## Business Statistics assignment question

Question Description

## Question in Business Statistics

Every year, millions of high school students apply and vie for acceptance to a college of their choice. For many students and their parents, this requires years of preparation, especially for those wishing to attend a top-ranked college. In high schools, students usually work with college advisors to research different colleges and navigate the admissions process.

Elena Sheridan, a college counselor at Beachside High School, is working with 14 students who are interested in applying to the same selective four-year college. She is asked by her school principal to prepare a report that analyzes the chances of the 14 students getting accepted into one of the three academic programs. In a database of past college applicants available to counselors at Beachside High, predictor variables include the student’s high school GPA, SAT score, and the Male, White, and Asian dummy variables that capture the student’s sex and ethnicity. Elena also wants to know whether or not the parents’ education can be a predictor of a student’s college acceptance and plans to include the education level of both parents in her analysis.

Based on her conversation with college counselors at other high schools, she believes that high school students with a GPA of 3.5 or above have a much higher chance of getting accepted into a selective college. She also thinks that SAT scores of at least 1,200 substantially increase the chance of acceptance. To test these anecdotal assumptions, Elena wants to convert the GPAs and SAT scores into the categories corresponding to these thresholds. In addition, the database has a target variable indicating whether or not the past applicant was accepted to the college.

Develop the naïve Bayes classification model and create a report that presents an analysis of the factors that may influence whether or not a high school student is admitted to a selective four-year college. Predictor variables should include the applicant’s sex, ethnicity, parents’ education levels, GPA, and SAT scores. Transform the GPAs and SAT scores into appropriate categorical variables. Make predictions whether or not each of the 14 high school students at Beachside High in the College_Admission_Score worksheet will be admitted.

High school students work hard to excel academically and set themselves apart with extracurricular achievements. Getting into the right college and choosing the right major can help start them out on a successful professional career.

The college admissions data set that is available to Beachside High School counselors includes records of past students who had applied to a selective four-year college that has three academic units: School of Arts and Letters, School of Business and Economics, and School of Mathematics and Sciences. The data set is used to develop classification models based on a naïve Bayes algorithm to predict whether or not the 14 high-achieving students at Beachside High will be admitted to any of the three academic units at the college.

The 14 current students are the top students in their graduating class. However, because the admission process can be highly competitive, some of these students might not get admitted to the college they wish to attend. Moreover, different academic programs may have different admission criteria. As a result, a naïve Bayes classification model is developed for each of the three academic schools based on the following variables: parents’ education, high school.

GPAs, SAT scores, and the male, white, and Asian indicators. Because the naïve Bayes algorithm requires that all predictor variables are categorical, GPAs and SAT scores are converted into binary values where GPAs that are at least 3.50 are denoted as 1, 0 otherwise, and SAT scores that are at least 1,200 are denoted as 1, 0 otherwise. A summary of the students’ demographic and academic information is as follows.

Of the 14 students, eight of them are female. Four students are of Asian descent, and six are nonwhite.
The average high school GPA and SAT score of the 14 students are 3.64 and 1,261, respectively.
Nine students have a current GPA of 3.50 or higher, and 10 students scored at least 1,200 on the SAT exam.
All but three students have at least one parent who completed a four-year college degree.
Even though the current students have not decided which academic program they want to pursue, most of them express an interest in the School of Arts and Letters. The data set has 6,964 records of past applicants to this program, which are partitioned into training, validation, and test data sets. Based on the test data set, the naïve Bayes model for the School of Arts and Letters has an overall accuracy rate of 75.81%. The specificity and sensitivity rates are 84.65% and 48.83%, respectively.

A summary of performance measures of the classification models for the three academic schools is shown in Table 9.10. The naïve Bayes model predicts that only four of our 14 top students will be admitted to the School of Arts and Letters. This program appears to be the most selective of the three academic units. The scoring results of the 14 students for each of the three academic schools are presented in Table 9.11.

TABLE 9.10 Performance Measures of Naïve Bayes Classifiers
The School of Business and Economics is also a popular choice among the current students. The data set has 4,103 records of past applicants to this program, which are partitioned into training, validation, and test data sets. The accuracy, specificity, and sensitivity rates based on the test data are 77.44%, 83.20%, and 67.86%, respectively. The model predicts that six out of the 14 students will be admitted into this program.

A similar naïve Bayes classifier is developed based on the 6,272 records of past applicants to the School of Mathematics and Sciences. As presented in Table 9.10, the accuracy, specificity, and sensitivity rates based on the test data are 76.24%, 79.81%, and 69.19%, respectively. Based on the scoring results, six out of the 14 students are likely to be admitted into this program. These are the same six students that the previous model classifies as likely to be admitted into the School of Business and Economics.

