 179 | col row | 1 2 | Total -----------+----------------------+---------- 1 | 72 47 | 119 2 | 110 196 | 306 3 | 44 179 | 223 -----------+----------------------+---------- Total | 226 422 | 648 Pearson chi2(2) = 57.0873 Pr = 0.000 a) Calculate the (joint) probability that an individual with 13 years or more of education and who disagrees with the question will appear in the sample. b) Calculate the conditional probabilities of agreement given level of education. c) What is the marginal probability of agreeing with the statement? d) What null hypothesis does the chi-squared statistic test? e) What does the chi-squared statistic lead us to conclude about education and agreement with this question? 2. BRIEFLY describe a scenario which would result in Table 1-m, and which illustrates: a) Poisson sampling b) Product-multinomial sampling c) Multinomial sampling d) Hypergeometric sampling [Extra credit!] TABLE 3. Homicides, by type of assault, 1970 ------------------------------------------------------------ Race Sex Firearm Cutting of victim of victim /explosive /Piercing TOTAL White Male 3910 808 4718 Female 1050 234 1284 Black Male 5218 1385 6603 Female 929 298 1227 TOTAL 11107 2725 13832 3. a) For white victims, is there a relationship between type of assault and sex of the victim? [Hint: what would be an appropriate measure of association here?] b) For black victims, is there a relationship between type of assault and sex of the victim? c) Interpret the results of this logistic regression based on the data above: . list race sex firearm n in 1/4 race sex firearm n 1. 1 1 3910 4718 2. 1 2 1050 1284 3. 2 1 5218 6603 4. 2 2 929 1227 . blogit firearm n sex race Logit Estimates Number of obs = 13832 chi2(2) = 43.34 Prob > chi2 = 0.0000 Log Likelihood = -6842.1162 Pseudo R2 = 0.0032 ------------------------------------------------------------------------------ _outcome | Coef. Std. Err. z P>|z| [95% Conf. Interval] ---------+-------------------------------------------------------------------- sex | -.138384 .054564 -2.536 0.011 -.2453274 -.0314405 race | -.2731326 .0439379 -6.216 0.000 -.3592494 -.1870158 _cons | 2.002441 .1018308 19.664 0.000 1.802857 2.202026 ------------------------------------------------------------------------------ 4. Another logistic regression model calculated for the data above is given below. Use it to conduct a likelihood ratio test for the effect of race, given sex, on the chances of a homicide caused by firearms. . blogit firearm n sex Logit Estimates Number of obs = 13832 chi2(1) = 4.22 Prob > chi2 = 0.0399 Log Likelihood = -6861.6739 Pseudo R2 = 0.0003 ------------------------------------------------------------------------------ _outcome | Coef. Std. Err. z P>|z| [95% Conf. Interval] ---------+-------------------------------------------------------------------- sex | -.1123727 .054319 -2.069 0.039 -.2188359 -.0059094 _cons | 1.538449 .0681704 22.568 0.000 1.404837 1.67206 ------------------------------------------------------------------------------