QUESTION 1---

Financial advisors offer many types of advice to customers, but they generally agree that one of the best things people can do is invest as much as possible in tax-deferred retirement plans. Not only are the earnings from these investments exempt from income tax (until retirement), but the investment itself is tax-exempt. This means that if a person invests, say, $10,000 income of his $100,000 income in a tax-deferred retirement plan, he pays income tax that year on only $90,000of his income. This is probably the best method available to most people for avoiding tax payments. However, which group takes advantage of this attractive investment opportunity: everyone, people with low salaries, people with high salaries, or who?

The file Retireplan.xls lets you investigate this question. It contains data on 194 couples: number of dependent children, combined annual salary of husband and wife, current mortgage on home, average amount of other (nonmortgage) debt, and percentage of combined income invested in tax-deferred retirement plans (assumed to be limited to 15%, which is realistic). Using correlations, scatterplotts and regression analysis, what can you conclude about the tendency to invest in tax deferred retirement plans in this group of people?

<see retireplan.xls>

QUESTION 2---

The Artsy Corporation has been sued in the US Federal Court on charges of sex discrimination in employment under Title VII of the Civil Rights Act of 1964. The litigation at contention here is a class-action lawsuit brought on behalf of all females who were employed by the company, or who had applied for work with the company between 1979 and 1987. Artsy operates in several states, runs four quite distinct businesses, and has many different types of employees. The allegations of the plaintiffs deal with issues of hiring, pay, promotions, and other "conditions of employment."

In such large class-actions lawsuits, it has become common for statistical evidence to play a central role in the determination of guilt or damages. In an interesting twist in legal procedures, a precedent has developed in these cases that plaintiffs may make a prima facia case purely in terms of circumstantial statistical evidence. If that statistical evidence is reasonably strong, the burden of proof shifts to the defendants to rebut the plaintiff’s statistics with other data, other analysis of the same data, or non-statistical testimony. In practice statistical arguments often dominate the proceedings of such Equal Employment Opportunity (EEO) cases. Indeed, in this case the statistical data used as evidence filled numerous computer tapes and the supporting statistical analysis comprised thousands of pages of printouts and reports. We work here with a typical subset that pertain to one contested issue at one of the companies locations.

The data in the file Artsy.xls relate to the pay of 256 employees on the hourly payroll at one of the company’s production facilities. The data include an identification number (id) that would permit us to identify by name or social security number; the person’s gender (Gender), where 0 denotes female and 1 denotes male; the person’s job grade in 1986 (Grade); the length of time (In years); the person had been in that job grade as of December 31, 1986 (TInGrade); and the person’s weekly pay rate as of December 31, 1986 (Rate). The data permit a statistical examination of one of the issues in the case-fair pay for female employees. We deal with one of 3 paid classes of employees – those on the bi-weekly payroll and at one of the company’s location at Pocahantus, Maine.

The plaintiff’s attorneys have proposed settling the pay issues in the case for these groups of female employees for a "back pay" lump payment to female employees of 25% of their pay during the period 1979 to 1987. It is our task to examine the data statistically for evidence in favor of, or against, the charges. We are to advise the lawyers of the company on how to proceed. Consider the following issues as they have been laid out to us by the attorney representing the firm:

1. Overall, how different is pay by gender? Are the differences in pay statistically significant? Does a statistical significance test have meaning in a case like this? If so, how should it be performed? Lay out as succinctly as possible the arguments that you anticipate the plaintiff’s will make with this data set.
2. The company wishes to argue that a legitimate explanation of the pay rate differences may be the difference in job grades. (In this analysis, we will tacitly assume that each person’s job grade is, in fact, appropriate for him or her even though the plaintiff’s attorneys have charged that females have been unfairly in the lower grades. Other statistical data not available here are used in the analysis.) The lawyers asked, "Is there a relatively easy way to understand, analyze, and display the pay differences by job grade? It is easy enough that it could be presented to an average jury without confusing them?" Again, use the data to anticipate the possible arguments of the plaintiffs. To what extent does job grade appear to explain the pay rate differences between the genders? Propose and carry out appropriate hypothesis tests or confidence intervals to check whether the differences in pay between genders is statistically significant within each of the grades.
3. In the actual case, the previous analysis suggested to the attorney’s that differences in pay rates are due, at least in part, to differences in job grades. They had heard that in another EEO case, the dependents of pay rate on job grade had been investigated with regression analysis. Perform a simple linear regression of pay rate on job grade for them. Interpret the results fully. Is the regression significant? How much of the variability in pay does job grade account for? Carry out a full check of the quality of your regression. What light does this shed on the pay fairness issue? Does it help or hurt the company? Is it fair to the female employees?
4. It is argues that seniority within a job grade should be taken into account because the company’s written pay policy explicitly calls for the consideration of this factor. How different are times in grades by gender? Are they enough to matter?
5. The Artsy legal team wants an analysis of the simultaneous influence of grade and time in grade on pay. Perform the multiple regression of pay rate versus grade and time in grade. Is the regression significant? How much of the variability in pay rates is explained by this model? Will this analysis help your clients? Could the plaintiff’s effectively attack it? Consider residuals in your analysis of these issues.
6. Organize your analysis and conclusions in a brief report summarizing your findings for your client, The Artsy Corporation. Be complete but succinct. Be sure to advise them on the settlement issue. Be as forceful as you can be "The Artsy case" without misusing the data or statistical theory. Apprise your client of the risks they face by developing the forceful and legitimate counter argument the females plaintiffs could make.

Price: $24.79

Solution: The downloadable solution consists of 9 pages, 1579 words and 11 charts.
Deliverable: Word Document