QNT561 Week 1 Statistics Concepts and Descriptive Measures
Statistics Concepts and Descriptive Measures
Purpose of Assignment
The purpose of this assignment to orient students to the key concepts in statistics. This assignment will introduce students to the language of statistics. Students will also get a chance to warm-up on evaluating some basic descriptive statistics using Excel® prior to the course start.
Assignment Steps
This assignment has an Excel® dataset spreadsheet attached. You will be required to only do one of the three datasets.
Resource: Microsoft Excel®, Statistics Concepts and Descriptive Measures Data Set
Download the Statistics Concepts and Descriptive Measures Data Set.
Choose one of the following datasets to complete this assignment:
· Consumer Food
· Financial
· Hospital
Answer each of the following in a total of 90 words:
· For each column, identify whether the data is qualitative or quantitative.
· Identify the level of measurement for the data in each column.
· For each column containing quantitative data:
o Evaluate the mean and median
o Interpret the mean and median in plain non-technical terms
o Use the Excel =AVERAGE function to find the mean
o Use the Excel =MEDIAN function to find the median
· For each column containing quantitative data:
o Evaluate the standard deviation and range
o Interpret the standard deviation and range in plain non-technical terms
o Use the Excel =STDEV.S function to find the standard deviation
o For range (maximum value minus the minimum value), find the maximum value using the Excel =MAX function and find the minimum value using the Excel's =MIN function
QNT561 Week 2 Case Study MBA Schools in Asia-Pacific
Case Study: MBA Schools in Asia-Pacific
The pursuit of a higher education degree in business is now international. A survey shows more and more Asians choose the master of business administration (MBA) degree route to corporate success. As a result, the number of applicants for MBA courses at Asia-Pacific schools continues to increase.
Across the region, thousands of Asians show an increasing willingness to temporarily shelve their careers and spend two years in pursuit of a theoretical business qualification. Courses in these schools are notoriously tough and include statistics, economics, banking, marketing, behavioral sciences, labor relations, decision making, strategic thinking, business law, and more.
After your MBA, you get a job at Bloomberg in its media division, Bloomberg Business. Your division publishes reviews and rankings for business schools in the US and internationally. Because of your strong analytical education from University of Phoenix, your boss assigns you to work on preparing an analysis for data gathered for leading business schools in the Asia-Pacific. The data set in the Excel® file shows some of the characteristics of the leading Asia-Pacific business schools.
Case Study: MBA Schools in Asia-Pacific
Purpose of Assignment
The purpose of this assignment is to develop students' analytical capabilities to evaluate, analyze, and apply descriptive statistics techniques to real-world datasets.
Assignment Steps
Resources: Microsoft Excel®, Case Study: MBA Schools in Asia-Pacific
Review the Case Study: MBA Schools in Asia-Pacific and the Case Study: MBA Schools in Asia-Pacific data set.
Prepare a 1,050-word managerial report for your boss.
Use the following questions for guidelines and directions on what to include in the report:
1. What is the type of data (Quantitative or Qualitative) for each of the columns (variables) in the dataset? If quantitative, is the data discrete or continuous? Neatly summarize your response in a table for all the columns (variables).
2. Using Excel®, find the mean, median, standard deviation, minimum, maximum, and the three quartiles for each of the quantitative variables identified in part 1 above. Neatly summarize in a table on this document. Comment on what you observe.
3. What are the minimum and maximum full-time enrollments? Which schools have the minimum and maximum full-time enrollments?
4. What is the average number of students per faculty member? Is this low or high? What does this mean to prospective applicants who are interested in pursuing an MBA in one of the leading international business schools?
5. What are the mean, median, and modal ages? What does this mean to prospective applicants?
6. What is the mean percentage of foreign students? How many and which schools have 1% and 0% foreign students? Which schools have highest percentage of foreign students? Please state these percentages.
7. What percentage of schools require the GMAT test?
8. What percentage of schools require English tests such as Test of English as a Foreign Language (TOEFL)?
9. What percentage of schools require work experience? From this percentage, does this appear to be a significant factor in gaining admissions?
10. What are the mean and median starting salaries? Which schools have the minimum and maximum starting salaries? How much are these minimum and maximum salaries?
11. What are the mean tuition for foreign students and for local students? Does there appear to be a significant difference? What is the difference between the two means?
12. How many schools require work experience and how many of them don't? What is the mean starting salary for schools requiring work experience? What is the mean starting salary for schools requiring no work experience?
13. How many schools require English tests and how many don't? What is the mean starting salary for schools requiring English tests? What is the mean starting salary for schools requiring no English tests?
14. Does there appear to be a correlation between age and starting salaries? Comment on the strength and the direction of the correlation.
15. Comment on the skewness for the data on starting salaries:
a. Plot a histogram and determine the skewness.
b. Find the skewness coefficient.
c. Find the mean, median, and mode for starting salaries and compare the three measures to determine skewness.
