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Business Analytics Methods Models And Decisions 1st Edition James R. Evans - Solutions
8. The director of a nonprofit ballet company in a medium-sized U.S. city is planning its next fundraising campaign. In recent years, the program has found the following percentages of donors and gift levels:Gift Level Amount Average Number of Gifts Benefactor $10,000 2 Philanthropist $5,000 5
7. A stockbroker calls on potential clients from referrals. For each call, there is a 15% chance that the client will decide to invest with the firm. Sixty percent of those interested are found not to be qualified, based on the brokerage firm’s screening criteria. The remaining are qualified. Of
6. For a new product, sales volume in the first year is estimated to be 100,000 units and is projected to grow at a rate of 7% per year. The selling price is $10 and will increase by $0.50 each year. Per-unit variable costs are $3, and annual fixed costs are $200,000. Per-unit costs are expected to
5. The Radio Shop sells two popular models of portable sport radios, model A and model B. The sales of these products are not independent of each other (in economics, we call these substitutable products, because if the price of one increases, sales of the other will increase). The store wishes to
4. A garage band wants to hold a concert. The expected crowd is 3,000. The average expenditure on concessions is $15. Tickets sell for $10 each, and the band’s profit is 80% of the gate, along with concession sales, minus a fixed cost of $10,000.Develop a general mathematical model and implement
3. Return on investment (ROI) is computed in the following manner: ROI is equal to turnover multiplied by earnings as a percent of sales. Turnover is sales divided by total investment. Total investment is current assets (inventories, accounts receivable, and cash) plus fixed assets. Earnings equal
2. A (greatly) simplified model of the national economy can be described as follows.The national income is the sum of three components: consumption, investment, and government spending. Consumption is related to the total income of all individuals and to the taxes they pay on income. Taxes are
1. A company is trying to predict the long-run market share of a new men’s deodorant.4 Based on initial marketing studies, they believe that 35% of new purchasers in this market will ultimately try this brand. They believe that customers will purchase their brand about 40% of the time in the
• Create data tables and tornado charts using Risk Solver Platform.
• Construct one- and two-way data tables.
• Apply the Excel Trendline tool to fit models to data.
• Use data-driven approaches to develop predictive analytic models.
• Implement mathematical decision models on spreadsheets.
• Develop analytic models mathematically using logicdriven approaches.
• Explain how to use influence diagrams to help develop predictive analytic models.
27. For the data in the Excel file New Account Processing, perform chi-square tests for independence to determine if certification is independent of gender, and if certification is independent of having prior industry background.
26. For the data in the Excel file Graduate School Survey, perform a chi-square test for independence to determine if plans to attend graduate school are independent of gender.
25. For the data in the Excel file Accounting Professionals, perform a chi-square test of independence to determine if age group is independent of having a graduate degree.
24. Using the data in the Excel file Freshman College Data, use ANOVA to determine whether the mean retention rate is the same for all colleges over the fouryear period. Second, use ANOVA to determine if the mean ACT and SAT scores are the same each year over all colleges.
23. Using the data in the Excel file Cell Phone Survey, apply ANOVA to determine if the mean response for Value for the Dollar is the same for different types of cell phones.
22. In the Excel file Restaurant Sales, determine if the variance of weekday sales is the same as that of weekend sales for each of the three variables (lunch, dinner, and delivery).
21. Using the data in the Excel file Student Grades, which represent exam scores in one section of a large statistics course, test the hypothesis that the variance in grades is the same for both tests.
20. The Excel file Unions and Labor Law Data reports the percent of public- and private-sector employees in unions in 1982 for each state, along with indicators whether the states had a bargaining law that covered public employees or right-towork laws.a. Test the hypothesis that the percent of
19. Using the data in the Excel file Ohio Education Performance, test the hypotheses that the mean difference in writing and reading scores is zero and that the mean difference in math and science scores is zero. Use the paired-sample procedure.
