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mathematics
statistics

Questions and Answers of Statistics

Rerun the new car simulation from Example 16.4, but now use the RISKSIMTABLE function appropriately to simulate discount rates of 5%, 7.5%, 10%, 12.5%, and 15%. Comment on how the outputs change as
In the cash balance model from Example 16.5, the timing is such that some receipts are delayed by one or two months, and the payments for materials and labor must be made a month in advance. Change
In the cash balance model from Example 16.5, is the $250,000 minimum cash balance requirement really “costing” the company very much? Answer this by rerunning the simulation with minimum required
Run the retirement model from Example 16.6 with a damping factor of 1.0 (instead of 0.98), again using the same three sets of investment weights. Explain in words what it means, in terms of the
The simulation output from Example 16.6 indicates that an investment heavy in stocks produces the best results. Would it be better to invest entirely in stocks? Answer this by rerunning the
Modify the model from Example 16.6 so that you use only the years 1975 to 2007 of historical data. Run the simulation for the same three sets of investment weights. Comment on whether your results
Referring to the retirement example in Example 16.6, rerun the model for a planning horizon of 10 years; 15 years; 25 years. For each, which set of investment weights maximizes the VAR 5% (the 5th
Change the new car simulation from Example 16.4 as follows. It is the same as before for years 1 through 5, including depreciation through year 5. However, the car might sell through year 10. Each
Amanda has 30 years to save for her retirement. At the beginning of each year, she puts $5000 into her retirement account. At any point in time, all of Amanda’s retirement funds are tied up in the
In the financial world, there are many types of complex instruments called derivatives that derive their value from the value of an underlying asset. Consider the following simple derivative. A
Suppose you currently have a portfolio of three stocks, A, B, and C. You own 500 shares of A, 300 of B, and 1000 of C. The current share prices are $42.76, $81.33, and $58.22, respectively. You plan
Suppose that Coke and Pepsi are fighting for the cola market. Each week each person in the market buys one case of Coke or Pepsi. If the person’s last purchase was Coke, there is a 0.90 probability
Seas Beginning sells clothing by mail order. An important question is when to strike a customer from the company’s mailing list. At present, the company strikes a customer from its mailing list if
Based on Babich (1992). Suppose that each week each of 300 families buys a gallon of orange juice from company A, B, or C. Let pA denote the probability that a gallon produced by company A is of
The customer loyalty model in Example 16.7 assumes that once a customer leaves (becomes disloyal), that customer never becomes loyal again. Assume instead that there are two probabilities that drive
Suppose that GLC earns a $2000 profit each time a person buys a car. We want to determine how the expected profit earned from a customer depends on the quality of GLC’s cars. We assume a typical
The Mutron Company is thinking of marketing a new drug used to make pigs healthier. At the beginning of the current year, there are 1,000,000 pigs that could use the product. Each pig will use
The game of Chuck-a-Luck is played as follows: You pick a number between 1 and 6 and toss three dice. If your number does not appear, you lose $1. If your number appears x times, you win $x. On the
A martingale betting strategy works as follows. You begin with a certain amount of money and repeatedly play a game in which you have a 40% chance of winning any bet. In the first game, you bet $1.
You have $5 and your opponent has $10. You flip a fair coin and if heads comes up, your opponent pays you $1. If tails comes up, you pay your opponent $1. The game is finished when one player has all
Assume a very good NBA team has a 70% chance of winning in each game it plays. During an 82-game season what is the average length of the team’s longest winning streak? What is the probability that
Based on Morrison and Wheat (1984). When his team is behind late in the game, a hockey coach usually waits until there is one minute left before pulling the goalie out of the game. Using simulation,
You are playing Andy Roddick in tennis, and you have a 42% chance of winning each point.a. Use simulation to estimate the probability you will win a particular game. Note that the first player to
You now have $3000. You will toss a fair coin four times. Before each toss you can bet any amount of your money (including none) on the outcome of the toss. If heads comes up, you win the amount you
You now have $10,000, all of which is invested in a sports team. Each year there is a 60% chance that the value of the team will increase by 60% and a 40% chance that the value of the team will
Suppose you have invested 25% of your portfolio in four different stocks. The mean and standard deviation of the annual return on each stock are shown in the file S16_38.xlsx. The correlations
A ticket from Indianapolis to Orlando on Deleast Airlines sells for $150. The plane can hold 100 people. It costs Deleast $8000 to fly an empty plane. Each person on the plane incurs variable costs
Based on Marcus (1990). The Balboa mutual fund has beaten the Standard and Poor’s 500 during 11 of the last 13 years. People use this as an argument that you can beat the market. Here is another
You have been asked to simulate the cash inflows to a toy company for the next year. Monthly sales are independent random variables. Mean sales for the months January through March and October
