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Business Statistics A Decision Making Approach 8th Edition David F. Groebner, Patrick W. Shannon, Phillip C. Fry, Kent D. Smith - Solutions
The Haines Lumber Company makes plywood for the furniture industry. One product it makes is 3/4-inch oak veneer panels. It is very important that the panels conform to specifications. One specification calls for the panels to be made to an average thickness of 0.75 inches. Each hour, 5 panels are
The Wilson Company uses a great deal of water in the process of making industrial milling equipment. To comply with the federal clean water laws, it has a water purification system that all wastewater goes through before being discharged into a settling pond on the company’s property. To
The AJ Fitness Center has surveyed 1,214 of its customers. Of particular interest is whether over 60% of the customers who express overall service satisfaction with the club (represented by codes 4 or 5) are female.If this is not the case, the promotions director feels she must initiate new
The Cell Tone Company sells cellular phones and airtime in several northwestern states. At a recent meeting, the marketing manager stated that the average age of its customers is under 40. This came up in conjunction with a proposed advertising plan that is to be directed toward a young audience.
Many companies have moved employee retirement plans to ones based on 401(k) savings. In fact, most large mutual fund companies, like Vanguard, offer 401(k) options. However, according to Nancy Trejos of the Washington Post, the average amount in a 401(k)plan decreased from $69,200 in 2007 to
Cisco Systems, Inc., is the leading maker of networking gear that connects computers to the Internet. Company managers are concerned with the productivity of their workers as well as their job satisfaction. Kate D’Camp is the senior vice president for human resources. She often initiates surveys
The Lazer Company has a contract to produce a part for Boeing Corporation that must have an average diameter of 6 inches and a standard deviation of 0.10 inch. The Lazer Company has developed the process that will meet the specifications with respect to the standard deviation, but it is still
The personnel manager for a large airline has claimed that, on average, workers are asked to work no more than 3 hours overtime per week. Past studies show the standard deviation in overtime hours per worker to be 1.2 hours. Suppose the union negotiators wish to test this claim by sampling payroll
About 74% of Freddie Mac–owned loans were refinanced in the second quarter of 2005 (USA Today, Lifeline, August 3, 2005), resulting in new mortgages carrying loan amounts at least 5% above the original mortgage balance. The median loan refinanced in the second quarter was 2.6 years old. If a
The Sledge Tire and Rubber Company plans to warranty its new mountain bike tire for 12 months.However, before it does this, the company wants to be sure that the mean lifetime of the tires is at least 18 months under normal operations. It will put the warranty in place unless the sample data
ACNielsen is a New York–based leading global provider of marketing research information services, analytical systems and tools, and professional client service. A recent issue of its magazine (Todd Hale,“Winning Retail Strategies Start with High Value Consumers,” Consumer Insight, Spring
The makers of Mini-Oats Cereal have an automated packaging machine that can be set at any targeted fill level between 12 and 32 ounces. At the end of every shift (eight hours), 16 boxes are selected at random and the mean and standard deviation of the sample are computed. Based on these sample
The college of business at a state university has a computer literacy requirement for all graduates.Students must show proficiency with a computer spreadsheet software package and with a wordprocessing software package. To assess whether students are computer literate, a test is given at the end of
USA Today reports (Darryl Haralson, “It’s All about Overstock.com”) on an ad for Overstock.com, which sells discounted merchandise on its Web site. To evaluate the effectiveness of the ads, Harris Interactive conducted a nationwide poll of 883 adults. Of the 883 adults, 168 thought the ads
Technological changes in golf equipment have meant people, in particular professional golfers, are able to hit golf balls much farther. Golf Digest reported on a survey conducted involving 300 golfers in which the respondents were asked their views about the impact of new technologies on the game
The Utah State Tax Commission attempts to set up payroll tax–withholding tables such that by the end of the year, an employee’s income tax withholding is about $100 below his actual income tax owed to the state. The commission director claims that when all the Utah tax returns are in, the
Sanchez Electronics sells electronic components for car stereos. It claims that the average life of a component exceeds 4,000 hours. To test this claim, it has selected a random sample of n 12 of the components and traced the life between installation and failure. The following data were
Fairfield Automotive is the local dealership selling Honda automobiles. It recently stated in an advertisement that Honda owners average more than 85,000 miles before trading in or selling their Hondas. To test this, an independent agency selected a simple random sample of 80 Honda owners who have
For each of the following scenarios, indicate which test statistic would be used or which test could not be conducted using the materials from this chapter:a. testing a mean when s is known and the population sampled from has a normal distributionb. testing a mean when s is unknown and the
The Oasis Chemical Company develops and manufactures pharmaceutical drugs for distribution and sale in the United States. The pharmaceutical business can be very lucrative when useful and safe drugs are introduced into the market. Whenever the Oasis research lab considers putting a drug into
While conducting a hypothesis test, indicate the effect ona. b when a is decreased while the sample size remains constantb. b when a is held constant and the sample size is increasedc. the power when a is held constant and the sample size is increasedd. the power when a is decreased and the sample
In a hypothesis test, indicate the type of statistical error that can be made ifa. The null hypothesis is rejected.b. The null hypothesis is not rejected.c. The null hypothesis is true.d. The null hypothesis is not true.
