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mathematics
statistics

Questions and Answers of Statistics

The errors in the inventory records of a company were analyzed for their causes. The findings were 164 cases of omissions, 103 cases of wrong quantity entered, 45 cases of wrong part numbers entered,
In 1979, Nashua Corporation, with an increasing awareness of the importance of always maintaining and improving quality, invited Dr. W. Edwards Deming for a visit and a consultation. Dr. Deming, then
Discuss what is meant by quality control and quality improvement.
Out of 1,000 automobile engines tested for quality, 62 had cracked blocks, 17 had leaky radiators, 106 had oil leaks, 29 had faulty cylinders, and 10 had ignition problems. Draw a Pareto diagram for
In an effort to improve quality, AT&T has been trying to control pollution problems. Problem causes and their relative seriousness, as a percentage of the total, are as follows:
The journal People Management reports on new ways to use directive training to improve the performance of managers. The percentages of managers who benefited from the training from 2003 to 2007 are:
What is the logic behind the control chart for the sample mean, and how is the chart constructed?
Boston-based Legal Seafoods prides itself on having instituted an advanced quality control system that includes the control of both food quality and service quality. The following are successive
Rolls Royce makes the Trent 900 jet engines used in the new Airbus A380 planes, and needs to control the maximum thrust delivered by the engines. The following are readings related to power for
The following data are tensile strengths, in pounds, for a sample of string for industrial use made at a plant. Construct a control chart for the mean, using groups of 5 observations each. Test for
Create R and s charts. Is the process in control?5, 6, 5, 5.5, 7, 4, 12, 4.5, 2, 5, 5.5, 6, 6, 13, 2, 5, 4, 4.5, 6.5, 4, 1, 2, 3, 5.5, 4, 4, 8, 12, 3, 4.5, 6.5, 6, 7, 10, 6, 6.5, 5, 3, 6.5, 7
Create R and s charts. Is the process in control?121, 122, 121, 125, 123, 121, 129, 123, 122, 122, 120, 121, 119, 118, 121, 125, 139, 150, 121, 122, 120, 123, 127, 123, 128, 129, 122, 120, 128, 120
Create R and s charts. Is the process in control?5, 6, 4, 6, 5, 7, 7, 7, 6, 5, 3, 5, 5, 5, 6, 5, 5, 6, 7, 7, 7, 7, 6, 7, 5, 5, 5, 6, 7, 7, 7, 7, 7, 5, 5, 6, 4, 6, 6, 6, 7, 6, 6, 6, 6, 6, 7, 5, 7, 6
Create X-bar, R, and s charts for the following data on the diameter of pins produced by an automatic lathe. The data summarize 12 samples of size 5 each, obtained at random on 12 different days. Is
An article in Bloomberg Markets compares returns for the Hermitage Fund with those of the Russian Trading System Index. Paired data of rates of return for the two funds during 12 randomly chosen
Bids for a government contract are supposed to be opened in a random order. For a given contract, there were 42 bids, 30 of them from domestic firms and 12 from foreign firms. The order in which the
The May 1, 2007, College Retirement Equity Fund (CREF) prospectus lists the following sample returns on $1 invested in two of the fund's accounts, per yearEquity Index Account ($): 1.636, 1.441,
Explain when you would use the Mann-Whitney test, when you would use the two-sample t test, and when you would use the Wald-Wolfowitz test. Discuss your reasons for choosing each test in the
An article in Money compares investment in an income annuity, offered by insurance companies, and a mix of low-cost mutual funds.6 Suppose the following data are annualized returns (in percent)
Shearson Lehman Brothers, Inc., now encourages its investors to consider real estate limited partnerships. The company offers two limited partnerships-one in a condominium project in Chicago and one
An article in BusinessWeek discusses the salvage value of bankrupt hedge funds compared with the salvage value of bankrupt consumer lenders. Suppose the following data are the value a shareholder can
Breakstone Company makes whipped butter and whipped margarine. A company market analyst wanted to test whether people prefer the taste of one of these products over the other. A random sample of
According to an article in the New York Times, a new trend has been introduced by some of America's finest restaurants: refusing to offer diners bottled water, and pushing instead the restaurant's
According to Money, a water filter (which costs about $26) will save a consumer more than $1 per gallon of water over one year compared with buying bottled water. Suppose that a random sample of 15
Fidelity Investments' February 2007 prospectus compares the value of $10,000 invested in the S&P 500 versus its value invested in Fidelity's Select Natural Resources Portfolio over the life of
The median amount of accounts payable to a CVS retail outlet in May 2007 is believed to be $78.50. Conduct a test to assess whether this assumption is still true after several changes in company
The following data are the one-year return to investors in world stock investment funds, as published in Pensions & Investments. The data are in percent return (%): 35.9, 34.5, 33.7, 31.7, 27.5,
With the continuing surge in the number of mergers and acquisitions in 2007, research effort has been devoted to determining whether the size of an acquisition has an effect on stockholders' abnormal
An analyst in the publishing industry wants to find out whether the cost of a newspaper advertisement of a given size is about the same in four large newspaper groups. Random samples of seven
Lawyers representing the Beatles filed a $15 million suit in New York against Nike, Inc., over Nike's Air Max shoe commercial set to the Beatles' 1968 hit song "Revolution." As part of all such
According to Mediaweek, there are three methods of advertising on the Web.Method 1 is to serve ads to users who clicked on an icon for the ad; Method 2 serves ads through visits to the company's Web
According to an article in Real Estate Finance, developers and hotel operators have three ways of controlling shared facilities: the square footage allocation (SF) method, the revenue-generating (RG)
According to an article in Risk, three Danish financial institutions recently offered new structured investment programs. Suppose that data, in percent return, for a random sample of investments
What assumptions did you use when solving problems 14-31 through 14-36? What assumptions did you not make about the populations in question? Explain.
