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Data Analysis And Decision Making 4th Edition Christian Albright, Wayne Winston, Christopher Zappe - Solutions
FineHair is developing a new product to promote hair growth in cases of male pattern baldness. If FineHair markets the new product and it is successful, the company will earn $1,000,000 in additional profit. If the marketing of this new product proves to be unsuccessful, the company will lose
A product manager at Clean & Brite (C&B) wants to determine whether her company should market a new brand of toothpaste. If this new product succeeds in the marketplace, C&B estimates that it could earn $1,800,000 in future profits from the sale of the new toothpaste. If this new product fails,
Ford is going to produce a new vehicle, the Pioneer, and wants to determine the amount of annual capacity it should build. Ford’s goal is to maximize the profit from this vehicle over the next 10 years. Each vehicle will sell for $13,000 and incur a variable production cost of $10,000. Building
Pizza King (PK) and Noble Greek (NG) are competitive pizza chains. PK believes there is a 25% chance that NG will charge $6 per pizza, a 50% chance NG will charge $8 per pizza, and a 25% chance that NG will charge $10 per pizza. If PK charges price p1 and NG charges price p2, PK will sell 100 +
Many decision problems have the following simple structure. A decision maker has two possible decisions, 1 and 2. If decision 1 is made, a sure cost of c is incurred. If decision 2 is made, there are two possible outcomes, with costs c1 and c2 and probabilities p and 1 - p. We assume that c1 < c <
A nuclear power company is deciding whether to build a nuclear power plant at Diablo Canyon or at Roy Rogers City. The cost of building the power plant is $10 million at Diablo and $20 million at Roy Rogers City. If the company builds at Diablo, however, and an earthquake occurs at Diablo during
Consider again Techware’s decision problem described in Problem 40. Suppose now that Techware’s utility function of net revenue x (measured in dollars), earned from the given marketing opportunities, is U(x) = 1 – e-x/350000.a. Find the decision that maximizes Techware’s expected utility.
Consider again the bank’s customer loan decision problem in Problem 51. Suppose now that the bank’s utility function of profit x (in dollars) is U(x) = 1 – e-x/500000. Find the strategy that maximizes the bank’s expected utility in this case.How does this optimal strategy compare to the
The Indiana University basketball team trails by two points with eight seconds to go and has the ball. Should it attempt a two-point shot or a three-point shot? Assume that the Indiana shot will end the game and that no foul will occur on the shot. Assume that a three point shot has a 30% chance of
George Lindsey (1959) looked at box scores of more than 1000 baseball games and found the expected number of runs scored in an inning for each on-base and out situation to be as listed in the file P06_64.xlsx. For example, if a team has a man on first base with one out, it scores 0.5 run on average
One controversial topic in basketball (college or any other level) is whether to foul a player deliberately with only a few seconds left in the game. Specifically, consider the following scenario. With about 10 seconds left in the game, team A is ahead of team B by three points, and team B is just
The following situation actually occurred in a 2009 college football game between Washington and Notre Dame. With about 3.5 minutes left in the game, Washington had fourth down and one yard to go for a touchdown, already leading by two points. Notre Dame had just had two successful goal-line stands
Mr. Maloy has just bought a new $30,000 sport utility vehicle. As a reasonably safe driver, he believes that there is only about a 5% chance of being in an accident in the coming year. If he is involved in an accident, the damage to his new vehicle depends on the severity of the accident. The
The purchasing agent for a PC manufacturer is currently negotiating a purchase agreement for a particular electronic component with a given supplier. This component is produced in lots of 1000, and the cost of purchasing a lot is $30,000. Unfortunately, past experience indicates that this supplier
A home appliance company is interested in marketing an innovative new product. The company must decide whether to manufacture this product in house or employ a subcontractor to manufacture it. The file P06_69.xlsx contains the estimated probability distribution of the cost of manufacturing one unit
A grapefruit farmer in central Florida is trying to decide whether to take protective action to limit damage to his crop in the event that the overnight temperature falls to a level well below freezing. He is concerned that if the temperature falls sufficiently low and he fails to make an effort to
A retired partner from a large brokerage firm has one million dollars available to invest in particular stocks or bonds. Each investment’s annual rate of return depends on the state of the economy in the coming year. The file P06_71.xlsx contains the distribution of returns for these stocks and
A city in Ohio is considering replacing its fleet of gasoline-powered automobiles with electric cars. The manufacturer of the electric cars claims that this municipality will experience significant cost savings over the life of the fleet if it chooses to pursue the conversion. If the manufacturer
A manufacturer must decide whether to extend credit to a retailer who would like to open an account with the firm. Past experience with new accounts indicates that 45% are high-risk customers, 35% are moderate risk customers, and 20% are low-risk customers. If credit is extended, the manufacturer
A television network earns an average of $1.6 million each season from a hit program and loses an average of $400,000 each season on a program that turns out to be a flop. Of all programs picked up by this network in recent years, 25% turn out to be hits and 75% turn out to be flops. At a cost of C
A publishing company is trying to decide whether to publish a new business law textbook. Based on a careful reading of the latest draft of the manuscript, the publisher’s senior editor in the business textbook division assesses the distribution of possible payoffs earned by publishing this new
Sharp Outfits is trying to decide whether to ship some customer orders now via UPS or wait until after the threat of another UPS strike is over. If Sharp Outfits decides to ship the requested merchandise now and the UPS strike takes place, the company will incur $60,000 in delay and shipping costs.