17. The director of human resources for a large bank has compiled data on about 70 former employees at one of the bank’s call centers (see the Excel file Call Center Data). For each of the following, assume equal variances of the two populations.a. Test the null hypothesis that the average length
16. Determine if there is evidence to conclude that the proportion of males who plan to attend graduate school is larger than the proportion of females who plan to attend graduate school using the data in the Excel file Graduate School Survey. Use a level of significance of 0.10.
15. In the Excel file Credit Risk Data, test the hypotheses that the number of months employed is the same for applicants with low credit risk as those with high credit risk evaluations.
14. In the Excel file Cell Phone Survey, test the hypothesis that the mean responses for Value for the Dollar and Customer Service do not differ by gender.
13. The Excel file Accounting Professionals provides the results of a survey of 27 employees in a tax division of a Fortune 100 company.a. Test the null hypothesis that the average number of years of service is the same for males and females.b. Test the null hypothesis that the average years of
12. Determine if there is evidence to conclude that the mean number of vacations taken by married individuals is less than the number taken by single/divorced individuals using the data in the Excel file Vacation Survey.
11. Using the Excel file Facebook Survey, determine if the mean number of hours spent online per week is the same for males as it is for females.
10. Using the data in the Excel file Consumer Transportation Survey, test the following null hypotheses:a. Individuals spend at least 10 hours per week in their vehicles.b. Individuals drive an average of 450 miles per week.c. The average age of SUV drivers is no greater than 35.d. At least 75% of
9. An employer is considering negotiating its pricing structure for health insurance with its provider if there is sufficient evidence that customers will be willing to pay a lower premium for a higher deductible. Specifically, they want at least 30%of their employees to be willing to do this.
8. The Excel file Room Inspection provides data for 100 room inspections at 25 hotels in a major chain. Management would like the proportion of nonconforming rooms to be less than 2%. Test an appropriate hypothesis to determine if management can make this claim.
7. The Excel file Sales Data provides data on a sample of customers. An industry trade publication stated that the average profit per customer for this industry was at least $4,500. Using a test of hypothesis, do the data support this claim or not?The company believes that their average profit
6. Formulate and test a hypothesis to determine if statistical evidence suggests that the graduation rate for either top liberal arts colleges or research universities in the sample Colleges and Universities exceeds 90%. Do the data support a conclusion that the graduation rate exceeds 85%? Would
5. The State of Ohio Department of Education has a mandated ninth-grade proficiency test that covers writing, reading, mathematics, citizenship (social studies), and science. The Excel file Ohio Education Performance provides data on success rates (defined as the percent of students passing) in
4. Using the data in the Excel file Computer Repair Times, determine if the company can claim that its average repair time is less than 12 days.
3. Using the data in the Excel file Airport Service Times, determine if the airline can claim that its average service time is less than 2 minutes.
2. Call centers typically have high turnover. The director of human resources for a large bank has compiled data on about 70 former employees at one of the bank’s call centers in the Excel file Call Center Data. In writing an article about call center working conditions, a reporter has claimed
1. A retailer believes that its new advertising strategy will increase sales. Previously, the mean spending in 15 categories of consumer items in both the 18–34 and 35+ age groups was $70.00.a. Formulate a hypothesis test to determine if the mean spending in these categories has statistically
• Conduct and interpret the results of a chi-square test for independence.
• Explain the purpose of hypothesis testing.
23. If a manufacturer conducted a survey among randomly selected target market households and wanted to be 95% confident that the difference between the sample estimate and the actual market share for its new product was no more than {3, what sample size would be needed?
22. Trade associations such as the United Dairy Farmers Association frequently conduct surveys to identify characteristics of their membership. If this organization conducted a survey to estimate the annual per-capita consumption of milk and wanted to be 95% confident that the estimate was no more
21. For the Excel file Credit Approval Decisions, find 95% confidence and prediction intervals for the credit scores and revolving balance of homeowners and nonhomeowners.How do they compare?