What is the maximum probability of committing a Type I error called? How is this probability determined?Discuss.
Recall that the power of the test is the probability the null hypothesis is rejected when H0 is false. Explain whether power is definable if the given parameter is the value specified in the null hypothesis.
Examine the test statistic used in testing a population proportion. Why is it impossible to test the hypothesis that the population proportion equals zero using such a test statistic? Try to determine a way that such a test could be conducted.
Discuss why it is necessary to use an estimate of the standard error for a confidence interval and not for a hypothesis test concerning a population proportion.
Discuss the two types of statistical errors that can occur when a hypothesis is tested. Illustrate what you mean by using a business example for each.
Discuss the issues a decision maker should consider when determining the significance level to use in a hypothesis test.
What is meant by the term critical value in a hypothesis-testing situation? Illustrate what you mean with a business example.
In an article in Business Week (“Living on the Edge at American Apparel”), Dov Chaney, the CEO of American Apparel, indicated that the apparel store industry’s average sales were $1,800/7 ( $257.14)a square foot. A hypothesis test was requested to determine if the data supported the
USA Today reports (Gary Stoller, “Hotel Bill Mistakes Mean Many Pay Too Much”) that George Hansen, CEO of Wichita-based Corporate Lodging Consultants, conducted a recent review of hotel bills over a 12-month period. The review indicated that, on average, errors in hotel bills resulted in
The union negotiations between labor and management at the Stone Container paper mill in Minnesota hit a snag when management asked labor to take a cut in health insurance coverage. As part of its justification, management claimed that the average amount of insurance claims filed by union employees
Runzheimer International, a management consulting firm specializing in transportation reimbursement, released the results of a survey on July 28, 2005. It indicated that it costs more to own a car in Detroit, an amazing $11,844 a year for a mid-sized sedan, than in any other city in the country.
According to the Internet source Smartbrief.com, per capita U. S. beer consumption increased in 2008 after several years of decline. Current per capita is 22 gallons per year. A survey is designed to determine if the per capita consumption has changed in the current year. A hypothesis test is to be
According to CNN business partner Careerbuilder.com, the average starting salary for accounting graduates in 2008 was at least $47,413. Suppose that the American Society for Certified Public Accountants planned to test this claim by randomly sampling 200 accountants who graduated in 2008.a. State
Nationwide Mutual Insurance, based in Columbus, Ohio, is one of the largest diversified insurance and financial services organizations in the world, with more than $157 billion in assets. Nationwide ranked 108th on the Fortune 100 list in 2008. The company provides a full range of insurance and
Waiters at Finegold’s Restaurant and Lounge earn most of their income from tips. Each waiter is required to“tip-out” a portion of tips to the table bussers and hostesses. The manager has based the “tip-out” rate on the assumption that the mean tip is at least 15% of the customer bill. To
Swift is the holding company for Swift Transportation Co., Inc., a truckload carrier headquartered in Phoenix, Arizona. Swift operates the largest truckload fleet in the United States. Before Swift switched to its current computer-based billing system, the average payment time from customers was
According to data from the Environmental Protection Agency, the average daily water consumption for a household of four people in the United States is approximately at least 243 gallons. (Source: http://www.catskillcenter.org/programs/csp/H20/Lesson3/house3.htm) Suppose a state agency plans to test
The following hypotheses are to be tested:H0: p 0.35 HA: p 0.35 A random sample of 400 is taken. Using each set of information following, compute the power of the test.a. a 0.01, true p 0.32b. a 0.025, true p 0.33c. a 0.05, true p 0.34
The following hypotheses are to be tested:H0: p 0.65 HA: p 0.65 A random sample of 500 is taken. Using each set of information following, compute the power of the test.a. a 0.01, true p 0.68b. a 0.025, true p 0.67c. a 0.05, true p 0.66
Consider the following hypotheses:H0: m 201 HA: m 201 A sample is to be taken from a population with a mean of 203 and a standard deviation of 3. The hypothesis test is to be conducted using a significance level of 0.05. Determine the probability of committing a Type II error whena. n 10b. n
Consider the following hypotheses:H0: m 30 HA: m 30 A sample of size 50 is to be taken from a population with a standard deviation of 13. The hypothesis test is to be conducted using a significance level of 0.05.Determine the probability of committing a Type II error whena. m 22b. m 25c. m
For each of the following situations, indicate what the general impact on the Type II error probability will be:a. The alpha level is increased.b. The “true” population mean is moved farther from the hypothesized population mean.c. The alpha level is decreased.d. The sample size is increased.
