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mathematics
statistics
Business Statistics for Contemporary Decision Making 6th Edition Ken Black - Solutions
Based on population figures and other general information on the U.S. population, suppose it has been estimated that, on average, a family of four in the United States spends about $1135 annually on dental expenditures. Suppose further that a regional dental association wants to test to determine
According to data released by the World Bank, the mean PM10 (particulate matter) concentration for the city of Kabul, Afghanistan, in 1999 was 46. Suppose that because of efforts to improve air quality in Kabul, increases in modernization, and efforts to establish environmental-friendly businesses,
According to a National Public Transportation survey, the average commuting time for people who commute to a city with a population of 1 to 3 million is 19.0 minutes. Suppose a researcher lives in a city with a population of 2.4 million and wants to test this claim in her city. Assume that commuter
Suppose you are testing H0; p =.45 versus Ha: p > .45. A random sample of 310 people produces a value of p = .465. Use α = .05 to test this hypothesis.
Suppose you are testing H0: p = .63 versus Ha: p < .63. For a random sample of 100 people, x = 55, where x denotes the number in the sample that have the characteristic of interest. Use a .01 level of significance to test this hypothesis.
Suppose you are testing H0: p = .29 versus Ha: p ≠ .29. A random sample of 740 items shows that 207 have this characteristic. With a .05 probability of committing a Type I error, test the hypothesis. For the p-value method, what is the probability of the observed z value for this problem? If you
The Independent Insurance Agents of America conducted a survey of insurance consumers and discovered that 48% of them always reread their insurance policies, 29% sometimes do, 16% rarely do, and 7% never do. Suppose a large insurance company invests considerable time and money in rewriting policies
A study by Hewitt Associates showed that 79% of companies offer employees flexible scheduling. Suppose a researcher believes that in accounting firms this figure is lower. The researcher randomly selects 415 accounting firms and through interviews determines that 303 of these firms have flexible
A survey was undertaken by Bruskin/Goldring Research for Quicken to determine how people plan to meet their financial goals in the next year. Respondents were allowed to select more than one way to meet their goals. Thirty-one percent said that they were using a financial planner to help them meet
Eighteen percent of U.S.-based multinational companies provide an allowance for personal long-distance calls for executives living overseas, according to the Institute for International Human Resources and the National Foreign Trade Council. Suppose a researcher thinks that U.S.-based multinational
A large manufacturing company investigated the service it received from suppliers and discovered that, in the past, 32% of all materials shipments were received late. However, the company recently installed a just-in-time system in which suppliers are linked more closely to the manufacturing
Where do CFOs get their money news? According to Robert Half International, 47% get their money news from newspapers, 15% get it from communication/colleagues, 12% get it from television, 11% from the Internet, 9% from magazines, 5% from radio, and 1% don’t know. Suppose a researcher wants to
Test each of the following hypotheses by using the given information. Assume the populations are normally distributed.a. H0: σ2 = 20Ha: σ2 > 20α = .05, n = 15, s2 = 32b. H0: σ2 = 8.5Ha: σ2 ≠ 8.5α = .10, n = 22, s2 = 17c. Ha: σ2 = 45Ha: σ2 < 45α = .01, n = 8, s = 4.12d. Ha: σ2 =
Previous experience shows the variance of a given process to be 14. Researchers are testing to determine whether this value has changed. They gather the following dozen measurements of the process. Use these data and α = .05 to test the null hypothesis about the variance. Assume the measurements
A manufacturing company produces bearings. One line of bearings is specified to be 1.64 centimeters (cm) in diameter. A major customer requires that the variance of the bearings be no more than .001 cm2. The producer is required to test the bearings before they are shipped, and so the diameters of
A savings and loan averages about $100,000 in deposits per week. However, because of the way pay periods fall, seasonality, and erratic fluctuations in the local economy, deposits are subject to a wide variability. In the past, the variance for weekly deposits has been about $199,996,164. In terms
A company produces industrial wiring. One batch of wiring is specified to be 2.16 centimeters (cm) thick. A company inspects the wiring in seven locations and determines that, on the average, the wiring is about 2.16 cm thick. However, the measurements vary. It is unacceptable for the variance of
Suppose a null hypothesis is that the population mean is greater than or equal to 100. Suppose further that a random sample of 48 items is taken and the population standard deviation is 14. For each of the following α values, compute the probability of committing a Type II error if the population
For Problem 9.36, use α = .05 and solve for the probability of committing a Type II error for the following possible true alternative means.a. µa = 98.5.b. µa = 98.c. µa = 97.d. µa = 96.e. What happens to the probability of committing a Type II error as the alternative value of the mean gets
Suppose a hypothesis states that the mean is exactly 50. If a random sample of 35 items is taken to test this hypothesis, what is the value of β if the population standard deviation is 7 and the alternative mean is 53? Use α = .01. Explain.