Based on the overall accuracy rate, the naïve Bayes classifiers perform reasonably well. The lift ratios and the decile-wise lift chart also indicate that the naïve Bayes classifiers are more effective than a baseline random model. As shown in Table 9.10, the lift values of the first decile of the three models are above 2.0, and the AUC values are around 80%. However, compared to other performance measures, the sensitivity rate of the models is relatively low, especially for the School of Arts and Letters. This may be because the schools also use qualitative information that is not captured in the database, making it difficult to correctly classify all of the past applicants who were admitted to the college (i.e., identifying true positive cases). The qualitative factors that are relevant to the admission process include letters of recommendations, written essays, and, for the School of Arts and Letters, a student’s artwork.

Table 9.11 presents the scoring results of the 14 current students. In general, the only students who are likely to be admitted into any of the three academic programs are those who maintain a GPA of at least 3.50 and score 1,200 or above on the SAT exam. Out of the 14 students, only six of them meet both criteria. A high GPA or a high SAT score alone is not likely to result in an acceptance to the college.

These data-driven results confirm the anecdotal intuition that a GPA of 3.50 and an SAT score of 1,200 are the minimum thresholds that students at Beachside High need to achieve in order to be admitted into a more selective college or university. Moreover, the School of Arts and Letters appears to be more selective than the other two schools. Only four of the six students with a GPA above 3.50 and an SAT score above 1,200 are likely to get accepted into this program. With this information, it is advised that some of the 14 students wishing to attend the School of Arts and Letters apply to additional colleges and universities with a similar degree program as a back-up plan.

TABLE 9.11 Prediction Results for the 14 Students

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## Richards Chapter 4 Quizzes HIST106: Aftershocks of the Great Wat

HIST106 Modern World SP23 Richards Chapter 4 Quizzes: Aftershocks of the Great War
Qn1. Life for which of the following groups of people was NOT significantly impacted by the Great War?

`` - Peasants``

Qn2. Europe termed the twentieth century the _ due the traumatic events that occurred and the changes that took place.

``-Age of Anxiety``

Qn3. How was it believed that the fine arts could be used as ideological weapons?

``- They could unlock the conscious and subconscious mind and further the inner conversion of the individual``

Qn4. What is one way in which World War I contributed to the conceivability of the Holocaust?
Qn5. Which of the following areas of study most challenged the foundations of the Enlightenment and the ideas surrounding it?
Qn6. Which of the following traditions proposed that humans are naturally good and that they can build a better world with the help of reason?
Qn7. Which art movement supported the same concept of “no fixed reality” that was established by physics?
Qn8. Which group least benefitted during the period of post-war prosperity?
Qn9. Which of the following is another name for the middling classes?
Qn10. Whose nineteenth century theories supported the Enlightenment tradition that humans are moving toward some type of improvement?

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## FIN3125 Coursework Assignment 2022/23

Marylebone plc is a leading multi-divisional organisation based in the UK and specialising in manufacturing household consumables. To address the major advances in technology over recent years and a shift in consumer behaviour, Marylebone plc is entering a period of significant capital investment to secure future growth and enhance shareholder value.
Several capital budgeting projects due to be implemented next year are being considered and require immediate evaluation, including new product lines, modifications to or discontinuation of existing lines, relocations, and long-term contracts. The financing of which will be funded entirely by long-term borrowing.
The Financial Director has allocated to you one of the investment proposals (Polaris) for evaluation by considering the relevant cash flows involved and by performing financial appraisals on the basis of net present value. A report on your main findings is required.
In addition to the information gathered on the particulars of each investment proposal, the following general information regarding Marylebone plc is given:

1. It is the last quarter of 2022 and the company prepares accounts with a financial year ending 31st December.
2. Company earnings are subject to 20% corporation tax, payable on a current year basis.
3. Land and buildings qualify for 4% reducing balance industrial buildings allowances whilst plant, equipment and machinery are subject to ‘short-life’ asset election and attract 22% reducing balance tax allowances. Capital allowances can be claimed in the year of acquisition and every subsequent year of ownership except for the last year where a balancing allowance can be claimed or there will be a balancing charge to the company, unless otherwise specified in the particulars of each case.
4. All operating cash flows (revenues and operating costs) are quoted at current 2022 prices and subject to annual inflation, unless otherwise specified in the particulars of each case.
5. General rate of inflation is expected to be 2% next year and 3% p.a. in subsequent years.
6. Management consider the company’s overall existing average cost of capital of 16% is an appropriate rate to appraise all capital investments (unless otherwise specified).

