STA 6126 – Exam 3 – Fall 2005 PRINT Name ______________STA 6126 – Exam 3 – Fall 2005 PRINT Name ______________1. Interchanging the rows (levels of the independent variable) in a contingency table will:a) Effect the chi-square statistic, but not the numbers of concordant/discordant pairsb) Effect the numbers of concordant/discordant pairs, but not the chi-square statisticc) Effect both the chi-square statistic and the numbers of concordant/discordant pairsd) Effect neither the chi-square statistic or numbers of concordant/discordant pairs2. A study considered the effect of executive succession circumstances in small companies. Of 19 companies with planned successions (e.g. long-planned retirement of chief executive), 12 had undiminished profitability and 7 had diminished profitability. Of 17 companies without planned successions (e.g. untimely death or legal problems of chief executive) 3 had undiminished profitability and 14 had diminished profitability. Which method of analysis would be most appropriate for thisstudy.a) McNemar’s Testb) Linear Regressionc) Gamma / Kendall’s Taud) Fisher’s Exact Test3. Two researchers conduct a chi-square test with contingency tables of the exact same dimensions (say r=2 and c=3). Jack sampled 100 individuals from each of the 2 populations and Jill sampled 200 individuals from each population. They obtained theexact same conditional distributions for each of the two populations (although the conditional distribution for population 1 is not identical to the conditional distributionfor population 2). a) Their chi-square statistics will be the sameb) Jack’s chi-square statistic will be twice as large as Jill’sc) Jill’s chi-square statistic will be twice as large as Jack’sd) Jill’s chi-square statistic will be 4 times as large as Jack’se) Jack’s chi-square statistic will be 4 times Jack’s chi-square statistic will be twice as large as Jill’s as large as Jill’s4. A linear regression model is fit, relating the general merchandise sales (in millions) in cities to their population (in 1000s). A model is fit and the estimated regression equation is 1.0+0.80x. As x increases by 1 unit (1000 people), general merchandise sales increase by approximately?a) $0.80 b) $8000 c) $800,000 d) $1.80 e) $8005. A researcher is interested in comparing married men’s and women’s attitudes toward same-sex marriage. A random sample of 1000 married couples is obtained. Of these couples, both the male and female opposed it for 200 of the couples, both the maleand female favored it for 300 of the couples. The male favored and the female opposed it for 260 of the couples. For the remaining couples the male opposed and the female favored.(a) Give the test statistic for testing whether the proportions of males and females favoring same sex marriage are the same (H0) or differ (HA)(b) What do we conclude at the =0.05 significance level? Do not conclude the proportions differ Conclude a higher proportion of males favor same-sex marriage Conclude a higher proportion of females favor same-sex marriage6. A study compared St. John’s Wort (SJW), Sertraline, and placebo in patients with major depressive disorder. Patients were assigned at random to one of the three treatments and were classified as having any response or no response. The contingency table is given below.Trt \ Outcome Any Response No Response TotalSJW 43 70 113Sertraline 53 56 109Placebo 50 66 116Total 146 192 338a) Give the conditional distributions for each treatment and overall.Trt \ Outcome Any Response No Response TotalSJW 100%Sertraline 100%Placebo 100%Total 100%b) Give the expected count for Any Response among SJW patients under the hypothesis of no association between response and treatment.7. A study considered the association between governors’ strength and their control overstate agencies. State administrators were classified by the strength of their state governor (very weak, weak, moderately strong, strong) and were asked who had control over their agency (legislature, about equal between legislature and governor,governor). The following table contains the measures gamma and Kendall’s tau basedon this sample. Symmetric Measures ValueAsymp.Std.Error(a)Approx.T(b) Approx. Sig.Ordinal by Ordinal Kendall's tau-b.177 .028 6.250 .000Gamma.255 .040 6.250 .000N of Valid Cases865 a Not assuming the null hypothesis.b Using the asymptotic standard error assuming the null hypothesis.Obtain a 95% confidence interval for the true (population) value of Kendall’s tau. 8. A study considered the occurrence of upholstery in households in Philadelphia during 4 time periods. The following table gives a cross-tabulation of period by upholstery for samples of households within the periods.PERIOD * UPHOLSTE CrosstabulationCount UPHOLSTETotalNo YesPERIOD161 19 80268 14 82364 18 82453 27 80Total246 78 324a) Give the expected number of Yes in Period 1 under the hypothesis that upholstery occurrence is independent of period.b) Give the contribution for that cell to the chi-square