16. Finally, use Empirical Rule on the starting salaries and determine whether the salaries follow the Empirical Rule.
Format your assignment consistent with APA format.
Click the Assignment Files tab to submit your assignment
QNT561 Week 3 Expansion Strategy and Establishing a Re-Order Point- Bell Computer Case
Purpose of Assignment
This assignment has two cases. Select one of the two cases for this assignment. The first case is on expansion strategy. Managers constantly have to make decisions under uncertainty. This assignment gives students an opportunity to use the mean and standard deviation of probability distributions to make a decision on expansion strategy. The second case is on determining at which point a manager should re-order a printer so he or she doesn't run out-of-stock. The second case uses normal distribution. The first case demonstrates application of statistics in finance and the second case demonstrates application of statistics in operations management.
Assignment Steps
Resources: Microsoft Excel®, Bell Computer Company Forecasts data set, Case Study Scenarios
Write a 500-word report based on the case you selected: Bell Computer Company Forecasts data set and Case Study Scenarios.
Include answers to the following:
Case 1: Bell Computer Company
- Compute the expected value for the profit associated with the two expansion alternatives. Which decision is preferred for the objective of maximizing the expected profit?
- Compute the variation for the profit associated with the two expansion alternatives. Which decision is preferred for the objective of minimizing the risk or uncertainty?
Case 2: Kyle Bits and Bytes
- What should be the re-order point? How many HP laser printers should he have in stock when he re-orders from the manufacturer?
QNT561 Week 3 SuperFun Toys Case Study
Purpose of Assignment
The purpose of this assignment is for students to learn how to make managerial decisions using a case study on Normal Distribution. This case uses concepts from Weeks 1 and 2. It provides students an opportunity to perform sensitivity analysis and make a decision while providing their own rationale. This assignment also shows students that statistics is rarely used by itself. It shows tight integration of statistics with product management.
Assignment Steps
Resources: Microsoft Excel®, SuperFun Toys Case Study, SuperFun Toys Case Study Data Set
Review the SuperFun Toys Case Study and Data Set.
Develop a 1,050-word case study analysis including the following:
- Use the sales forecaster's prediction to describe a normal probability distribution that can be used to approximate the demand distribution.
- Sketch the distribution and show its mean and standard deviation. Hint: To find the standard deviation, think Empirical Rule covered in Week 1.
- Compute the probability of a stock-out for the order quantities suggested by members of the management team (i.e. 15,000; 18,000; 24,000; 28,000).
- Compute the projected profit for the order quantities suggested by the management team under three scenarios: pessimistic in which sales are 10,000 units, most likely case in which sales are 20,000 units, and optimistic in which sales are 30,000 units.
- One of SuperFun's managers felt the profit potential was so great the order quantity should have a 70% chance of meeting demand and only a 30% chance of any stock- outs. What quantity would be ordered under this policy, and what is the projected profit under the three sales scenarios?
Format your assignment consistent with APA format.
Click the Assignment Files tab to submit your assignment.
Case Study – SuperFun Toys
SuperFun Toys, Inc., sells a variety of new and innovative children's toys. Management learned the pre-holiday season is the best time to introduce a new toy because many families use this time to look for new ideas for December holiday gifts. When SuperFun discovers a new toy with good market potential, it chooses an October market entry date. To get toys in its stores by October, SuperFun places one-time orders with its manufacturers in June or July of each year.
Demand for children's toys can be highly volatile. If a new toy catches on, a sense of shortage in the marketplace often increases the demand to high levels and large profits can be realized. However, new toys can also flop, leaving SuperFun stuck with high levels of inventory that must be sold at reduced prices. The most important question the company faces is deciding how many units of a new toy should be purchased to meet anticipated sales demand. If too few are purchased, sales will be lost; if too many are purchased, profits will be reduced because of low prices realized in clearance sales.
This is where SuperFun feels that you, as an MBA student, can bring value.
For the coming season, SuperFun plans to introduce a new product called Weather Teddy. This variation of a talking teddy bear is made by a company in Taiwan. When a child presses Teddy's hand, the bear begins to talk. A built-in barometer selects one of five responses predicting the weather conditions. The responses range from "It looks to be a very nice day! Have fun" to "I think it may rain today. Don't forget your umbrella." Tests with the product show even though it is not a perfect weather predictor, its predictions are surprisingly good. Several of SuperFun's managers claimed Teddy gave predictions of the weather that were as good as many local television weather forecasters.
As with other products, SuperFun faces the decision of how many Weather Teddy units to order for the coming holiday season. Members of the management team suggested order quantities of 15,000, 18,000, 24,000, or 28,000 units. The wide range of order quantities suggested indicates considerable disagreement concerning the market potential.
Having a sound background in statistics and business, you are required to perform statistical analysis and the profit projections which is typically done by the product management group. You want to provide management with an analysis of the stock-out probabilities for various order quantities, an estimate of the profit potential, and to help make an order quantity recommendation.