A random sample of 12 consumers are asked to rank their preferences of four new fragrances that Calvin Klein wants to introduce to the market in the fall of 2008. The data are as follows (best liked
While considering three managers for a possible promotion, the company president decided to solicit information from employees about the managers' relative effectiveness. Each person in a random
Biometrics is a technology that helps identify people by facial and body features and is used by banks to reduce fraud. If in 15 trials the machine correctly identified 10 people, test the hypothesis
In testing to find a cure for congenital heart disease, the condition of a patient after he or she has been treated with a drug cannot be directly quantified, but the patient's condition can be
Four different processes for baking Oreo cookies are considered for the 2008 season. The cookies produced by each process are evaluated in terms of their overall quality. Since the cookies sometimes
The director of a management training program wants to test whether there is a positive association between an applicant's score on a test prior to her or his being admitted to the program and the
An article in Money looks at the relationship between people’s investments in large-cap stocks and international stocks. Suppose that the following data are available for a random sample of
An advertising research analyst wanted to test whether there is any relationship between a magazine advertisement's color intensity using a new digital photography technique introduced in 2007 and
A company is considering five possible names for its new product. Before choosing a name, the firm decides to test whether all five names are equally appealing. A random sample of 100 people is
A study reports an analysis of 35 key product categories. At the time of the study, 72.9% of the products sold were of a national brand, 23% were private label, and 4.1% were generic. Suppose that
Overbooking of airline seats has now become a major problem for everyone who flies, because in order to stay profitable despite rising fuel costs, airlines now fly at unprecedented average seat
Returns on an investment have been known to be normally distributed with mean 11% (annualized rate) and standard deviation 2%. A brokerage firm wants to test the null hypothesis that this statement
The median age of a tourist to Aruba in the summer of 2007 was believed to be 41 years. A random sample of 18 tourists gives the following ages:25, 19, 38, 52, 57, 39, 46, 46, 30, 49, 40, 27, 39, 44,
Using the data provided in problem 14-49, test the null hypothesis that returns on the investment are normally distributed, but with unknown mean and standard deviation. That is, test only for the
An article reports that smaller firms seem to be hiring more than large ones as the economy picks up its pace. The table below gives numbers of employees hired and those laid off, out of a random
An article in the Journal of Business reports the results of an analysis of takeovers of U.S. firms by foreign corporations. The article looked at the reaction to the attempted takeover by the
A study was conducted to determine whether a relationship existed between certain shareholder characteristics and the level of risk associated with the shareholders' investment portfolios. As part of
When new paperback novels are promoted at bookstores, a display is often arranged with copies of the same book with differently colored covers. A publishing house wanted to find out whether there is
An advertiser runs a commercial on national television and wants to determine whether the proportion of people exposed to the commercial is equal throughout the country. A random sample of 100 people
An article in Business Week describes how three online news services now supply Web surfers quick information on developing stories. Suppose that a random sample of users is available from various
A computer is used for generating random numbers. It is necessary to test whether the numbers produced are indeed random. A common method of doing this is to look at runs of odd versus even digits.
Data mining for use in marketing products to consumers has recently undergone much growth. HP, NCR, and IBM have been involved in this business, and suppose the following data are available about
New production methods stressing teamwork have recently been instituted at car manufacturing plants in Detroit. Three teamwork production methods are to be compared to see if they are equally
The Hyatt Gold Passport is a card designed to allow frequent guests at Hyatt hotels to enjoy privileges similar to the ones enjoyed by frequent air travelers. When the program was initiated, a random
Two telecommunication systems are to be compared. A random sample of 14 users of one system independently rate the system on a scale of 0 to 100. An independent random sample of 12 users of the other
The following data are the net wealth, in billions of dollars, of a random sample of U.S. billionaires in the Forbes 2007 list: 1.0, 1.0, 1.2, 1.3, 2.5, 2.3, 4.1, 4.8, 2.5, 2.5, 2.7, 5.2, 2.3, 5.5,
In a chi-square analysis, the expected count in one of the cells is 2.1. Can you conduct the analysis? If not, what can be done?