A homeowner wants to decide whether he should install an electronic heat pump in his home. Given that the cost of installing a new heat pump is fairly large, the homeowner wants to do so only if he can count on being able to recover the initial expense over five consecutive years of cold winter
Sarah Chang is the owner of a small electronics company. In six months, a proposal is due for an electronic timing system for the next Olympic Games. For several years, Chang’s company has been developing a new microprocessor, a critical component in a timing system that would be superior to any
The Ventron Engineering Company has just been awarded a $2 million development contract by the U.S. Army Aviation Systems Command to develop a blade spar for its Heavy Lift Helicopter program. The blade spar is a metal tube that runs the length of and provides strength to the helicopter blade. Due
Suppose an investor has the opportunity to buy the following contract, a stock call option, on March 1. The contract allows him to buy 100 shares of ABC stock at the end of March, April, or May at a guaranteed price of $50 per share. He can exercise this option at most once. For example, if he
An electric utility company is trying to decide whether to replace its PCB transformer in a generating station with a new and safer transformer. To evaluate this decision, the utility needs information about the likelihood of an incident, such as a fire, the cost of such an incident, and the cost
The ending of the game between the Indianapolis Colts and the New England Patriots (NFL teams) in Fall 2009 was quite controversial. With about two minutes left in the game, the Patriots were ahead 34 to 28 and had the ball on their own 28-yard line with fourth down and two yards to go. Their
Suppose you believe that the price of a particular stock goes up each day with probability p and goes down with probability 1 - p. You also believe the daily price changes are independent of one another. However, you are not sure of the value of p. Based on your current information; you believe p
The file P02_07.xlsx includes data on 204 employees at the (fictional) company Beta Technologies. For this problem, consider this data set as the population frame.a. Using the method in this section (not StatTools), generate a simple random sample of size 20 from this population.b. Use StatTools to
The file P07_02.xlsx contains data on the 1995 students who have gone through the MBA program at State University. You can consider this the population of State University’s MBA students. a. Find the mean and standard deviation for each of the numerical variables in this population. Also, find
The file P02_35.xlsx contains data from a survey of 500 randomly selected households.a. Suppose you decide to generate a systematic random sample of size 25 from this population of data. How many such samples are there? What is the mean of Debt for each of the first three such samples, using the
Recall from Chapter 2 that the file Supermarket Transactions.xlsx contains over 14,000 transactions made by supermarket customers over a period of approximately two years. For this problem, consider this data set the population of transactions. a. If you were interesting in estimating the mean of
This problem illustrates an interesting variation of simple random sampling.a. Open a blank spreadsheet and use the RAND() function to create a column of 1000 random numbers. Don’t freeze them. This is actually a simple random sample from the uniform distribution between 0 and 1. Use the COUNTIF
Another type of random sample is called a bootstrap sample. Given a data set with n observations, a bootstrap sample, also of size n, is when you randomly sample from the data set with replacement. To do so, you keep choosing a random integer from 1 to n and include that item in the sample.The
A manufacturing company’s quality control personnel have recorded the proportion of defective items for each of 500 monthly shipments of one of the computer components that the company produces. The data are in the file P07_07.xlsx. The quality control department manager does not have sufficient
The manager of a local fast-food restaurant is interested in improving the service provided to customers who use the restaurant’s drive-up window. As a first step in this process, the manager asks his assistant to record the time it takes to serve a large number of customers at the final window
The file P02_16.xlsx contains traffic data from 256 weekdays on four variables. Each variable lists the number of arrivals during a specific 5-minute period of the day. For this problem, consider this data set a simple random sample from all possible weekdays. a. For each of the four variables,
The file P02_35.xlsx contains data from a survey of 500 randomly selected households. For this problem, consider this data set a simple random sample from all possible households, where the number of households in the population is well over 1,000,000. a. Create a new variable, Total Income that is
The file P02_10.xlsx contains midterm and final exam scores for 96 students in a corporate finance course. For this problem, assume that these 96 students represent a sample of the 175 students taking the course, and that these 175 students represent the relevant population.a. Assuming the same
Create a simulation similar to the one in the Wheel of Fortune Similation.xlsx file. However, suppose that the outcome of each spin is no longer uniformly distributed between $0 and $1000. Instead, it is the number of 7s you get in 20 rolls of two dice. In other words, each spin results in a