SuperFun expects to sell Weather Teddy for $24 based on a cost of $16 per unit. If inventory remains after the holiday season, SuperFun will sell all surplus inventories for $5 per unit. After reviewing the sales history of similar products, SuperFun's senior sales forecaster predicted an expected demand of 20,000 units with a 95% probability that demand would be between 10,000 units and 30,000 units.
§ Use the sales forecaster's prediction to describe a normal probability distribution that can be used to approximate the demand distribution.
§ Sketch the distribution and show its mean and standard deviation. Hint: To find the standard deviation, think Empirical Rule covered in Week 1.
§ Compute the probability of a stock-out for the order quantities suggested by members of the management team (i.e. 15,000; 18,000; 24,000; 28,000).
§ Compute the projected profit for the order quantities suggested by the management team under three scenarios: pessimistic in which sales are 10,000 units, most likely case in which sales are 20,000 units, and optimistic in which sales are 30,000 units.
QNT561 Week 4 Payment Time Case Study
Case Study – Payment Time Case Study
Major consulting firms such as Accenture, Ernst & Young Consulting, and Deloitte & Touche Consulting employ statistical analysis to assess the effectiveness of the systems they design for their customers. In this case, a consulting firm has developed an electronic billing system for a Stockton, CA, trucking company. The system sends invoices electronically to each customer's computer and allows customers to easily check and correct errors. It is hoped the new billing system will substantially reduce the amount of time it takes customers to make payments. Typical payment times—measured from the date on an invoice to the date payment is received—using the trucking company's old billing system had been 39 days or more. This exceeded the industry standard payment time of 30 days.
The new billing system does not automatically compute the payment time for each invoice because there is no continuing need for this information. The management consulting firm believes the new system will reduce the mean bill payment time by more than 50 percent. The mean payment time using the old billing system was approximately equal to, but no less than, 39 days. Therefore, if µ denotes the new mean payment time, the consulting firm believes that µ will be less than 19.5 days. Therefore, to assess the system's effectiveness (whether µ < 19.5 days), the consulting firm selects a random sample of 65 invoices from the 7,823 invoices processed during the first three months of the new system's operation. Whereas this is the first time the consulting company has installed an electronic billing system in a trucking company, the firm has installed electronic billing systems in other types of companies.
Analysis of results from these other companies show, although the population mean payment time varies from company to company, the population standard deviation of payment times is the same for different companies and equals 4.2 days. The payment times for the 65 sample invoices are manually determined and are given in the Excel® spreadsheet named "The Payment Time Case". If this sample can be used to establish that new billing system substantially reduces payment times, the consulting firm plans to market the system to other trucking firms.
Purpose of Assignment
The purpose of the assignment is to develop students' abilities in using datasets to apply the concepts of sampling distributions and confidence intervals to make management decisions.
Assignment Steps
Resources: Microsoft Excel®, The Payment Time Case Study, The Payment Time Case Data Set
Review the Payment Time Case Study and Data Set.
Develop a 700-word report including the following calculations and using the information to determine whether the new billing system has reduced the mean bill payment time:
- Assuming the standard deviation of the payment times for all payments is 4.2 days, construct a 95% confidence interval estimate to determine whether the new billing system was effective. State the interpretation of 95% confidence interval and state whether or not the billing system was effective.
- Using the 95% confidence interval, can we be 95% confident that µ ≤ 19.5 days?
- Using the 99% confidence interval, can we be 99% confident that µ ≤ 19.5 days?
- If the population mean payment time is 19.5 days, what is the probability of observing a sample mean payment time of 65 invoices less than or equal to 18.1077 days?
Format your assignment consistent with APA format.
QNT561 Week 5 One-Sample Hypothesis Testing Cases
Purpose of Assignment
The purpose of this assignment is to develop students' abilities to combine the knowledge of descriptive statistics covered in Weeks 1 and 2 and one-sample hypothesis testing to make managerial decisions. Select one of the two cases for this assignment. In this assignment, students will learn how statistical analysis is used in predicting an election winner in the first case. In the second case, students will conduct a hypothesis test to decide whether or not a shipping plan will be profitable.
Assignment Steps
Resources: Microsoft Excel®, Case Study Scenarios, SpeedX Payment Times
Develop a 500 word statistical analysis based on the Case Study Scenarios and SpeedX Payment Times.
Include answers to the following:
Case 1: Election Results
- Use 0.10 as the significance level (α).
- Conduct a one-sample hypothesis test to determine if the networks should announce at 8:01 P.M. the Republican candidate George W. Bush will win the state.
Case 2: SpeedX
- Use 0.10 and the significance level (α).
- Conduct a one-sample hypothesis test and determine if you can convince the CFO to conclude the plan will be profitable.
Format your assignment consistent with APA format.
Case Study – Election Results
When an election for political office takes place, the television networks cancel regular programming and instead, provide election coverage. When the ballots are counted, the results are reported. However, for important offices such as president or senator in large states, the networks actively compete to see which will be the first to predict a winner. This is done through exit polls, wherein a random sample of voters who exit the polling booth is asked for whom they voted. From the data, the sample proportion of voters supporting the candidates is computed. Hypothesis testing is applied to determine whether there is enough evidence to infer the leading candidate will garner enough votes to win.