Investment Particulars
Polaris – New Product Line ?
Research and development expenditure to date on this new product has totalled £50,000, payable at the end of this year. The work is now complete, resulting in a marketable product Polaris.
The company will need to build and equip a new factory specifically and a suitable site has been found with a purchase price of £750,000. Acquisition of the land and construction of the factory will commence at the beginning of January 2023. Construction will take one year at a total cost of £1 million. Half of this sum will be payable at the start of construction, the balance being payable on completion. The cost of the necessary equipment and installation will cost a total of £900,000 and can be done during the last two months of construction. £400,000 of this will be paid on delivery and the balance in two equal annual instalments on the anniversary of delivery. The above acquisition prices are fixed and not subject to inflation.

After 3 years of production the equipment will need replacing. The old machine will be sold for £500,000 and new equipment acquired at the end of 2026 at the same cost and on the same terms of payment as the original equipment. This replacement can be achieved without disruption to production.

At the end of six years of production, Polaris will be abruptly discontinued, and the production facility will then be surplus to requirement. It is expected that the equipment can be sold at the time for £500,000 and the factory and site will command a price of £2 million. Capital allowances for both of these categories of non-current assets will begin in the year of production.

A 3-year advertising campaign will need to be undertaken for the new product Polaris, commencing at the beginning of construction of the factory. Fixed advertising fees totalling £1,200,000 have been agreed, payable in three equal instalments at the end of each of the 3 years. As a result of the advertising campaign, the Sales Director is forecasting an annual demand of 500,000 units of Polaris in 2024 and expects this demand to continue for six years after. Initial production will begin immediately after completion of the factory at an annual output rate to match the forecasted demand from 2024 onwards.
Production overheads will consist of variable costs of £6.50 per unit and annual fixed costs of £400,000. Both production costs are quoted in current terms and are subject to general inflation p.a.
The working capital requirement of 5% of the annual variable costs, is to be in place at the beginning of each year of production and released on discontinuation.

Despite extensive market research during the last 6 months at a cost of £20,000 payable on 1st January 2023, management remains uncertain as to the price it will be able to charge for Polaris. The Sales Director is suggesting an initial selling price in 2024 of £10 per unit, subject to general inflation thereafter.

# Financial Director Requirements

:

1. Assuming the Sales Director’s suggested selling price is adopted, evaluate whether the company should go ahead with the proposed production of Polaris? (16 marks)
2. What would be the minimum selling price that must be achieved in order to ensure Polaris is viable? (4 marks)
3. Since Polaris will be financed through long term borrowing, discuss whether the company’s weighted average cost of capital is an appropriate discount rate to evaluate the investment, as opposed to the company’s long term borrowing rate. (5 marks)

Assignment Requirements Total 25 marks
Task 1 – Investment Proposal allocation
Students should read through the general information and review the investment particulars and then make preliminary notes ahead of week 8 seminars.

Task 2 – Relevant Cash Flow Discussion & Feedback in Week 8 seminars
During the weekly seminar session, students will have the opportunity to discuss the case for including or ignoring cash flows and the method of recognition in the appraisal as per the particulars of their assigned investment proposal. Tutors will be available for feedback during this session.
Task 3 – Investment Appraisals

Each student should perform Cash Flow Analysis and Net Present Value Appraisal(s) for their assigned investment proposal as per the Financial Director’s specific requirements.
Task 4 - Compilation of Report to Financial Director
The Report to Financial Director should address the main findings of the work undertaken and your recommendations to the Financial Director’s specific requirements. Your report should include a copy of your investment appraisal(s).

Extra Guidance
Time Zones for Appraisal - We are in the last quarter of 2022:
• 2022 is Year 0 i.e. cash flows occurring at the end of 2022/beginning of 2023
• 2023 is Year 1 i.e. cash flows occurring at the end of 2023/beginning of 2024
• 2024 is Year 2 i.e. cash flows occurring at the end of 2024/beginning of 2025 and so on

Relevant module material – Lectures 4, 5 & 6 lecture notes, workshop activities and seminar questions

Feedback, Submission Requirements & Deadline
Tutors are available all year to clarify or help with any queries, along with the following:
• Week 8 Seminar Relevant Cash Flows Analysis Feedback Session
• Week 15 Draft Investment Appraisal submission via the Excel Draft Submissions box in the Assessment 2 Coursework folder by Friday 27th January 2023 – feedback will be given on your numeric work within one week.

Submission Deadline: Week 19 - Monday 20th February 2023 by 5pm
Students should submit their Report and Excel workings via the Individual Coursework Submission box located in the Assessment 2 Coursework folder.