Week 5: Consumer Mathematics

Everyone benefits from effective money management. Money is earned, bills are paid, and savings accounts are created. But what happens when the money you earn is not enough to cover your immediate needs or wants? This is where a loan comes in.

No matter how much money you make in your lifetime, it is likely that at some point you will take out a loan. This could be for education, a home, a car, or a hobby, such as a boat. If you have taken out a loan, you already know there is a cost for taking that loan. How much of that loan is interest, or money paid to the financial institution for lending you the cash? How much of your monthly payment is paying down the debt, and how much is paying interest on that amount? If you haven’t taken out a loan before, you will be glad to work through this math now so that you are prepared for the true costs involved.

This week, you will explore the math behind finances, loans, and interest payments. You also re-examine your own personal financial management techniques.

Discussion: Repaying Loans

Before taking out a loan, it is important to know the repayment terms and how your interest rate and the time of the loan affect the total loan balance.

For this Discussion, you examine the effect of simple and compound interest, as well as time on the principal balance of a loan. You also explore how these variables affect loan repayment.

To prepare for this Discussion:

• Think of a big-ticket item you might need to take out a loan to purchase. Dream big. What have you always wanted? This could be a boat, car, motorcycle, a trip around the world, etc. Research the cost of this item.
• Select a reasonable interest rate for your item (between 2% and 10% is standard).
• Select a time period to pay off your loan (between 3 and 10 years is common

• Post at least 2 paragraphs in response to the following:
  • Paragraph 1:
    • Describe the item you are taking a loan out for and the purchase price.
    • Include your chosen interest rate and amount of time for your loan.
    • Determine the amount of interest you will pay throughout the term of the loan and the final cost of the item when the loan is paid in full. Note: Assume your bank uses the simple interest formula: Interest = Principal * Rate * Time.
    • Show the work needed to find the amount of interest and total cost.
    • Determine the monthly payment for this loan.
  • Paragraph 2:
    • Repeat the interest computation however lower the time frame by one year. Show your work.
    • Determine the total amount of the loan when paid in full.
    • Compute the new monthly payment.
    • Explain if you are surprised by the results. Why, or why not?
    • Discuss one change you could make in your life to make the new monthly payment possible.

Competency

Apply the normal distribution, standard normal distribution, and central limit theorem.

Scenario

Frank has only had a brief introduction to statistics when he was in high school 12 years ago, and that did not cover inferential statistics. He is not confident in his ability to answer some of the problems posed in the course.

As Frank’s tutor, you need to provide Frank with guidance and instruction on a spreadsheet he has partially filled out. Your job is to help him understand and comprehend the material. You should not simply be providing him with an answer as this will not help when it comes time to take the test. Instead, you will be providing a step-by-step breakdown of the problems including an explanation on why you did each step and using proper terminology.

To complete this assignment, you must first download the spreadsheet, and then complete it by including the following items on the spreadsheet:

Incorrect Answers – Correct any wrong answers. You must also explain the error performed in the problem in your own words.

Partially Finished Work – Complete any partially completed work. Make sure to provide step-by-step instructions including explanations.

Blank Questions – Show how to complete any blank questions by providing step-by-step instructions including explanations.

Your step-by-step breakdown of the problems, including explanations and calculations performed, should be present within the Excel spreadsheet provided.

Competency

Describe the data using the measures of central tendency and measures of variability.

Instructions

Scenario (information repeated for deliverable 01, 03, and 04)

A major client of your company is interested in the salary distributions of jobs in the state of Minnesota that range from $30,000 to $200,000 per year. As a Business Analyst, your boss asks you to research and analyze the salary distributions. You are given a spreadsheet that contains the following information:

• A listing of the jobs by title
• The salary (in dollars) for each job
• The client needs the preliminary findings by the end of the day. Your boss asks you to first compute some basic statistics and then analyze the results in the four questions given in the Excel spreadsheet.
• Background information on the DataThe data set in the spreadsheet consists of 364 records that you will be analyzing from the Bureau of Labor Statistics. The data set contains a listing of several jobs titles with yearly salaries ranging from approximately $30,000 to $200,000 for the state of Minnesota.
   

Competency

Evaluate hypothesis tests for population parameters from two populations.

Dealing with Two Populations

Inferential statistics involves forming conclusions about a population parameter. We do so by constructing confidence intervals and testing claims about a population mean and other statistics. Typically, these methods deal with a sample from one population. We can extend the methods to situations involving two populations (and there are many such applications). This deliverable looks at two scenarios.

Concept being Studied

Your focus is on hypothesis tests and confidence intervals for two populations using two samples, some of which are independent and some of which are dependent. These concepts are an extension of hypothesis testing and confidence intervals which use statistics from one sample to make conclusions about population parameters.

Competency

Evaluate hypothesis tests for population parameters from one population.

Instructions

Scenario (information repeated for deliverable 01, 03, and 04)

A major client of your company is interested in the salary distributions of jobs in the state of Minnesota that range from $30,000 to $200,000 per year. As a Business Analyst, your boss asks you to research and analyze the salary distributions. You are given a spreadsheet that contains the following information:

• A listing of the jobs by title
• The salary (in dollars) for each job

Deliverable 4 – Hypothesis Tests.xlsx

In prior engagements, you have already explained to your client about the basic statistics and discussed the importance of constructing confidence intervals for the population mean. Your client says that he remembers a little bit about hypothesis testing, but he is a little fuzzy. He asks you to give him the full explanation of all steps in hypothesis testing and wants your conclusion about two claims concerning the average salary for all jobs in the state of Minnesota.