Suppose in the exit poll from the state of Florida during the 2000 year elections, the pollsters recorded only the votes of the two candidates who had any chance of winning: Democrat Al Gore and Republican George W. Bush. In a sample of 765 voters, the number of votes cast for Al Gore was 358 and the number of votes cast for George W. Bush was 407. The network predicts the candidate as a winner if he wins more than 50% of the votes. The polls close at 8:00 P.M. Based on the sample results, conduct a one-sample hypothesis test to determine if the networks should announce at 8:01 P.M. the Republican candidate George W. Bush will win the state. Use 0.10 as the significance level (α).
Case Study – SpeedX
SpeedX, a large courier company, sends invoices to customers requesting payment within 30 days. The bill lists an address, and customers are expected to use their own envelopes to return their payments. Currently, the mean and standard deviation of the amount of time taken to pay bills are 24 days and 6 days, respectively. The chief financial officer (CFO) believes including a stamped self-addressed envelope would decrease the amount of time. She calculates the improved cash flow from a 2-day decrease in the payment period would pay for the costs of the envelopes and stamps. You have an MBA from the University of Phoenix, and work for SpeedX as a business analyst. One of your job duties is to run analytics and present the results to the senior management for critical decision-making. You see this as an opportunity to utilize some of the skills you gained in the Statistics course. Because of your strong understanding and background in inferential statistics, you decide to take up this important assignment. You have learned any analysis in inferential statistics starts with sampling. To test the CFO's belief, you decide to randomly select 220 customers and propose to include a stamped self-addressed envelope with their invoices. The CFO accepts your proposal and allows you to run a pilot study. You then record the numbers of days until payment is received. Using your statistical expertise and skills you gained in the class, conduct a one-sample hypothesis test and determine if you can convince the CFO to conclude that the plan will be profitable. Use 0.10 and the significance level (α).
QNT561 Week 5 Spicy Wings Case Study
Case Study – Spicy Wings Case Study
Following his graduation from the MBA program at the University of Phoenix, John Tyler wanted to live and work in the little town of Hood. However, the community was small and there were not a lot of readily available opportunities for college graduates. Fortunately, John had some experience working in the food service industry gained in summers and throughout high school at his uncle's restaurant in Franklin, a few miles away from the town of Hood. When John decided to leverage his experience into a small delivery and take-out restaurant located close to his home, he thought he had hit on a great idea. John would offer a limited fare consisting of the buffalo wings his uncle had perfected at his restaurant. John called his restaurant, Spicy Wings. Although success came slowly, the uniqueness of John's offering coupled with the growth of the community made Spicy Wings a success.
John's business was pretty simple. John purchased wings locally. The wings were then seasoned and prepared in John's restaurant. Once an order was received, John cooked the wings, which were then delivered or picked up by the customer. John's establishment was small, and there was no place for customers to dine in the restaurant. However, his wings proved so popular that over time, John hired several employees, including three delivery drivers. Business was steady and predictable during the week, with the biggest days being home-game football Saturdays.
A little over a year ago, the little town of Hood began to grow and expand. John noticed his business was beginning to suffer when other fast-food delivery restaurants opened around the town. Some of these restaurants were offering guarantees such as "30 minutes or it's free." John's Spicy Wings now had to compete with fish tacos, specialty pizzas, and gourmet burgers. Most of these new restaurants, however, were dine-in establishments providing carry-out and delivery as a customer convenience. However, John was certain he would need to offer a delivery guarantee to remain competitive with the newer establishments.
John was certain a delivery guarantee of "30 minutes or it's free" could easily be accomplished every day except on football Saturdays. John thought if he could offer a 30-minute guarantee on his busiest day, he would be able to hold onto and perhaps even recover market share from the competition. However, before he was willing to commit to such a guarantee, John wanted to ensure that it was possible to meet the 30-minute promise.
John knew it would be no problem for customers to pick up orders within 30 minutes of phoning them in. However, he was less confident about delivering orders to customers in 30 minutes or less. Not only would the wings need to be cooked and packaged, but the delivery time might be affected by the availability of drivers. John decided he needed to analyze the opportunity further.
As a part of his analysis, John decided to take a random sample of deliveries over five different football weekends. Cooking time and packaging time were not considered in his analysis because wings were not cooked for individual orders. Rather, large numbers of wings were cooked at a single time and then packaged in boxes of 12. John decided to focus his analysis on the time required to deliver cooked and packaged wings. He collected information on the amount of time an order had to wait for a driver (the pick-up time), as well as the amount of time required to transport the wings to the customer (the drive time). The sampled information is in the Excel® file, Spicy Wings Data Set. John is not willing to offer the guarantee on football Saturdays, unless he can be reasonably sure the total time to deliver a customer's order is less than 30 minutes, on average. John would also like to have an estimate of the actual time required to deliver a customer's order on football Saturdays. Finally, John would like to know how likely it is the total time to make a delivery would take more than 30 minutes. Based on the sampled data, should John offer the guarantee? What percent of the Saturday deliveries would result in a customer receiving a free order? What recommendations might help John improve his Saturday delivery times?