20. The Excel file Restaurant Sales provides sample information on lunch, dinner, and delivery sales for a local Italian restaurant. Develop 95% prediction intervals for the dollar sales of each of these variables for next Saturday.
19. Using the data in the worksheet Consumer Transportation Survey, develop 95%and 99% prediction intervals for the following:a. the hours per week that an individual will spend in his or her vehicleb. the number of miles driven per week
18. A study of nonfatal occupational injuries in the United States found that about 31% of all injuries in the service sector involved the back. The National Institute for Occupational Safety and Health (NIOSH) recommended conducting a comprehensive ergonomics assessment of jobs and workstations.
17. A marketing study found that the mean spending in 15 categories of consumer items for 297 respondents in the 18–34 age group was $71.86 with a standard deviation of$70.90. For 736 respondents in the 35+ age group, the mean and standard deviation were $61.53 and $45.29, respectively. Develop
16. The Excel file Baseball Attendance shows the attendance in thousands at San Francisco Giants’ baseball games for the 10 years before the Oakland A’s moved to the Bay Area in 1968, as well as the combined attendance for both teams for the next 11 years. Develop 95% confidence intervals for
15. Using data in the Excel file Colleges and Universities, find 95% confidence intervals for the median SAT for each of the two groups, liberal arts colleges and research universities. Based on these confidence intervals, does there appear to be a difference in the median SAT scores between the
14. A manufacturer conducted a survey among 400 randomly selected target market households in the test market for its new disposable diapers. The objective of the survey was to determine the market share for its new brand. If the sample point estimate for market share is 18%, develop a 95%
13. Using the data in the worksheet Consumer Transportation Survey, develop 95%confidence for the following:a. the proportion of individuals who are satisfied with their vehicleb. the proportion of individuals who have at least one child
12. If, based on a sample size of 200, a political candidate found that 125 people would vote for her in a two-person race, what is the 95% confidence interval for her expected proportion of the vote? Would she be confident of winning based on this poll?
11. If, based on a sample size of 600, a political candidate finds that 318 people would vote for him in a two-person race, what is the 95% confidence interval for his expected proportion of the vote? Would he be confident of winning based on this poll?
10. The Excel file Restaurant Sales provides sample information on lunch, dinner, and delivery sales for a local Italian restaurant. Develop 95% confidence intervals for the mean of each of these variables, as well as for weekday and weekend sales.What conclusions can you reach?
9. Find the standard deviation of the total assets held by the bank in the Excel file Credit Risk Data.a. Treating the records in the database as a population, use your sample in Problem 2 and compute 90%, 95%, and 99% confidence intervals for the total assets held in the bank by loan applicants
8. Using the data in the Excel file Accounting Professionals, find and interpret 95%confidence intervals for the following:a. mean years of serviceb. proportion of employees who have a graduate degree
7. A popular soft drink is sold in 2-liter (2,000-milliliter) bottles. Because of variation in the filling process, bottles have a mean of 2,000 milliliters and a standard deviation of 20, normally distributed.a. If the manufacturer samples 100 bottles, what is the probability that the mean is less
6. In determining automobile mileage ratings, it was found that the mpg in the city for a certain model is normally distributed, with a mean of 24 mpg and a standard deviation of 1.0 mpg. Suppose that the car manufacturer samples 9 cars from its assembly line and tests them for mileage ratings.a.
5. Repeat the sampling experiment in Example 6.3 for sample sizes 50, 100, 250, and 500. Compare your results to the example and use the empirical rules to analyze the sampling error. For each sample, also find the standard error of the mean using formula (6.1).
4. Find the current 30 stocks that comprise the Dow Jones Industrial Average. Set up an Excel spreadsheet for their names, market capitalization, and one or two other key financial statistics (search Yahoo! Finance or a similar Web source). Using the Excel Sampling tool, obtain a random sample of 5
3. Describe how to apply stratified sampling to sample from the Credit Risk Data file based on the different types of loans. Implement your process in Excel to choose a random sample consisting of 10% of the records for each type of loan.