Suppose you plan to take a simple random sample from a population with N members. Specifically, you plan to sample a percentage p of the population. If p is 1%, is the finite population correction really necessary? Does the answer depend on N? Explain. Then answer the same questions when p is 5%,
The file P07_14.xlsx contains a very small population of only five members. For each member, the height of the person is listed. The purpose of this problem is to let you see exactly what a sampling distribution is. Find the exact sampling distribution of the sample mean with sample size 3. Verify
The file DVD Movies.xlsx contains a large data set of 10,000 customer transactions for a fictional chain of video stores in the United States. Each row corresponds to a different customer and lists (1) A customer ID number (1–10,000), (2) The state where the customer lives, (3) The city where the
Calculate the following probabilities using Excel. a. P(t10 ≥ 1.75), where t10 has a t distribution with 10 degrees of freedom.b. P(t100 ≥ 1.75), where t100 has a t distribution with 100 degrees of freedom. How do you explain the difference between this result and the one obtained in part a?c.
Calculate the following quantities using Excel. a. P(-2.00 ≤ t10 ≤ 1.00), where t10 has a t distribution with 10 degrees of freedom.b. P(-2.00 ≤ t100 ≤ 1.00), where t100 has a t distribution with 100 degrees of freedom. How do you explain the difference between this result and the one
Calculate the following quantities using Excel. a. Find the value of x such that P(t10 > x) = 0.75, where t10 has a t distribution with 10 degrees of freedom. b. Find the value of y such that P(t100 > y) = 0.75, where t100 has a t distribution with 100 degrees of freedom. How do you explain the
A manufacturing company’s quality control personnel have recorded the proportion of defective items for each of 500 monthly shipments of one of the computer components that the company produces. The data are in the file P07_07.xlsx. The quality control department manager does not have sufficient
The file P08_05.xlsx contains salary data on all NFL players in each of the years 2002 to 2009. Because this file contains all players for each of these years, you can calculate the population mean for each year if population is defined as all NFL players that year. However, proceed as in the
The file P08_06.xlsx contains data on repetitive task times for each of two workers. John has been doing this task for months, whereas Fred has just started. Each time listed is the time (in seconds) to perform a routine task on an assembly line. The times shown are in chronological order.a. Find a
The manager of a local fast-food restaurant is interested in improving the service provided to customers who use the restaurant’s drive-up window.As a first step in this process, the manager asks an assistant to record the time (in seconds) it takes to serve a large number of customers at the
Continuing Problem 5, generate a random sample of 50 players for each of the eight years in the P08_05.xlsx file. For each of these samples, construct a 95% confidence interval for the mean total salary for that year. What is the confidence level that any particular one of these confidence
The file P02_16.xlsx contains the number of arrivals at a turnpike tollbooth for each of four 5-minute intervals for each of 256 days. For this problem, assume that each column, such as arrivals from 8:00 AM to 8:05 AM, is a random sample of all arrivals from the corresponding hour of the day, such
A light bulb manufacturer wants to estimate the total number of defective bulbs contained in all of the boxes shipped by the company during the past week. Production personnel at this company have recorded the number of defective bulbs found in each of 50 randomly selected boxes shipped during the
Auditors of a particular bank are interested in comparing the reported value of all 2265 customer savings account balances with their own findings regarding the actual value of such assets. Rather than reviewing the records of each savings account at the bank, the auditors decide to examine a
Suppose you are gambling on a roulette wheel. Each time the wheel is spun, the result is one of the outcomes 0, 1, and so on through 36. Of these outcomes, 16 are red, 16 are black, and 1 is green. On each spin you bet $5 that a red outcome will occur and $1 that the green outcome will occur. If
A drugstore manager needs to purchase adequate supplies of various brands of toothpaste to meet the ongoing demands of its customers. In particular, the company is interested in estimating the proportion of its customers who favor the country’s leading brand of toothpaste, Crest. The Data sheet
The same data as in the previous problem are stored in a different format in the last two sheets of the P08_15.xlsx file.a. Use StatTools to find a 95% confidence interval for the proportion who favor Crest from the data in the Counts sheet. Using this same data on counts, calculate the confidence
The employee benefits manager of a large public university would like to estimate the proportion of full-time employees who prefer adopting the first (plan A) of three available health care plans in the next annual enrollment period. A random sample of the university’s employees and their
A market research consultant hired by a leading soft drink company wants to determine the proportion of consumers who favor its low-calorie brand over the leading low-calorie competitor in a particular geographic region. A random sample of 250 consumers from the market under investigation is
Starting with the data from problem 17 in the file P08_17.xlsx, restructure the data so that you have a table of counts. Then use StatTools on the counts to answer the same questions as in problem 17.