Purpose of Assignment
The purpose of this assignment is to develop students' abilities to combine the knowledge of descriptive statistics covered in Weeks 1 and 2 and one-sample hypothesis testing to make managerial decisions. In this assignment, students will develop the ability to use statistical analysis and verify whether or not a claim is valid before advertising it.
Assignment Steps
Resources: Microsoft Excel®, Spicy Wings Case Study, Spicy Wings Data Set
Develop a 700-word statistical analysis.
Use descriptive statistics to compute a measure of performance John can use to analyze his delivery performance. Find the following for your measures:
· Mean
· Standard deviation
· Sample size
· Five-number summary on the total time
Conduct a formal hypothesis testing to help John decide whether to offer the delivery guarantee or not.
Estimate the probability of an order taking longer than 30 minutes.
Make a recommendation in a short narrative including the following:
· Based on the sampled data, should John offer the guarantee?
· What percent of the Saturday deliveries would result in a customer receiving a free order?
· What recommendations might help John improve his Saturday delivery times?
QNT561 Week 6 Signature assignment Consumer Database
Assignment Steps
Resources: Microsoft Excel®, Signature Assignment Databases, Signature Assignment Options, Part 3: Inferential Statistics
Scenario: Upon successful completion of the MBA program, say you work in the analytics department for a consulting company. Your assignment is to analyze one of the following databases:
· Manufacturing
· Hospital
· Consumer Food
· Financial
Select one of the databases based on the information in the Signature Assignment Options.
Provide a 1,600-word detailed, statistical report including the following:
· Explain the context of the case
· Provide a research foundation for the topic
· Present graphs
· Explain outliers
· Prepare calculations
· Conduct hypotheses tests
· Discuss inferences you have made from the results
This assignment is broken down into four parts:
· Part 1 - Preliminary Analysis
· Part 2 - Examination of Descriptive Statistics
· Part 3 - Examination of Inferential Statistics
· Part 4 - Conclusion/Recommendations
Part 1 - Preliminary Analysis (3-4 paragraphs)
Generally, as a statistics consultant, you will be given a problem and data. At times, you may have to gather additional data. For this assignment, assume all the data is already gathered for you.
State the objective:
· What are the questions you are trying to address?
Describe the population in the study clearly and in sufficient detail:
· What is the sample?
Discuss the types of data and variables:
· Are the data quantitative or qualitative?
· What are levels of measurement for the data?
Part 2 - Descriptive Statistics (3-4 paragraphs)
Examine the given data.
Present the descriptive statistics (mean, median, mode, range, standard deviation, variance, CV, and five-number summary).
Identify any outliers in the data.
Present any graphs or charts you think are appropriate for the data.
Note: Ideally, we want to assess the conditions of normality too. However, for the purpose of this exercise, assume data is drawn from normal populations.
Part 3 - Inferential Statistics (2-3 paragraphs)
Use the Part 3: Inferential Statistics document.
· Create (formulate) hypotheses
· Run formal hypothesis tests
· Make decisions. Your decisions should be stated in non-technical terms.
Hint: A final conclusion saying "reject the null hypothesis" by itself without explanation is basically worthless to those who hired you. Similarly, stating the conclusion is false or rejected is not sufficient.
Part 4 - Conclusion and Recommendations (1-2 paragraphs)
Include the following:
· What are your conclusions?
· What do you infer from the statistical analysis?
· State the interpretations in non-technical terms. What information might lead to a different conclusion?
· Are there any variables missing?
· What additional information would be valuable to help draw a more certain conclusion?
Option 1: Manufacturing Database
This database contains six variables taken from 20 industries and 140 subindustries in the United States. Some of the industries are food products, textile mill products, furniture, chemicals, rubber products, primary metals, industrial machinery, and transportation equipment. The six variables are Number of Employees, Number of Production Workers, Value Added by Manufacture, Cost of Materials, End-of-Year Inventories, and Industry Group. Two variables, Number of Employees and Number of Production Workers, are in units of 1000. Three variables, Value Added by Manufacture, Cost of Materials, and End-of-Year Inventories, are in million-dollar units. The Industry Group variable consists of numbers from 1 to 20 to denote the industry group to which the particular subindustry belongs.
Option 2: Hospital Database
This database contains observations for six variables on U.S. hospitals. These variables include Geographic Region, Control, Service, Census, Number of Births, and Personnel.