2. Number the rows in the Excel file Credit Risk Data to identify each record. The bank wants to sample from this database to conduct a more-detailed audit. Use the Excel Sampling tool to find a simple random sample of 20 unique records.
1. Your college or university wishes to obtain reliable information about student perceptions of administrative communication. Describe how to design a sampling plan for this situation based on your knowledge of the structure and organization of your college or university. How would you implement
• Calculate the standard error of the mean.
46. Use Risk Solver Platform to fit a distribution to the data in the Excel file Computer Repair Times. Try the three different statistical measures for evaluating goodness of fit and see if they result in different best-fitting distributions.
45. A government agency is putting a large project out for low bid. Bids are expected from 10 different contractors and will have a normal distribution with a mean of$3.5 million and a standard deviation of $0.25 million. Devise and implement a sampling experiment for estimating the distribution of
44. A formula in financial analysis is: Return on equity net profit margin total asset turnover equity multiplier. Suppose that the equity multiplier is fixed at 4.0, but that the net profit margin is normally distributed with a mean of 3.8% and a standard deviation of 0.4%, and that the
43. Use the Excel Random Number Generation tool to generate 100 samples of the number of customers that the financial consultant in Problem 28 will have on a daily basis. What percentage will meet his target of at least 5?
42. Use formula (5.22) to obtain a sample of 25 outcomes for a game of Battleship™as described in Problem 31. Find the average and standard deviation for these 25 outcomes.
41. Develop a procedure to sample from the probability distribution of two-card hands in Problem 2. Implement your procedure on a spreadsheet and use the VLOOKUP function to sample 10 outcomes from the distribution.
40. Develop a procedure to sample from the probability distribution of soft-drink choices in Problem 1. Implement your procedure on a spreadsheet and use the VLOOKUP function to sample 10 outcomes from the distribution.
39. The actual delivery time from Giodanni’s Pizza is exponentially distributed with a mean of 20 minutes.a. What is the probability that the delivery time will exceed 30 minutes?b. What proportion of deliveries will be completed within 20 minutes?
38. A lightbulb is warranted to last for 3,000 hours. If the time to failure is exponentially distributed with a true mean of 2,750 hours, what is the probability that it will last at least 3,000 hours?
37. Historical data show that customers who download music from a popular Web service spend approximately $20 per month, with a standard deviation of $4. Find the probability that a customer will spend at least $15 per month. If the company samples 100 customers, find the mean and standard
36. A supplier contract calls for a key dimension of a part to be between 1.96 and 2.04 centimeters. The supplier has determined that the standard deviation of its process, which is normally distributed, is 0.10 centimeter.a. If the actual mean of the process is 1.98, what fraction of parts will
35. A popular soft drink is sold in 2-liter (2,000-milliliter) bottles. Because of variation in the filling process, bottles have a mean of 2,000 milliliters and a standard deviation of 20, normally distributed.a. If the process fills the bottle by more than 60 milliliters, the overflow will cause
34. The distribution of the SAT scores in math for an incoming class of business students has a mean of 580 and standard deviation of 25. Assume that the scores are normally distributed.a. Find the probability that an individual’s SAT score is less than 550.b. Find the probability that an
33. In determining automobile-mileage ratings, it was found that the mpg (X) for a certain model is normally distributed, with a mean of 30 mpg and a standard deviation of 1.5 mpg. Find the following:a. P1X 6 282b. P128 6 X 6 322c. P1X 7 332d. P1X 6 312e. The mileage rating that the upper 5% of
32. A contractor has estimated that the minimum number of days to remodel a bathroom for a client is 10 days. He also estimates that 80% of similar jobs are completed within 18 days. If the remodeling time is uniformly distributed, what should be the parameters of the uniform distribution?