An alternative hypothesis is that p < .65. To test this hypothesis, a random sample of size 360 is taken. What is the probability of committing a Type II error if α = .05 and the alternative proportion is as follows?a. pa = .60.b. pa = .55.c. pa = .50.
The New York Stock Exchange recently reported that the average age of a female shareholder is 44 years. A broker in Chicago wants to know whether this figure is accurate for the female shareholders in Chicago. The broker secures a master list of shareholders in Chicago and takes a random sample of
A Harris poll was taken to determine which of 13 major industries are doing a good job of serving their customers. Among the industries rated most highly by Americans for serving their customers were computer hardware and software companies, car manufacturers, and airlines. The industries rated
Use the information given and the HTAB system to test the hypotheses. Let α = .01.H0: µ = 36 Ha: µ ≠ 36 n = 63 ẍ = 38.4 σ = 5.93
Use the information given and the HTAB system to test the hypotheses. Let Assume the population is normally distributed.H0: µ = 7.82 Ha: µ ≠ 7.82 n = 17 ẍ = 17.1 s = 1.69
For each of the following problems, test the hypotheses. Incorporate the HTAB system with its eight-step process.a. H0: p = .28 Ha: p > .28 n = 783 x = 230 σ = .10b. H0: p = .61 Ha: p ≠.61 n = 401 p = .56 σ = .05
Test the following hypotheses by using the information given and the HTAB system. Let alpha be .01. Assume the population is normally distributed.H0: σ2 = 15.4 Ha: σ2 > 15.4 n = 18 s2 = 29.6
Solve for the value of beta in each of the following problems.a. H0: µ = 130 Ha: µ > 130 n = 75 σ = 12 α = .01.The alternative mean is actually 135.b. H0: p = 44 Ha: p < .44 n = 1095 α = .05.The alternative proportion is actually .42.
According to one survey taken a few years ago, 32% of American households have attempted to reduce their long-distance phone bills by switching long-distance companies. Suppose that business researchers want to test to determine if this figure is still accurate today by taking a new survey of 80
According to Zero Population Growth, the average urban U.S. resident consumes 3.3 pounds of food per day. Is this figure accurate for rural U.S. residents? Suppose 64 rural U.S. residents are identified by a random procedure and their average consumption per day is 3.60 pounds of food. Assume a
Brokers generally agree that bonds are a better investment during times of low interest rates than during times of high interest rates. A survey of executives during a time of low interest rates showed that 57% of them had some retirement funds invested in bonds. Assume this percentage is constant
Highway engineers in Ohio are painting white stripes on a highway. The stripes are supposed to be approximately 10 feet long. However, because of the machine, the operator, and the motion of the vehicle carrying the equipment, considerable variation occurs among the stripe lengths. Engineers claim
A computer manufacturer estimates that its line of minicomputers has, on average, 8.4 days of downtime per year. To test this claim, a researcher contacts seven companies that own one of these computers and is allowed to access company computer records. It is determined that, for the sample, the
Life insurance experts have been claiming that the average worker in the city of Cincinnati has no more than $25,000 of personal life insurance. An insurance researcher believes that this is not true and sets out to prove that the average worker in Cincinnati has more than $25,000 of personal life
A financial analyst watched a particular stock for several months. The price of this stock remained fairly stable during this time. In fact, the financial analyst claims that the variance of the price of this stock did not exceed $4 for the entire period. Recently, the market heated up, and the
A study of MBA graduates by Universum for the American Graduate Survey 1999 revealed that MBA graduates have several expectations of prospective employers beyond their base pay. In particular, according to the study 46% expect a performance-related bonus, 46% expect stock options, 42% expect a