Solve for beta when the “true” population mean is 103 and the following information is given:H0: m 100 HA: m 100 a 0.05 s 10 n 49
Consider the following hypotheses:H0: m 103 HA: m 103 A sample of size 20 is to be taken from a population with a mean of 100 and a standard deviation of 4.Determine the probability of committing a Type II error for each of the following significance levels:a. a 0.01b. a 0.025c. a 0.05
You are given the following null and alternative hypotheses:H0: m 500 HA: m 500 a 0.01 Calculate the probability of committing a Type II error when the population mean is 505, the sample size is 64, and the population standard deviation is known to be 36.
You are given the following null and alternative hypotheses:H0: m 4,350 HA: m 4,350 a 0.05a. If the true population mean is 4,345, determine the value of beta. Assume the population standard deviation is known to be 200 and the sample size is 100.b. Referring to parta, calculate the power of the
You are given the following null and alternative hypotheses:H0: m 1.20 HA: m 1.20 a 0.10a. If the true population mean is 1.25, determine the value of beta. Assume the population standard deviation is known to be 0.50 and the sample size is 60.b. Referring to parta, calculate the power of the
You are given the following null and alternative hypotheses:H0: m 200 HA: m 200 a 0.10 Calculate the probability of committing a Type II error when the population mean is 197, the sample size is 36, and the population standard deviation is known to be 24.
Joseph-Armand Bombardier in the 1930s founded the company that is now known as Seadoo in Canada.His initial invention of the snowmobile in 1937 led the way to what is now a 7,600-employee, worldwide company specializing in both snow and water sports vehicles. The company stresses high quality in
Cell phones are becoming an integral part of our daily lives. Commissioned by Motorola, a new behavioral study took researchers to nine cities worldwide from New York to London. Using a combination of personal interviews, field studies, and observation, the study identified a variety of behaviors
The Electronic Controls Company (ECCO) is one of the largest makers of backup alarms in the world.Backup alarms are the safety devices that emit a highpitched beeping sound when a truck, forklift, or other equipment is operated in reverse. ECCO is well known in the industry for its high quality and
According to the Employee Benefit Research Institute(www.ebri.org), 34% of workers between the ages of 35 and 44 owned a 401(k)-type retirement plan in 2002. Suppose a recent survey was conducted by the Atlanta Chamber of Commerce to determine the rate of 35- to 44-year-old working adults in the
A study by the Investment Company Institute (ICI) in 2004, which randomly surveyed 3,500 households and drew on information from the IRS, found that 72% of households have conducted at least one IRA rollover from an employer-sponsored retirement plan (www.financial-planning.com). Suppose a recent
A survey by the Pew Internet & American Life Project found that 21% of workers with an e-mail account at work say they are getting more spam than a year ago.Suppose a large multinational company, after implementing a policy to combat spam, asked 198 randomly selected employees with e-mail accounts
Harris Interactive Inc., the 15th largest market research firm in the world, is a Rochester, New York–based company. One of its surveys indicated that 26% of women have had experience with a Global Positioning System (GPS) device. The survey indicated that 36%of the men surveyed have used a GPS
A large number of complaints have been received in the past six months regarding airlines losing fliers’ baggage.The airlines claim the problem is nowhere near as great as the newspaper articles have indicated. In fact, one airline spokesman claimed that less than 1% of all bags fail to arrive at
The practice of “phishing,” or using the Internet to pilfer personal information, has become an increasing concern, not only for individual computer users but also for online retailers and financial institutions. The Wall Street Journal reported 28% of people who bank online have cut back on
CEO Chris Foreman of Pacific Theaters Exhibition Corp. is taking steps to reverse the decline in movie attendance. Moviegoers’ comfort is one of the issues facing theaters. Pacific Theaters has begun offering assigned seating, no in-theater advertising, and a live announcer who introduces films
An Associated Press article written by Eileen Powell entitled “Credit Card Payments Going Up” described a recent change in credit card policies. Under pressure from federal regulators, credit card issuers have started to raise the minimum payment that consumers are required to pay on
Assume that the sports page of your local newspaper reported that 65% of males over the age of 17 in the United States would skip an important event such as a birthday party or an anniversary dinner to watch their favorite professional sports team play. A random sample of 676 adult males over the