The region variable is coded from 1 to 7, and the numbers represent the following regions:
1 = South
2 = Northeast
3 = Midwest
4 = Southwest
5 = Rocky Mountain
6 = California
7 = Northwest
Control is a type of ownership. Four categories of control are included in the database:
1 = government, nonfederal
2 = nongovernment, not-for-profit
3 = for-profit
4 = federal government
Service is the type of hospital. The two types of hospitals used in this database are:
1 = general medical
2 = psychiatric
Option 3: Consumer Food
The consumer food database contains five variables: Annual Food Spending per Household, Annual Household Income, Non-Mortgage Household Debt, Geographic Region of the U.S. of the Household, and Household Location. There are 200 entries for each variable in this database representing 200 different households from various regions and locations in the United States. Annual Food Spending per Household, Annual Household Income, and Non-Mortgage Household Debt are all given in dollars. The variable Region tells in which one of four regions the household resides. In this variable, the Northeast is coded as 1, the Midwest is coded 2, the South is coded as 3, and the West is coded as 4. The variable Location is coded as 1 if the household is in a metropolitan area and 2 if the household is outside a metro area. The data in this database were randomly derived and developed based on actual national norms.
Option 4: Financial Database
The financial database contains observations on seven variables for 100 companies. The variables are Type of Industry, Total Revenues ($ millions), Total Assets ($ millions), Return on Equity (%), Earnings per Share ($), Dividends per Share ($), and Average Price per Earnings (P/E) ratio. The companies represent seven different types of industries. The variable Type displays a company's industry type as:
1 = apparel
2 = chemical
3 = electric power
4 = grocery
5 = healthcare products
6 = insurance
7 = petroleum
Option 1: Manufacturing Database
1. The National Association of Manufacturers (NAM) contracts with your consulting company to determine the estimate of mean number of production workers. Construct a 95% confidence interval for the population mean number of production workers. What is the point estimate? How much is the margin of error in the estimate?
2. Suppose the average number of employees per industry group in the manufacturing database is believed to be less than 150 (1000s). Test this belief as the alternative hypothesis by using the 140 SIC Code industries given in the database as the sample. Let α = .10. Assume that the number of employees per industry group are normally distributed in the population.
3. You are also required to determine whether there is a significant difference between mean Value Added by the Manufacturer and the mean Cost of Materials in manufacturing using alpha of 0.01.
4. You are requested to determine whether there is a significantly greater variance among values of Cost of Materials than of End-of-Year Inventories.
Option 2: Hospital Database
1. As a consultant, you need to use the Hospital database and construct a 90% confidence interval to estimate the average census for hospitals. Change the level of confidence to 99%. What happened to the interval? Did the point estimate change?
2. Determine the sample proportion of the Hospital database under the variable "service" that are "general medical" (category 1). From this statistic, construct a 95% confidence interval to estimate the population proportion of hospitals that are "general medical." What is the point estimate? How much error is there in the interval?
3. Suppose you want to "prove" that the average hospital in the United States averages more than 700 births per year. Use the hospital database as your sample and test this hypothesis. Let alpha be 0.01.
4. On average, do hospitals in the United States employ fewer than 900 personnel? Use the hospital database as your sample and an alpha of 0.10 to test this figure as the alternative hypothesis. Assume that the number of births and number of employees in the hospitals are normally distributed in the population.
Option 3: Consumer Food
1. Suppose you want to test to determine if the average annual food spending for a household in the Midwest region of the U.S. is more than $8,000. Use the Midwest region data and a 1% level of significance to test this hypothesis. Assume that annual food spending is normally distributed in the population.
2. Test to determine if there is a significant difference between households in a metro area and households outside metro areas in annual food spending. Let α = 0.01.
3. The Consumer Food database contains data on Annual Food Spending, Annual Household Income, and Non-Mortgage Household Debt broken down by Region and Location. Using Region as an independent variable with four classification levels (four regions of the U.S.), perform three different one-way ANOVA's—one for each of the three dependent variables (Annual Food Spending, Annual Household Income, Non-Mortgage Household Debt). Did you find any significant differences by region?
Option 4: Financial Database
1. Use this database as a sample and estimate the earnings per share for all corporations from these data. Select several levels of confidence and compare the results.
2. Are the average earnings per share for companies in the stock market less than $2.50? Use the sample of companies represented by this database to test that hypothesis. Let α = .05.
3. Test to determine whether the average return on equity for all companies is equal to 21. Use this database as the sample and α = .10. Assume that the earnings per share and return on equity are normally distributed in the population.
4. Do various financial indicators differ significantly according to type of company? Use a one-way ANOVA and the financial database to answer this question. Let Type of Company be the independent variable with seven levels (Apparel, Chemical, Electric Power, Grocery, Healthcare Products, Insurance, and Petroleum). Compute three one-way ANOVAs, one for each of the following dependent variables: Earnings Per Share, Dividends Per Share, and Average P/E Ratio.
QNT561 Week 6 Final Exam SCORE 87 PERCENT
1. Suppose a population has a mean of 400 and a standard deviation of 24. If a random sample of size 144 is drawn from the population, the probability of drawing a sample with a mean less than 402 is _______.
