Problems in book:Chapter 16 (page 683): 16.19, 16.24-16.27Problems not in book:Marital status and jo

Problems in book:Chapter 16 (page 683): 16.19, 16.24-16.27Problems not in book:Marital status and job level. We sometimes hear that getting married is good for yourcareer. The Table below presents data from one of the studies behind this generalization.To avoid gender effects, the investigators looked only at men. The data describe the maritalstatus and the job level of all 8235 male managers and professionals employed by a largemanufacturing firm.1 The firm assigns each position a grade that reflects the value of thatparticular job to the company. The authors of the study grouped the many job grades intoquarters. Grade 1 contains jobs in the lowest quarter of the job grades, and Grade 4contains those in the highest quarter. Exercises 1 – 8 are based on these data.Marital StatusSingle Married Divorced Widowed Totals Job 1 58 874 15 8 955 Grade 2 222 3,927 70 20 4,2393 50 2,396 34 10 2,4904 7 533 7 4 551Totals 337 7,730 126 42 8,2351. Marginal distributions. Give (in percents) the two marginal distributions, for maritalstatus and for job grade. Do each of your two sets of percents add to exactly 100%?If not, why not?2. Percents. What percent of single men hold Grade 1 jobs? What percent of Grade 1jobs are held by single men?3. Conditional distribution. Give (in percents) the conditional distribution of job gradeamong single men. Should your percents add to 100% (up to roundoff error)?4. Marital status and job grade. One way to see the relationship is to look at who holdsGrade 1 jobs.a. There are 874 married men with Grade 1 jobs, and only 58 single men withsuch jobs. Explain why these counts by themselves don’t describe therelationship between marital status and job grade.b. Find the percent of men in each marital status group who have Grade 1 jobs.Then find the percent in each marital group who have Grade 4 jobs. What dothese percents say about the relationship?5. Give a 99% confidence interval for the proportion of men who hold grade 3 jobs.1Sanders Korenman and David Neumark, “Does marriage really make men more productive?” Journal of HumanResources, 26 (1991), pp. 282–307.Homework #10Business Statistics with Computer Applications II6. Carry out the chi–square test for the hypothesis of no difference between job gradeand marital status. What would be the mean of the test statistic if the null hypothesiswere true? The value of the statistic is so far above this mean that you can see atonce that it must be highly significant. What is the approximate P–value?7. Look at the terms of the chi–square statistic and compare observed and expectedcounts in the cells that contribute the most to chi–square. Based on this and yourfindings in part 4(b), write a short comparison of the differences in job grade andmarital status.8. Association is not causation. The data show that single men are more likely to holdlower-grade jobs than are married men. We should not conclude that single men canhelp their career by getting married. What lurking variables might help explain theassociation between marital status and job grade?