Starting with the data from problem 18 in the file P08_18.xlsx, restructure the data so that you have a table of proportions. Then use StatTools on the proportions to answer the same questions as in problem 18.
Senior management of a large consulting firm is concerned about a growing decline in the organization’s weekly number of billable hours. Ideally, the organization expects each professional employee to spend at least 40 hours per week on work. The file P08_21.xlsx contains the work hours reported
The file P08_06.xlsx contains data on repetitive task times for each of two workers. John has been doing this task for months, whereas Fred has just started. Each time listed is the time (in seconds) to perform a routine task on an assembly line. The times shown are in chronological order.a. Find a
The director of a university’s career development center is interested in comparing the starting annual salaries of male and female students who recently graduated from the university and commenced fulltime employment. The director has formed pairs of male and female graduates with the same major
A real estate agent has collected a random sample of 75 houses that were recently sold in a suburban community. She is particularly interested in comparing the appraised value and recent selling price of the houses in this particular market. The data are provided in the file P08_24.xlsx. Using this
The Wall Street Journal CEO Compensation Study analyzed CEO pay from many U.S. companies with fiscal year 2008 revenue of at least $5 billion that filed their proxy statements between October 2008 and March 2009. The data are in the file P02_30.xlsx. a. Create a new column, Total, that is the sum
A company employs two shifts of workers. Each shift produces a type of gasket where the thickness is the critical dimension. The average thickness and the standard deviation of thickness for shift 1, based on a random sample of 30 gaskets, are 10.53 mm and 0.14 mm. The similar figures for shift 2,
A company that advertises on the Web wants to know which search engine its customers prefer as their primary search engine: Google or Bing. Specifically, the company wants to know whether the preference depends on the browser being used. The file P08_28.xlsx contains counts of 800 customers'
A market research consultant hired by a leading soft-drink company is interested in estimating the difference between the proportions of female and male consumers who favor the company’s low-calorie brand over the leading competitor’s low-calorie brand in a particular geographical region. A
The file P02_35.xlsx contains data from a survey of 500 randomly selected households. Researchers would like to use the available sample information to see whether home ownership rates vary by household location. For example, is there a nonzero difference between the proportions of individuals who
Continuing problem 29, marketing managers at the soft-drink company have asked their market research consultant to explore further the difference between the proportions of women and men who prefer drinking their brand over the leading competitor. Specifically, the company’s managers would like
Elected officials in a California city are preparing the annual budget for their community. They would like to estimate how much their constituents living in this city are typically paying each year in real estate taxes. Given that there are over 100,000 homeowners in this city, the officials have
You have been assigned to determine whether more people prefer Coke or Pepsi. Assume that roughly half the population prefers Coke and half prefers Pepsi. How large a sample do you need to take to ensure that you can estimate, with 95% confidence, the proportion of people preferring Coke within 2%
You are trying to estimate the average amount a family spends on food during a year. In the past the standard deviation of the amount a family has spent on food during a year has been approximately $1000. If you want to be 99% sure that you have estimated average family food expenditures within
In past years, approximately 20% of all U.S. families purchased potato chips at least once a month. You are interested in determining the fraction of all U.S. families that currently purchase potato chips at least once a month. How many families must you survey if you want to be 99% sure that your
Continuing Problem 32, suppose that the officials in this city want to estimate the proportion of taxpayers whose annual real estate tax payments exceed $2000. a. What sample size is required to generate a 99% confidence interval for this proportion with a half length of 0.10? Assume for now that
Continuing the previous problem, suppose that the officials in this city want to estimate the difference between the proportions, labeled p1 and p2, of taxpayers living in neighborhood 1 whose annual real estate tax payments exceed $2000 and the similar proportion for taxpayers living in
A sample of 15 quality control managers with more than 20 years experience have an average salary of $68,000 and a sample standard deviation of $19,000. a. You can be 95% confident that the mean salary for all quality managers with at least 20 years of experience is between what two numbers? What
Political polls typically sample randomly from the U.S. population to investigate the percentage of voters who favor some candidate or issue. The number of people polled is usually on the order of 1000. Suppose that one such poll asks voters how they feel about the President’s handling of