·
0.8413
·
0.1587
·
0.9875
·
0.6826
·
0.3413
2. The empirical rule says that approximately what percentage of the values would be within 2 standard deviations of the mean in a bell shaped set of data?
·
95%
·
68%
·
97.7%
·
100%
·
50%
3. A large industrial firm allows a discount on any invoice that is paid within 30 days. Of all invoices, 10% receive the discount. In a company audit, 10 invoices are sampled at random. The probability that fewer than 3 of the 10 sampled invoices receive the discount is approximately_______________.
·
0.057
·
0.9298
·
0.3486
·
0.1937
·
0.001
4. James Desreumaux, VP of Human Resources of American First Banks (AFB), is reviewing the employee training programs of AFB banks. His staff randomly selected personnel files for 100 tellers in the Southeast Region and determined that their mean training time was 25 hours. Assume that the population standard deviation is 5 hours. The 95% confidence interval for the population mean of training times is ________.
·
24.02 to 25.98
·
23.32 to 35.46
·
15.20 to 34.80
·
16.78 to 33.23
·
24.18 to 25.82
5. A market research team compiled the following discrete probability distribution on the number of sodas the average adult drinks each day. In this distribution, x represents the number of sodas which an adult drinks.
| x | P(x) |
| 0 | 0.30 |
| 1 | 0.10 |
| 2 | 0.50 |
| 3 | 0.10 |
The mean (average) value of x is _______________.
·
1.4
·
2.55
·
1.75
·
3.02
·
2.10
6. A large national company is considering negotiating cellular phone rates for its employees. The Human Resource department would like to estimate the proportion of its employee population who own an Apple iPhone. A random sample of size 250 is taken and 40% of the sample own and iPhone.. The 95% confidence interval to estimate the population proportion is _______.
·
0.35 to 0.45
·
0.37 to 0.43
·
0.34 to 0.46
·
0.40 to 0.42
·
0.39 to 0.41
7. If x is a binomial random variable with n=10 and p=0.8, what is the probability that x is equal to 4?
·
.0055
·
.0063
·
.232
·
.994
·
.124
8. The mean life of a particular brand of light bulb is 1200 hours and the standard deviation is 75 hours. Tests show that the life of the bulb is approximately normally distributed. It can be concluded that approximately 68% of the bulbs will last between _______.
·
1050 and 1350 hours
·
900 and 1100 hours
·
1125 and 1275 hours
·
950 and 1050 hours
·
975 and 1475 hours
9. The normal distribution is used to test about a population mean for large samples if the population standard deviation is known. "Large" is usually defined as _______.
·
at least 100
·
at least 5% of the population size
·
at least 10
·
at least 30
·
at least 12
10. Completion time (from start to finish) of a building remodeling project is normally distributed with a mean of 200 work-days and a standard deviation of 10 work-days. To be 99% sure that we will not be late in completing the project, we should request a completion time of _______ work-days.
·
250
·
207
·
200
·
223
·
211
11. The expected (mean) life of a particular type of light bulb is 1,000 hours with a standard deviation of 50 hours. The life of this bulb is normally distributed. What is the probability that a randomly selected bulb would last fewer than 940 hours?
·
0.1151
·
0.3849
·
0.6563
·
0.8849
·
0.6151
12. Life tests performed on a sample of 13 batteries of a new model indicated: (1) an average life of 75 months, and (2) a standard deviation of 5 months. Other battery models, produced by similar processes, have normally distributed life spans. The 98% confidence interval for the population mean life of the new model is _________.
·
71.77 to 78.23
·
79.86 to 81.28
·
61.60 to 88.41
·
63.37 to 86.63
·
71.28 to 78.72
13. Elwin Osbourne, CIO at GFS, Inc., is studying employee use of GFS e-mail for non-business communications. He plans to use a 95% confidence interval estimate of the proportion of e-mail messages that are non-business; he will accept a 0.05 error. Previous studies indicate that approximately 30% of employee e-mail is not business related. Elwin should sample _______ e-mail messages.
·
457
·
323
·
14
·
100
·
12
14. According to the central limit theorem, for samples of size 64 drawn from a population with µ = 800 and σ = 56, the standard deviation of the sampling distribution of sample means would equal _______.
·
800
·
8
·
7
·
80
·
100
15. Maureen McIlvoy, owner and CEO of a mail order business for wind surfing equipment and supplies, is reviewing the order filling operations at her warehouses. Her goal is 100% of orders shipped within 24 hours. In previous years, neither warehouse has achieved the goal, but the East Coast Warehouse has consistently out-performed the West Coast Warehouse. Her staff randomly selected 200 orders from the West Coast Warehouse (population 1) and 400 orders from the East Coast Warehouse (population 2), and reports that 190 of the West Coast Orders were shipped within 24 hours, and the East Coast Warehouse shipped 372 orders within 24 hours. Maureen's alternative hypothesis is _______.
p1 – p2 > 0
·
m1 - m2 > 0
·
m1 - m2 ≥ 0
·
m1 - m2 ≠0
·
p1 – p2 ≠0
16. According to the central limit theorem, for samples of size 64 drawn from a population with µ = 800 and σ = 56, the mean of the sampling distribution of sample means would equal _______.