An article in The Economist compares divorce procedures in New York to those in England, France, and Germany. Suppose the following data are available for these places on numbers of divorces, broken
In a regression analysis, 12 out of 30 residuals are greater than 1.00 in value, and the rest are not. With A denoting a residual greater than 1 and B a residual less than 1, the residuals are as
A messenger service employs eight men and nine women. Every day, the assignments of errands are supposed to be done at random. On a certain day, all the best jobs, in order of desirability, were
A fascinating article in the Journal of Marketing (April 1986), "The Nine Nations of North America and the Value Basis of Geographic Segmentation," Professor Lynn Kahle explores the possible
Bank of America recently launched a special credit card designed to reward people who pay their bills on time by allowing them to pay a lower-than-usual interest rate. Some research went into
An article in the Harvard Business Review discusses new products and services offered by the famous British department store Marks & Spencer.3 Suppose that Marks & Spencer plans to offer a
The partner-manager of a franchise of Au Bon Pain, Inc., the French bakery restaurant chain, believes that the average daily revenue of her business may be viewed as a random variable (she adheres to
Money surveyed mutual funds as a good investment instrument. Suppose that the annual average percentage return from mutual funds is a normally distributed random variablewith mean 8.7% and standard
Claude Vrinat, owner of Taillevent-one of Europe's most highly acclaimed restaurants-is reported to regularly sample the tastes of his patrons. From experience, Vrinat believes that the average
In the context of problem 15-13, a second random sample of 15 diners is asked to rate the foie gras, giving a mean rating of 95 and standard deviation of 1. Incorporate the new information to give a
An article in Forbes discusses the problem of oil and gas reserves around the world. Forecasting the amount of oil available is difficult. If the average number of barrels that can be pumped daily
Continuing problem 15-15, suppose that a second random sample of 20 days reveals an average of 5,020 barrels and standard deviation of 650. Create a new 95% HPD credible set.
In the situation of problem 15-1, suppose that a second random sample of cardholders was selected, and 7 out of the 17 people in the sample were found to pay their bills on time. Construct the new
List the elements of a decision problem, and explain how they interrelate.
What is the role of probabilities in a decision problem, and how do these probabilities arise?
During the Super Bowl, a 30-second commercial costs $2.5 million. The maker of Doritos corn chips was considering purchasing such an ad. The marketing director felt that there was a 0.35 probability
An article in the Asia Pacific Journal of Management discusses the importance for firms to invest in social ties. A company is considering paying $150,000 for social activities over one year, hoping
Drug manufacturing is a risky business requiring much research and development. Recently, several drug manufacturers had to make important decisions. Developing a new drug for Alzheimer's can cost
Predicting the styles that will prevail in a coming year is one of the most important and difficult problems in the fashion industry. A fashion designer must work on designs for the coming fall long
For Example 15-1 suppose that a third sample is obtained. Three out of 10 people in the sample are product users. Update the probabilities of market share after the third sampling, and produce the
Explain why Bayes' theorem is necessary for handling additional information in a decision problem.
For problem 15-23, suppose that before deciding whether to advertise on television, the company can test the commercial. The test costs $300,000 and has the following reliability. If sales volume
One of the most powerful people in Hollywood is not an actor, director, or producer. It is Richard Soames, an insurance director for the London-based Film Finances Ltd. Soames is a leading provider
Many airlines flying overseas have recently considered changing the kinds of goods they sell at their in-flight duty-free services. Swiss, for example, is considering selling watches instead of the
The magazine Inc. recently surveyed managers to determine the proportion of managers who participate in planning meetings. Consider the following prior probability distribution for this
Explain how we compute the expected value of perfect information and why it is computed that way.
Compute the expected value of perfect information for the situation in problem 15-26.
For the situation in problem 15-26, suppose the designer is offered expert opinion about the new fall styles for a price of $300,000. Should she buy the advice? Explain why or why not.
A quality control engineer believes that the proportion of defective items in a production process is a random variable with a probability distribution that is approximated as follows:x
Recent years have seen a sharp decline in the Alaska king crab fishery. One problem identified as a potential cause of the decline has been the prevalence of a deadly parasite believed to infect a
For problem 15-49, suppose that the engineer collects a second sample of 20 items and finds that 5 items are defective. Update the probability distribution of the population proportion you computed
GM is designing a new car, the Chevrolet Volt, which is expected to get 100 mpg on the highway. In trying to estimate how much people would be willing to pay for the new car, the company assesses a
For problem 15-54, a second sample of 60 people gives a sample mean of $27,050. Update the distribution of the population mean, and give a new HPD credible set of probability 0.95 for µ.
Discuss the advantages and the limitations of the assessment of personal probabilities.
To continue problem 15-5, a second random sample of 12 adult crabs was collected, and it revealed that 4 individual crabs had been infected. Revise your probability distribution, and plot it. Give a
For problem 15-63, suppose that the chief executive officer may hire a consulting firm for a fee of $725,000. The consulting firm will advise the CEO about the possibility of success of the merger.
Money suggests an interesting decision problem for family investments. Start with $50,000 to invest over 20 years. There are two possibilities: a low-cost index fund and a fixed-interest investment
For problem 15-5, suppose the biologists believed the proportion of infected crabs in the population was equally likely to be anywhere from 10% to 90%. Using the discrete points 0.1, 0.2, etc.,
American Airlines is interested in the proportion of flights that are full during the 2008 summer season. The airline uses data from past experience and constructs the following prior distribution of

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