Consider a device that requires two batteries to function. If either of these batteries dies, the device will not work. Currently there are two new batteries in the device, and there are three extra
Appliances Unlimited (AU) sells refrigerators. Any refrigerator that fails before it is three years old is replaced for free. Of all refrigerators, 3% fail during their first year of operation; 5% of
The annual demand for Prizdol, a prescription drug manufactured and marketed by the NuFeel Company, is normally distributed with mean 50,000 and standard deviation 12,000. Assume that demand during
A company is trying to determine the proper capacity level for its new electric car. A unit of capacity provides the potential to produce one car per year. It costs $10,000 to build a unit of
The DC Cisco office is trying to predict the revenue it will generate next week. Ten deals may close next week. The probability of each deal closing and data on the possible size of each deal (in
A common decision is whether a company should buy equipment and produce a product in house or outsource production to another company. If sales volume is high enough, then by producing in house, the
Consider an oil company that bids for the rights to drill in offshore areas. The value of the right to drill in a given offshore area is highly uncertain, as are the bids of the competitors. This
Suppose you begin year 1 with $5000. At the beginning of each year, you put half of your money under a mattress and invest the other half in Whitewater stock. During each year, there is a 50% chance
You are considering a 10-year investment project. At present, the expected cash flow each year is $10,000. Suppose, however, that each year’s cash flow is normally distributed with mean equal to
Play Things is developing a new Hannah Montana doll. The company has made the following assumptions:• The doll will sell for a random number of years from 1 to 10. Each of these 10 possibilities is
An automobile manufacturer is considering whether to introduce a new model called the Racer. The profitability of the Racer depends on the following factors:The fixed cost of developing the Racer is
It costs a pharmaceutical company $40,000 to produce a 1000-pound batch of a drug. The average yield from a batch is unknown but the best case is 90% yield (that is, 900 pounds of good drug will be
A truck manufacturer produces the Off Road truck. The company wants to gain information about the discounted profits earned during the next three years. During a given year, the total number of
Suppose you buy an electronic device that you operate continuously. The device costs you $300 and carries a one-year warranty. The warranty states that if the device fails during its first year of
Rework the previous problem for a case in which the one-year warranty requires you to pay for the new device even if failure occurs during the warranty period. Specifically, if the device fails at
Chemcon has taken over the production of Nasacure from a rival drug company. Chemcon must build a plant to produce Nasacure by the beginning of 2010. Once the plant is built, the plant’s capacity
The Tinkan Company produces one-pound cans for the Canadian salmon industry. Each year the salmon spawn during a 24-hour period and must be canned immediately. Tinkan has the following agreement with
A popular restaurant in Indianapolis does a brisk business, filling virtually all of its seats from 6 P.M. until 9 P.M. Tuesday through Sunday. Its current annual revenue is $2.34 million. However,
Observational study Provide a deﬁnition using your own words.
List and describe the three major types of observational studies.
What is meant by the process of statistics?
List and explain the three sources of bias in sampling. Provide some methods that might be used to minimize bias in sampling.
Distinguish between sampling and nonsampling error.
Explain the steps in designing an experiment.
Number of new automobiles sold at a dealership on a given day Classify the variable as qualitative or quantitative. If the variable is quantitative, state whether it is discrete or continuous.
Weight in carats of an uncut diamond Classify the variable as qualitative or quantitative. If the variable is quantitative, state whether it is discrete or continuous.
Each of the following surveys has bias. Determine the type of bias and suggest a remedy. (a) A politician sends a survey about tax issues to a random sample of subscribers to a literary magazine. (b)
The mayor of a small town wants to conduct personal interviews with small business owners to determine if there is anything the mayor could do to help improve business conditions. The following list
A quality-control engineer wants to be sure that bolts coming off an assembly line are within prescribed tolerances. He wants to conduct a systematic sample by selecting every 9th bolt to come off
Based on the Military Standard 105E (ANS1/ASQC Z1.4, ISO 2859) Tables, a lot of 91 to 150 items with an acceptable quality level (AQL) of 1% and a normal inspection plan would require a sample of
Smoking and drinking coffee have a tendency to stain teeth. In an effort to determine the ability of chewing gum to remove stains on teeth, researchers conducted an experiment in which 64 bovine
Researchers wanted to assess the effect of low alcohol consumption on reaction time in seniors. Their belief was that even low levels of alcohol consumption can impair the ability to walk, thereby
A common tip for taking multiple-choice tests is to always pick (b) or (c) if you are unsure. The idea is that instructors tend to feel the answer is more hidden if it is surrounded by distractor
A marketing research ﬁrm wants to know whether information presented in a commercial is better recalled when presented using humor or serious commentary by adults between 18 and 35 years of age.