A Washington Post–ABC News poll found that 72% of people are concerned about the possibility that their personal records could be stolen over the Internet.If a random sample of 300 college students at a Midwestern university were taken and 228 of them were concerned about the possibility that
Because of the complex nature of the U.S. income tax system, many people have questions for the Internal Revenue Service (IRS). Yet, an article published by the Detroit Free Press entitled “Assistance: IRS Help Centers Give the Wrong Information” discusses the propensity of IRS staff employees
A recent article in The Wall Street Journal entitled “As Identity Theft Moves Online, Crime Rings Mimic Big Business” states that 39% of the consumer scam complaints by American consumers are about identity theft. Suppose a random sample of 90 complaints is obtained. Of these complaints, 40
A major issue facing many states is whether to legalize casino gambling. Suppose the governor of one state believes that more than 55% of the state’s registered voters would favor some form of legal casino gambling. However, before backing a proposal to allow such gambling, the governor has
An issue that faces individuals investing for retirement is allocating assets among different investment choices.Suppose a study conducted 10 years ago showed that 65% of investors preferred stocks to real estate as an investment. In a recent random sample of 900 investors, 360 preferred real
Suppose a recent random sample of employees nationwide that have a 401(k) retirement plan found that 18% of them had borrowed against it in the last year. A random sample of 100 employees from a local company who have a 401(k) retirement plan found that 14 had borrowed from their plan. Based on the
A sample of size 25 was obtained to test the hypotheses H0: p 0.30 HA: p 0.30 Calculate the p-value for each of the following sample results:a. p 0.12b. p 0.35c. p 0.42d. p 0.5 Business Applications
A test of hypothesis has the following hypotheses:H0: p 0.45 HA: p 0.45 For a sample size of 30, and a sample proportion of 0.55,a. For an a 0.025, determine the critical value.b. Calculate the numerical value of the test statistic.c. State the test’s conclusion.d. Determine the p-value.
For the following hypothesis test H0: p 0.75 HA: p 0.75 a 0.025 with n 100 and p 0.66, statea. the decision rule in terms of the critical value of the test statisticb. the calculated value of the test statisticc. the conclusion
For the following hypothesis test:H0: p 0.40 HA: p 0.40 a 0.01 with n 64 and p 0.42, statea. the decision rule in terms of the critical value of the test statisticb. the calculated value of the test statisticc. the conclusion
Given the following null and alternative hypotheses H0: p 0.60 HA: p 0.60 test the hypothesis using a 0.01 assuming that a sample of n 200 yielded x 105 items with the desired attribute.
Calculate the z-test statistic for a hypothesis test in which the null hypothesis states that the population proportion, p, equals 0.40 if the following sample information is present:n 150, x 30
Determine the appropriate critical value(s) for each of the following tests concerning the population proportion:a. upper-tailed test: a 0.025, n 48b. lower-tailed test: a 0.05, n 30c. two-tailed test: a 0.02, n 129d. two-tailed test: a 0.10, n 36
Hono Golf is a manufacturer of golf products in Taiwan and China. One of the golf accessories it produces at its plant in Tainan Hsing, Taiwan, is plastic golf tees. The injector molder produces golf tees that are designed to have an average height of 66 mm. To determine if this specification is
A key factor in the world’s economic condition is the population growth of the countries in the world. The file called Countries contains data for 74 countries in alphabetical order. Consider these 74 countries to be the population of all countries in the world.a. From this population, suppose a
The Center on Budget and Policy Priorities (www.cbpp.org) reported that average out-of-pocket medical expenses for prescription drugs for privately insured adults with incomes over 200% of the poverty level was $173 in 2002. Suppose an investigation was conducted in 2009 to determine whether the
The U.S. Bureau of Labor Statistics (www.bls.gov)released its Consumer Expenditures in 2006 report in October 2008. Among its findings is that average annual household spending on food at home for 2006 was $3,417. Suppose a random sample of 137 households in Detroit was taken to determine whether
At a recent meeting, the manager of a national call center for a major Internet bank made the statement that the average past-due amount for customers who have been called previously about their bills is now no larger than $20.00. Other bank managers at the meeting suggested that this statement may
Starting in 2008 an increasing number of people found themselves facing mortgages that were worth more than the value of their homes. A fund manager who had invested in debt obligations involving grouped mortgages was interested in determining the group most likely to default on their mortgage. He
