case report

1. Estimate the probability that a customer participating in the student purchase program will default. Compute the expected profit from selling the JCN-2001 system to a university student under the existing program. Has the student purchase program been profitable? Explain and attach supporting output.

Probability that a student defaults: 40%. They make money in 60% of transactions and lose money in 40% chance of transactions

For every paid in full they make $750

for ever default they lose$1200

Expected profit per transaction:

The student purchase program has not been profitable. Although more students are paying in full than profiting, the company loses more money for every given default then they gain for every student that pays in full. When calculating the amount of students likely to default (based on previous data) and how much they are going to lose per student, and combining that with how much they are going to gain for each student that is likely to pay in full, the company does not break even. The company is expected to lose about $31.14 per transaction.

2. Based on the data, is defaulting on the computer payments independent of the university attended by the student? Show your work. (Hint: Realize that this is only a sample of data.) If there were dependence, what might be possible causes for this dependence?

Some schools have a higher probability of defaulting than other schools. School 1 and School 2 are more likely to default than the other schools. This could be because schools select students based on their certain criteria that correlate with later being able to pay in full. School 4, with the lowest chance of defaulting, might be selecting students with higher scores, and those students may be more likely to pay in full. Or, these probabilities could be due to sheer chance based on the sample size that was collected.

3. Assume that 70 is a passing score on the screening test. Estimate the probability that a student who passes the screening test will eventually default. Compute the expected profit from selling the JCN-2001 system to a university student who passes the screening test. Is the screening test used in this fashion significantly better than not using the test at all? Explain your answer and attach any supporting output.

Assume that 70 is a passing score on the screening test. Estimate the probability that a student who passes the screening test will eventually default.

Passing score =70 percent

Number of Students who pass = 86 students

Number of students who pass then default = 23 students

Probability of default among passing students = (23/86) =0.26744

probability that a student who passes the screening test will eventually default = 0.26744

Compute the expected profit from selling the JCN-2001 system to a university student who passes the screening test.

Expected profit = profit (probability of no default) + loss (probability of default)

Probability of default = 0.26744

Probability of no default = 1 – 0.26744 = 0.73256

Expected profit = 750(0.73256) -1200(0.26744)

Expected profit = 228.492

Is the screening test used in this fashion significantly better than not using the test at all? Explain your answer and attach any supporting output.

This analysis will use the expected profit as a measure to define which is better.

Calculating Expected profit without screening test.

Number of students who default = 137

Total number of students = 342

Probability of default = (137/342) = 0.4

Expected profit = profit (probability of no default) + loss (probability of default)

Probability of default = 0.4

Probability of no default = 1 – 0.4 = 0.6

Expected profit = 750(0.6) - 1200(0.4)

Expected profit without screening test = -30(loss)

Expected profit = 228.492

Improvement in expected profit = 228-(-30) = 258

The screening test is better, since it raises expected profit by $258.

The test has proven to be a profitable method of evaluating students before selling to them a computing device. Before the test, the company suffered a default rate of forty percent and consequently suffered a loss of $30 for every device they sold. The test reduces the default rate to twenty six percent and consequently raise profits to $228 for every device.

4. Can you find a better way of using the screening test that results in higher expected profits for Berkshire Computer Sales? Explain your solution and attach any relevant supporting output.

A way that Berkshire can raise their expected profits is through raising the score so that students that achieve a score of 60 or above are only allowed to participate. The reason for this is because students that have a 60 + score based on their Gpa, work experience, scholarships etc, are more likely to pay the computer in full compared to students who have a lower score

5. Make your final recommendation for the student Purchase program to Jonathan Berkshire. Include any modifications that you would make to the program and discuss the potential changes caused by these modifications. Also discuss any other issues that should be considered.

· For the future analysis , Berkshire should consider making a co-signer mandatory for all participants and then analyse whether or not that has more success than what is currently being implemented.

STEPS:

1. Identifying the business analysis questions

2. Converting business questions into statistical questions

3. Performing a descriptive analysis of the data

4. Applying formal analysis procedures

5. Developing conclusions and recommendations

6. Identifying unusual outcomes and future analysis

Sections:

· Executive Summary: 1-3 paragraphs, ** Last part written *** identify the problem, indicate your approach to solving it and concisely state conclusion

· Introduction: ~1 Paragraph, intro to the case, project scope.

· BODY: indicate how you developed your conclusions and recommendations

· Part 1: Begin with concise presentation of the question from the business perspective and explain how you conducted the analysis

· Part 2: Define the data set and specify the statistical procedures used

· Include specific statements of statistical models and hypothesis tests

· Results: Discuss the statistical results, indicating how they provide a solution to the case problem

· Include additional observations and extensions of your results

· Identify unusual outcomes, go into detail on the unexplored questions in the study (Questions for future work), might be important enough to justify another study.

· Document the additional questions and suggest how they might be answered and decide whether or not additional work should be taken

· Conclusion

Introduction:

When examining the Berkshire Computer Sales case to determine whether or not

Body:

In order to come to a conclusion as to whether or not Berkshire should continue to offer this discount program to students, we first need to to see if the company is profiting off of the student transactions. First, the probability that a student pays in full versus defaults must be determined. The probability is based on the sample of students from the five different schools that participated in the program. This data is used to predict future profits and losses. About 60% of the 342 sampled students paid in full, while about 40% did not (Table 1).

Table 1

At first glance this looks promising for the company. However, it is known that for every student that pays in full, the company makes $750. For every student that defaults, the company loses $1200. If you calculate the amount of money gained through the 205 students that paid, with the amount of money lost through the 137 students that defaulted, the expected profit per transaction is $-31.14 Calculation: (205*650)+(137*-1200). This information means that the company is expected to lose about $31.14 per transaction. Thus far, the student purchase program has not been profitable. Although more students are paying in full than profiting, the company loses more money for every given default then they gain for every student that pays in full.

When breaking the data down by school, some schools have a higher probability of defaulting than other schools. School 1 and School 2 are more likely to default than the other schools, with the probabilities of .48 and .40, respectively (Table 2). This could be because schools select students based on their certain criteria that correlate with later being able to pay in full. School 4, with the lowest chance of defaulting, might be selecting students with higher scores, and those students may be more likely to pay in full. This information could argue the point that only certain schools, those with a lower probability of students defaulting, should be offered to participate in the student purchase program. Or, these probabilities could be due to sheer chance based on the sample size that was collected, so this might not be a risk the company would want to make.

Table 2:

Final Version of Berkshire Computer Sales Case

Executive Summary

Introduction

Body

Results

Conclusion