Background information on the Data

The data set in the spreadsheet consists of 364 records that you will be analyzing from the Bureau of Labor Statistics. The data set contains a listing of several jobs titles with yearly salaries ranging from approximately $30,000 to $200,000 for the state of Minnesota.

What to Submit

Your boss wants you to submit the spreadsheet with the completed calculations, answers, and analysis.

Competency

Develop a confidence interval for a population parameter.

Instructions

Scenario (information repeated for deliverable 01, 03, and 04)

A major client of your company is interested in the salary distributions of jobs in the state of Minnesota that range from $30,000 to $200,000 per year. As a Business Analyst, your boss asks you to research and analyze the salary distributions. You are given a spreadsheet that contains the following information:

• A listing of the jobs by title
• The salary (in dollars) for each job

Deliverable 3 – Confidence Intervals.xlsx

You have previously explained some of the basic statistics to your client already, and he really liked your work. Now he wants you to analyze the confidence intervals.

Background information on the Data

The data set in the spreadsheet consists of 364 records that you will be analyzing from the Bureau of Labor Statistics. The data set contains a listing of several jobs titles with yearly salaries ranging from approximately $30,000 to $200,000 for the state of Minnesota.

 Your boss wants you to submit the spreadsheet with the completed calculations, answers, and analysis.

Compile a data set of 20 points (observations, cases, study subjects, etc.) or more with two (2) quantitative variables (2 variables are needed for probability calculations and regression analysis).

Part 1: Globalization and Information Research

Context: Companies that perform well in their country of origin usually consider expanding operations in new international markets. Deciding where, how, and when to expand is not an easy task, though.

Many issues need to be considered before crafting an expansion strategy and investing significant resources to this end, including:

• the level of demand to be expected for the company’s products/services
• presence of local competitors
• the regulatory, economic, demographic, and political environments

Carefully researching and analyzing these and other factors can help mitigate the inherent risk associated with an overseas expansion strategy, thus increasing the likelihood of success.

As a data analyst in your company’s business development department, you’ve been tasked with the responsibility of recommending countries for international expansion. You’ll write a report to the company’s executive team with your research, analysis, and recommendations.

https://hbr.org/2018/10/how-netflix-expanded-to-19…

Instructions:

Write a 525-word summary covering the following items:

• According to the article listed above, what were the most important strategic moves that propelled Netflix’s successful international expansion?
• The article mentions investments in big data and analytics as one of the elements accompanying the second phase of overseas expansion. Why was this investment important? What type of information did Netflix derive from the data collected?
• According to the article, what is exponential globalization?
• Not all international expansion strategies are a resounding success, however. Research an article or video that discusses an instance in which an American company’s expansion efforts in another country failed. According to the article/video you selected, what were the main reasons for this failure? Do you agree with this assessment?
• Explain some of the reasons why certain companies’ expansion plans have failed in the past.

Part 2: Hypothesis testing

Context: Your organization is evaluating the quality of its call center operations. One of the most important metrics in a call center is Time in Queue (TiQ), which is the time a customer has to wait before he/she is serviced by a Customer Service Representative (CSR). If a customer has to wait for too long, he/she is more likely to get discouraged and hang up. Furthermore, customers who have to wait too long in the queue typically report a negative overall experience with the call. You’ve conducted an exhaustive literature review and found that the average TiQ in your industry is 2.5 minutes (150 seconds).

Another important metric is Service Time (ST), also known as Handle Time, which is the time a CSR spends servicing the customer. CSR’s with more experience and deeper knowledge tend to resolve customer calls faster. Companies can improve average ST by providing more training to their CSR’s or even by channeling calls according to area of expertise. Last month your company had an average ST of approximately 3.5 minutes (210 seconds). In an effort to improve this metric, the company has implemented a new protocol that channels calls to CSR’s based on area of expertise. The new protocol (PE) is being tested side-by-side with the traditional (PT) protocol.

Instructions:

Access the Call Center Waiting Time file. Each row in the database corresponds to a different call. The column variables are as follows:

• ProtocolType: indicates protocol type, either PT or PE
• QueueTime: Time in Queue, in seconds
• ServiceTime: Service Time, in seconds
• Perform a test of hypothesis to determine whether the average TiQ is lower than the industry standard of 2.5 minutes (150 seconds). Use a significance level of α=0.05.
• Evaluate if the company should allocate more resources to improve its average TiQ.
• Perform a test of hypothesis to determine whether the average ST with service protocol PE is lower than with the PT protocol. Use a significance level of α=0.05.
• Assess if the new protocol served its purpose. (Hint: this should be a test of means for 2 independent groups.)
• Submit your calculations and a 175-word summary of your conclusions.

Competency

Determine the linear correlation and regression equation between two variables to make predictions for the dependent variable.

Scenario

According to the U.S. Geological Survey (USGS), the probability of a magnitude 6.7 or greater earthquake in the Greater Bay Area is 63%, about 2 out of 3, in the next 30 years. In April 2008, scientists and engineers released a new earthquake forecast for the State of California called the Uniform California Earthquake Rupture Forecast (UCERF).

As a junior analyst at the USGS, you are tasked to determine whether there is sufficient evidence to support the claim of a linear correlation between the magnitudes and depths from the earthquakes. Your deliverables will be a PowerPoint presentation you will create summarizing your findings and an excel document to show your work.

Concepts Being Studied

Correlation and regression

Creating scatterplots

Constructing and interpreting a Hypothesis Test for Correlation using r as the test statistic

You are given a spreadsheet that contains the following information:

Magnitude measured on the Richter scale

Depth in km

Deliverable 6 – Analysis with Correlation and Regression.xlsx

Using the spreadsheet, you will answer the problems below in a PowerPoint presentation.