Describe what is meant by a matched-pairs design. Contrast this experimental design with a completely randomized design.
Time to complete the 500-meter race in speed skating. Determine if the variable is qualitative or quantitative. If the variable is quantitative, determine if it is discrete or continuous. State the
Video game rating system by the Entertainment Software Rating Board (EC, E, E10+, T, M, AO, RP) Determine if the variable is qualitative or quantitative. If the variable is quantitative, determine if
The number of surface imperfections on a camera lens. Determine if the variable is qualitative or quantitative. If the variable is quantitative, determine if it is discrete or continuous. State the
A sports reporter asks 100 baseball fans if Barry Bonds’s 756th homerun ball should be marked with an asterisk when sent to the Baseball Hall of Fame. Determine whether the study depicts an
Contrast the three major types of observational studies in terms of the time frame when the data are collected.
Compare and contrast observational studies and designed experiments. Which study allows a researcher to claim causality?
Explain why it is important to use a control group and blinding in an experiment.
List the steps required to conduct an experiment.
A cellular phone company is looking for ways to improve customer satisfaction. They want to select a simple random sample of four stores from their 15 franchises in which toconduct customer
A congresswoman wants to survey her constituency regarding public policy. She asks one of her staff members to obtain a sample of residents of the district. The frame she has available lists 9012
A farmer has a 500-acre orchard in Florida. Each acre is subdivided into blocks of 5. Altogether, there are 2500 blocks of trees on the farm. After a frost, he wants to get an idea of the extent of
A casino manager wants to inspect a sample of 14 slot machines in his casino for quality-control purposes. There are 600 sequentially numbered slot machines operating in the casino. Obtain a
Each of the following surveys has bias. Identify the type of bias. (a) A television survey that gives 900 phone numbers for viewers to call with their vote. Each call costs $2.00. (b) An employer
The four members of Skylab had their lymphocyte count per cubic millimeter measured 1 day before lift-off and measured again on their return to Earth. (a) What is the response variable in this
Nucryst Pharmaceuticals, Inc., announced the results of its ﬁrst human trial of NPI 32101, a topical form of its skin ointment. A total of 225 patients diagnosed with skin irritations were randomly
Katherine Tucker and associates wanted to determine whether consumption of cola is associated with lower bone mineral density. They looked at 1125 men and 1413 women in the Framingham Osteoporosis
The following represent information on smart phones recommended by CNET.
The following information relates to the 2011 model year product line of BMW automobiles.
The following data represent driver€™s license laws for various states.
The following represent information on MP3 players recommended by CNET.
Smoker’s IQ A study was conducted in which 20,211 18-year-old Israeli male military recruits were given an exam to measure IQ. In addition, the recruits were asked to disclose their smoking status.
A study conducted by researchers was designed “to determine if application of duct tape is as effective as cryotherapy (liquid nitrogen applied to the wart for 10 seconds every 2 to 3 weeks) in the
Gallup News Service conducted a survey of 1026 American adults aged 18 years or older, August 31–September, 2, 2009. The respondents were asked, “Of every tax dollar that goes to the federal
The Principal Financial Group conducted a survey of 1172 employees in the United States between July 28, 2010, and August 8, 2010, and asked if they were currently participating in the
Suppose a fundraiser holds a rafﬂe for which each person who enters the room receives a ticket. The tickets are numbered 1 to N, where N is the number of people at the fundraiser. The ﬁrst person
Read the newspaper article and identify(a) The research question the study addresses,(b) The population,(c) The sample,(d) The descriptive statistics, and(e) The inferences of the study.Study:
In your own words, deﬁne the four levels of measurement of a variable. Give an example of each.
Explain what is meant when we say “data vary.” How does this variability affect the results of statistical analysis?
Explain the process of statistics.
In your own words, deﬁne explanatory variable and response variable.
What is an observational study? What is a designed experiment? Which allows the researcher to claim causation between an explanatory variable and a response variable?
Explain what is meant by confounding. What is a lurking variable?
Given a choice, would you conduct a study using an observational study or a designed experiment? Why?
What is a cross-sectional study? What is a case-control study? Which is the superior observational study? Why?
The data used in the inﬂuenza study presented in Example 3 were obtained from a cohort study. What does this mean? Why is a cohort study superior to a case-control study?
Happiness and Your Heart Researchers wanted to determine if there was an association between the level of happiness of an individual and their risk of heart disease. The researchers studied 1739

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