Referring to the previous problem, you often hear the results of such a poll in the news. In fact, the newscasters usually report something such as, “44.9% of the population approve or strongly approve of the President’s handling of the environment. The margin of error in this result is plus or
The widths of 100 elevator rails have been measured. The sample mean and standard deviation of the elevator rails are 2.05 inches and 0.01 inch. a. Find a 95% confidence interval for the average width of an elevator rail. Do you need to assume that the widths of elevator rails are normally
You want to determine the percentage of Fortune 500 CEOs who think Indiana University (IU) deserves its current Business Week rating. You mail a questionnaire to all 500 CEOs and 100 respond. Exactly half of the respondents believe IU does deserve its ranking.a. Find a 95% confidence interval for
The SEC requires companies to file annual reports concerning their financial status. It is impossible to audit every account receivable. Suppose an auditor audits a random sample of 49 accounts receivable invoices and finds a sample average of $128 and a sample standard deviation of $53. a. Find a
An opinion poll surveyed 900 people and reported that 36% believe a certain governor broke campaign financing laws in his election campaign. a. Find a 95% confidence interval for the population proportion of people who believe the governor broke campaign financing laws. Does the result of the poll
The file P08_07.xlsx contains a random sample of 200 service times during the busiest hour of the day at a particular fast-food restaurant. Find a 95% confidence interval for each of the following population parameters. Then explain how each result might be useful to the manager of the restaurant
We know that IQs are normally distributed with a mean of 100 and standard deviation of 15. Suppose you want to verify this, so you take 100 random samples of size four each and, for each sample, find a 95% confidence interval for the mean IQ. You expect that approximately 95 of these intervals will
In Section 8.9, we gave a sample size formula for confidence interval estimation of a mean. If the confidence level is 95%, then because the z-multiple is about 2, this formula is essentiallyn = 4σ2 / B2However, this formula is based on the assumption that the sample size n will be small relative
Find a 95% confidence interval for the proportion of all customers whose order is for more than $100. Then do this separately for each of three times of day.
Find a 95% confidence interval for the proportion of all customers whose orders contain at least three items and cost at least $100 total.
Find a 95% confidence interval for the difference between the mean amount of the highest cost item purchased for the High customer category and the similar mean for the Medium customer category. Do the same for the difference between the Medium and Low customer categories. Because of the way these
Of the subpopulation of customers who order in the evening, consider the proportion who are female. Similarly, of the subpopulation of customers who order in the morning, consider the proportion who are female. Find a 95% confidence interval for the difference between these two proportions.
Find a 95% confidence interval for the difference between the following two proportions: the proportion of female customers who order during the evening and the proportion of male customers who order during the evening.
Find a 95% confidence interval for the difference between the mean cost per item for female orders and the similar mean for males.
Let pE,F be the proportion of female orders that are paid for with the ElecMart credit card, and let pE,M be the similar proportion for male orders. a. Find a 95% confidence interval for pE,F; for pE,M; for the difference pE,F - pE,M.b. Let pE,F,Wd be the proportion of female orders on weekdays
Suppose these 400 orders are a sample of the 4295 orders made during this time period, and suppose 2531 of these orders were placed by females. Find a 95% confidence interval for the total paid for all 4295 orders. Do the same for all 2531 orders placed by females. Do the same for all 1764 orders
Find a 95% confidence interval for the proportion of all large customers who pay bills of at least $1000 at least 15 days after they are billed.
Find a 95% confidence interval for the proportion of all bills paid within 15 days. Find a 95% confidence interval for the difference between the proportion of large customers who pay within 15 days and the similar proportion of medium-size customers. Find a 95% confidence interval for the
Suppose Rebco can earn interest at the rate of 0.011% daily on excess cash. The company realizes that it could earn extra interest if its customers paid their bills more promptly.a. Find a 95% confidence interval for the mean amount of interest it could gain if each of its customers paid exactly
The file P08_65.xlsx contains data on the first 100 customers who entered a two-teller bank on Friday. All variables in this file are times, measured in minutes.a. Find a 95% confidence interval for the mean amount of time a customer spends in service with a teller.b. The bank is most interested in
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