·
8
·
100
·
800
·
80
·
7
17. If x is a binomial random variable with n=10 and p=0.8, the mean value of x is _____.
·
8
·
3.2
·
6
·
4.8
·
48
18. Consider the following null and alternative hypotheses.
Ho: m ≤ 67
Ha: m > 67
These hypotheses _______________.
·
are not mutually exclusive
·
indicate a one-tailed test with a rejection area in the left tail
·
indicate a one-tailed test with a rejection area in the right tail
·
indicate a two-tailed test
·
19. A researcher wants to determine the sample size necessary to adequately conduct a study to estimate the population mean to within 5 points. The range of population values is 80 and the researcher plans to use a 90% level of confidence. The sample size should be at least _______.
·
44
·
700
·
692
·
216
·
62
Question 20
Medical Wonders is a specialized interior design company focused on healing artwork. The CEO, Kathleen Kelledy claims that artwork has healing effects for patients staying in a hospital, as measured by reduced length of stay. Her current client is a children's cancer hospital. Kathleen is interested in determining the effect of three different pieces of healing artwork on children. She chooses three paintings (a horse photo, a bright abstract, and a muted beach scene) and randomly assigns six hospital rooms to each painting. Kathleen's null hypothesis is _____________.
·
m 1 ≤ m 2 ≥ m 3
·
m 1 ≤ m 2 ≤ m 3
·
m 1 ≠ m 2 ≠ m 3
m 1 ≥ m 2 ≥ m 3
·
m 1 = m 2 = m 3
Question 21
A market researcher is interested in determining the average income for families in San Mateo County, California. To accomplish this, she takes a random sample of 300 families from the county and uses the data gathered from them to estimate the average income for families of the entire county. This process is an example of _______.
census
inferential statistics
nominal data
descriptive statistics
nonparametric statistics
Question 22
The number of bags arriving on the baggage claim conveyor belt in a 3 minute time period would best be modeled with the _________.
exponential distribution
hyperbinomial distribution
Poisson distribution
hypergeometric distribution
binomial distribution
Question 23
The number of finance majors within the School of Business is an example of _______.
a discrete random variable
the normal distribution
a constant
the Poisson distribution
a continuous random variable
Question 24
Lucy Baker is analyzing demographic characteristics of two television programs, American Idol (population 1) and 60 Minutes (population 2). Previous studies indicate no difference in the ages of the two audiences (The mean age of each audience is the same.) Lucy plans to test this hypothesis using a random sample of 100 from each audience. Her null hypothesis is ____________.
m1 - m2 = 0
m1 - m2 < 1
m1 - m2 > 0
m1 - m2 < 0
m1 - m2 ≠ 0
Question 25
Ophelia O'Brien, VP of Consumer Credit of American First Banks (AFB), monitors the default rate on personal loans at the AFB member banks. One of her standards is "no more than 5% of personal loans should be in default." On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 30 defaulted loans. Ophelia's null hypothesis is _______.
n = 0.05
n = 500
n = 30
p > 0.05
p = 0.05
Question 26
The mean life of a particular brand of light bulb is 1200 hours. If you know that at about 95% of this brand of bulbs will last between 1100 and 1300 hours, then what is the standard deviation of the light bulbs' life?
200
100
75
25
50
Question 27
The number of cars arriving at a toll booth in five-minute intervals is Poisson distributed with a mean of 3 cars arriving in five-minute time intervals. The probability of 5 cars arriving over a five-minute interval is _______.
0.1500
0.0940
0.1008
0.0417
0.2890
Question 28
The following frequency distribution was constructed for the wait times in the emergency room.
The frequency distribution reveals that the wait times in the emergency room are _______.
skewed to the left
not skewed
normally distributed
symmetrical
skewed to the right
Question 29
Catherine Chao, Director of Marketing Research, is evaluating consumer acceptance of a new toothpaste package. Her staff reports that 17% of a random sample of 200 households prefers the new package to all other package designs. If Catherine concludes that 17% of all households prefer the new package, she is using _______.
a range estimate
a point estimate
a statistical parameter
an exact estimate
an interval estimate
Question 30
The weight of a USB flash drive is 30 grams and is normally distributed. Periodically, quality control inspectors at Dallas Flash Drives randomly select a sample of 17 USB flash drives. If the mean weight of the USB flash drives is too heavy or too light the machinery is shut down for adjustment; otherwise, the production process continues. The last sample showed a mean and standard deviation of 31.9 and 1.8 grams, respectively. Using a = 0.10, the appropriate decision is _______.
reject the null hypothesis and do not shut down the process
fail to reject the null hypothesis and shut down the process
fail to reject the null hypothesis and do not shut down the process) do nothing
reject the null hypothesis and shut down the process
