Data Analysis Mba

1. Kate Denney was the Executive Vice President of Human Resources at a major Canadian financial institution. She had recently received a complaint from the Human Rights Commission of Ontario that suggested that the company's current compensation policy discriminated against women. Kate was interested in the answers to a number of managerial questions:

i) Does there appear to be any differences in the salary levels of men and women in her organization?

ii) The company has had an aggressive program to hire more women over the past 5-10 years. Could the apparent differences in salary between men and women be explained by the fact that most men have been with the company longer? Is there any relationship between salary level and years of experience?

iii) One of Kate's male subordinates indicated that he thought that the real reason for the salary differences was the fact that women were primarily employed in lower paying clerical jobs and men tended to be employed in higher paying managerial jobs. Kate wondered if this might explain the salary differences between men and women?

Kate decided to collect data on 80 employees (40 women and 40 men) of the company to shed some light on this matter. She collected data on the current salary (in $000) and the total years of employment with the company, which ranged from 1 to 17 years.

a) Is this a time series or cross-sectional study? Explain your answer.

b) What statistical questions should she ask to answer the three managerial questions?

c) Does the information in Tables 1 and 2 shed any light on the questions raised in the complaint by the Human Rights Commission? Do you think there is any discrimination? Explain.

d) What is the relationship between the current salary and years of experience for men and women in the company? Explain what this means. Use Figures 2 and 3 and Tables 3 and 4 to answer this question. Do you see anything unusual in the graphs?

e) Consider the Graphs in Figure 3 and 4. These graphs represent the frequency distributions for the current salary for women and men in classes of $10,000, i.e. 1-10, 11-20, etc. What can you tell me about the shape of these distributions? Are they normally distributed? If not, what do the distributions suggest with regard to the salary levels?

2. Gilbey Canada Inc., a producer of alcoholic beverages, operates four bottling lines. Each line fills bottles of varying sizes with different products. The bottling line represents a continuous process with change-over between different products or bottle size runs. The basic bottling process begins with the emptying of bottles from their respective cardboard cases using an uncasing machine. Cases generally contain 12 or 24 bottles, depending on bottle size and product. Bottles are then sent down the production line via a conveyer belt. The second stage consists of filling the bottles with the appropriate product using a filler machine. Next, the bottles are sealed with either a plastic or metal screw-on cap using a capper machine. At this point, labels are placed on the bottles using a labeller machine. The final stage of the process consists of UPC coding and packing the bottles back into the cases using a case packer machine. Once the process is complete, the cases are sent to the warehouse from where they are shipped to customers. The size of each batch will vary depending upon the size of order placed by the customer. Order size is measured by run length, which is the time in hours of the production run. A study was undertaken to analyze the efficiency of bottling line #3. Efficiency is:

the ratio of the ideal production time taken to produce a specified number of cases to the actual amount of time it took to produce this number of cases, including the downtime due to equipment malfunction, etc. expressed as a percentage.

The manager of the plant asks you to undertake a study to determine the relationship between the efficiency of the bottling process and the order size or run length. You collect data from the last 56 production runs and develop a regression model that attempts to identify the nature of the relationship.

a) Is this a time series or cross-sectional study? Explain your answer.

b) Consider the consider the descriptive statistics in the output in Table 1 and the regression model outlined in Table 2. What is the relationship between efficiency and run length? How good is this model?

c) Suppose you had a new order which suggested that the run length would be 75 hours. What is the expected level of efficiency for this order? Do you have much confidence in this estimate?

d) Is the model developed for this situation valid? Have the four assumptions of simple linear regression been met?

3. Rob Wilson is Executive Vice President of Vancouver Island Forest Products, a major supplier of softwood lumber to the American market. The company had a net profit of $2 Million on total revenue of $50 Million in 2004(4% of revenue). The company is currently working at full capacity. Rob is excited about the anticipated growth in the market for softwood lumber following the major disaster created by Hurricane Rita in Texas. He is giving some thought to a major expansion of his existing mill on the Island in order to ramp up output to meet the projected growth in the market. He has two options for expansion as follows:

* Adding 40% to their existing capacity (and revenues) by buying new equipment at a cost of $20 Million.

* Doubling their capacity (and revenues) by buying out a competitor at a cost of $35 Million.

One major hurdle to the full implementation of Rob's plans is the current import duty of 28% on all US sales imposed by the US Government. This duty has cut directly into Rob's profits resulting in a reduction in net profits for 2004 of 28% of revenue. Rob has noticed some recent movement by the US Government on the existing duty. There is a possibility that the duty will be eliminated completely for 2006. Another scenario would have the duty reduced to 10%. Rob has consulted with colleagues in the industry and has concluded that there is a 20% chance the duty will be completely eliminated, a 30% chance that it will be set at 10% and a 50% chance it will remain at 28%.

Vancouver Island Forest Products does all of it's capital planning on a 5 year time horizon, that is, they need to recover all capital investments within a 5 year period. Assume that the company can sell all of its output to the US market under both expansion scenarios, there are no price or cost increases and that all of any reduction in duty