The makers of Mini-Oats Cereal have an automated packaging machine that can be set at any targeted fill level between 12 and 32 ounces. Every box of cereal is not expected to contain exactly the targeted weight, but the average of all boxes filled should. At the end of every shift (eight hours), 16
A recent internal report issued by the marketing manager for a national oil-change franchise indicated that the mean number of miles between oil changes for franchise customers is at least 3,600 miles. One Texas franchise owner conducted a study to determine whether the marketing manager’s
A mail-order business prides itself in its ability to fill customers’ orders in six calendar days or less on the average. Periodically, the operations manager selects a random sample of customer orders and determines the number of days required to fill the orders. Based on this sample
The director of a state agency believes that the average starting salary for clerical employees in the state is less than $30,000 per year. To test her hypothesis, she has collected a simple random sample of 100 starting clerical salaries from across the state and found that the sample mean is
The National Club Association does periodic studies on issues important to its membership. The 2008 Executive Summary of the Club Managers Association of America reported that the average country club initiation fee was $31,912. Suppose a random sample taken in 2009 of 12 country clubs produced the
For each of the following scenarios, indicate which type of statistical error could have been committed or, alternatively, that no statistical error was made.When warranted, provide a definition for the indicated statistical error.a. Unknown to the statistical analyst, the null hypothesis is
A sample taken from a population yields a sample mean of 58.4. Calculate the p-value for each of the following circumstances:a. HA: m 58, n 16, s 0.8b. HA: m 45, n 41, s 35.407c. HA: m 45, n 41, s 35.407d. HA: m 69; data: 60.1, 54.3, 57.1, 53.1, 67.4
For the following hypothesis:H0: m 70 HA: m 70 with n 20, 71.2, s 6.9, and a 0.1, statea. the decision rule in terms of the critical value of the test statisticb. the calculated value of the test statisticc. the conclusion
For the following hypothesis test:H0: m 60.5 HA: m 60.5 a 0.05 with n 15, s 7.5, and 62.2, statea. the decision rule in terms of the critical value of the test statisticb. the calculated value of the test statisticc. the conclusion
For the following hypothesis test:H0: m 23 HA: m 23 a 0.025 with n 25, s 8, and 20, statea. the decision rule in terms of the critical value of the test statisticb. the calculated value of the test statisticc. the conclusion
For the following hypothesis test:H0: m 45 HA: m 45 a 0.02 with n 80, s 9, and 47.1, statea. the decision rule in terms of the critical value of the test statisticb. the calculated value of the test statisticc. the appropriate p-valued. the conclusion
For the following hypothesis test:H0: m 200 HA: m 200 a 0.01 with n 64, s 9, and 196.5, statea. the decision rule in terms of the critical value of the test statisticb. the calculated value of the test statisticc. the conclusion
For each of the following z-test statistics, compute the p-value assuming that the hypothesis test is a onetailed test:a. z 1.34b. z 2.09c. z1.55
Provide the relevant critical value(s) for each of the following circumstances:a. HA: m 13, n 15, s 10.3, a 0.05b. HA: m 21, n 23, s 35.40, a 0.02c. HA: m 35, n 41, s 35.407, a 0.01d. HA: m 49; data: 12.5, 15.8, 44.3, 22.6, 18.4;a 0.10e. HA: x 15, n 27, s 12.4
For each of the following pairs of hypotheses, determine whether each pair represents valid hypotheses for a hypothesis test. Explain reasons for any pair that is indicated to be invalid.a. H0: m 15, HA: m 15b. H0: m 20, HA: m 20c. H0: m 30, HA: m 30d. H0: m 40, HA: m 40e. H0: x 45,
Determine the appropriate critical value(s) for each of the following tests concerning the population mean:a. upper-tailed test: a 0.025; n 25; s 3.0b. lower-tailed test: a 0.05; n 30; s 9.0c. two-tailed test: a 0.02; n 51; s 6.5d. two-tailed test: a 0.10; n 36; s 3.8
Paper-R-Us is a national distributor of printer and copier paper for commercial use. The data file called Sales contains the annual, year-to-date sales values for each of the company’s customers. Suppose the internal audit department has decided to audit a sample of these accounts. Specifically,
The Jordeen Bottling Company recently did an extensive sampling of its soft-drink inventory in which 5,000 cans were sampled. Employees weighed each can and used these weights to determine the fluid ounces in the cans. The data are in a file called Jordeen. Based on this sample data, should the
The NPD Group recently released its annual U.S.Video Game Industry Retail Sales Report. The report contained the NPD Group’s selection of the top 10 video games based on units sold. The top-selling video game was Madden NFL, published by Electronic Arts.The average retail price for this video
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