31. The time required to play a game of Battleship™ is uniformly distributed between 20 and 60 minutes.a. Find the expected value and variance of the time to complete the game.b. What is the probability of finishing within 25 minutes?c. What is the probability that the game would take longer than
30. Verify that the function corresponding to the following figure is a valid probability density function. Then find the following probabilities:a. P1x 6 82b. P1x 7 72c. P16 6 x 6 102d. P18 6 x 6 112
29. The number and frequency of Atlantic hurricanes annually from 1940 through 2007 is shown here.Number Frequency 0 5 1 16 2 19 3 13 4 3 5 5 6 4 7 2 8 1a. Find the probabilities of 0–8 hurricanes each season using these data.b. Assuming a Poisson distribution and using the mean number of
28. A financial consultant has an average of 6 customers he consults with each day, which are assumed to be Poisson distributed. The consultant’s overhead requires that he consult with at least 5 customers in order that fees cover expenses. Find the probabilities of 0–4 customers in a given
27. A telephone call center where people place marketing calls to customers has a probability of success of 0.10. The manager is very harsh on those who do not get a sufficient number of successful calls. Find the number of calls needed to ensure that there is a probability of 0.90 of obtaining 5
26. A popular resort hotel has 300 rooms and is usually fully booked. About 4% of the time a reservation is canceled before the 6:00 p.m. deadline with no penalty.What is the probability that at least 280 rooms will be occupied? Use the binomial distribution to find the exact value and the normal
25. During one year, a particular mutual fund has outperformed the S&P 500 index 33 out of 52 weeks. Find the probability that this performance or better would happen only by chance.
24. If a cell phone company conducted a telemarketing campaign to generate new clients and the probability of successfully gaining a new customer was 0.05, what are the probabilities that contacting 25 potential customers would result in at least 5 new customers?
23. What type of distribution models the random variable Prior Call Center Experience in the file Call Center Data? Define the parameter(s) for this distribution based on the data.
22. A major application of analytics in marketing is determining the attrition of customers.Suppose that the probability of a long-distance carrier’s customer leaving for another carrier from one month to the next is 0.15. What distribution models the retention of an individual customer? What is
21. Based on the data in the Excel file Consumer Transportation Survey, develop a probability mass function and cumulative distribution function (both tabular and as charts) for the random variable Number of Children. What is the probability that an individual in this survey has fewer than two
20. Construct the probability distribution for the value of a 2-card hand dealt from a standard deck of 52 cards (all face cards have a value of 10 and an ace has a value of 11).a. What is the probability of being dealt 21?b. What is the probability of being dealt 16?c. Construct a chart for the
19. The weekly demand of a slow-moving product has the following probability mass function:Demand, x Probability, f(x)0 0.1 1 0.3 2 0.4 3 0.2 4 or more 0 Find the expected value, variance, and standard deviation of weekly demand.
18. An investor estimates that there is a 1 in 10 chance that a stock purchase will lose 20% of its value, a 2 in 10 chance that it will break even, a 4 in 10 chance that it will gain 15%, and a 3 in 10 chance that it will gain 30%. What is the expected return based on these estimates?
17. A consumer products company found that 48% of successful products also received favorable results from test market research, whereas 12% had unfavorable results but nevertheless were successful. They also found that 28% of unsuccessful products had unfavorable research results, whereas 12% of
16. In the roulette example described in Problem 7, what is the probability that the outcome will be green twice in a row? What is the probability that the outcome will be black twice in a row?
15. In drawing two cards in the scenario in Problem 2, what is the probability of drawing two 10s? If three cards are drawn, what is the probability of drawing three 10s?
14. A home pregnancy test is not always accurate. Suppose the probability is 0.02 that the test indicates that a woman is pregnant when she actually is not, and the probability is 0.03 that the test indicates that a woman is not pregnant when she really is. Assume that the probability that a woman
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