Suppose the number of beds filled per day in a mediumsized hospital is normally distributed. A hospital administrator tells the board of directors that, on the average, at least 185 beds are filled on any given day. One of the board members believes that the average is less than 185 and she sets
According to Gartner Inc., the largest share of the worldwide PC market is held by Hewlett-Packard with 18.4%. Suppose that a market researcher believes that Hewlett Packard holds a higher share of the market in the western region of the United States. To verify this theory, he randomly selects 428
A national publication reported that a college student living away from home spends, on average, no more than $15 per month on laundry. You believe this figure is too low and want to disprove this claim. To conduct the test, you randomly select 17 college students and ask them to keep track of the
A local company installs natural-gas grills. As part of the installation, a ditch is dug to lay a small natural-gas line from the grill to the main line. On the average, the depth of these lines seems to run about 1 foot. The company claims that the depth does not vary by more than 16 square inches
A study of pollutants showed that certain industrial emissions should not exceed 2.5 parts per million. You believe a particular company may be exceeding this average. To test this supposition, you randomly take a sample of nine air tests. The sample average is 3.4 parts per million, with a sample
The average cost per square foot for office rental space in the central business district of Philadelphia is $23.58, according to Cushman & Wakefield. A large real estate company wants to confirm this figure. The firm conducts a telephone survey of 95 offices in the central business district of
The American Water Works Association reports that, on average, men use between 10 and 15 gallons of water daily to shave when they leave the water running. Suppose the following data are the numbers of gallons of water used in a day to shave by 12 randomly selected men and the data come from a
Downtime in manufacturing is costly and can result in late deliveries, backlogs, failure to meet orders, and even loss of market share. Suppose a manufacturing plant has been averaging 23 minutes of downtime per day for the past several years, but during the past year, there has been a significant
According to the U.S. Census Bureau, the average American generates 4.4 pounds of garbage per day. Suppose we believe that because of recycling and a greater emphasis on the environment, the figure is now lower. To test this notion, we take a random sample of Americans and have them keep a log of
One survey conducted by RHI Management Resources determined that the Lexus is the favorite luxury car for 25% of CFOs. Suppose a financial management association conducts its own survey of CFOs in an effort to determine whether this figure is correct. They use an alpha of .05. Following is the
In a recent year, published statistics by the National Cattlemen’s Beef Association claimed that the average retail beef price for USDA All Fresh beef was $2.51. Suppose a survey of retailers is conducted this year to determine whether the price of USDA All Fresh beef has increased. The Excel
The American Express Retail Index states that the average U.S. household will spend $2747 on home improvement projects this year. Suppose a large national home improvement company wants to test that figure in the West, theorizing that the average might be lower in the West. The research firm hired
The Seitz Corporation, a QS 9000 certified organization based in Torrington,Connecticut, is a leading designer and manufacturer of thermoplastic motion control systems and components and an industry leader in plastics and gear trains. Founded in 1949 by the late Karl F. Seitz, the company began as
a. Test the following hypotheses of the difference in population means by using the following data (α = .10) and the eight-step process.H0: µ1 – µ2 = 0 Ha: µ1 – µ2b. Use the critical value method to find the critical difference in the mean values required to reject the
Use the following sample information to construct a 90% confidence interval for the difference in the two populationmeans.
Examine the following data. Assume the variances for the two populations are 22.74 and 26.65 respectively.a. Use the data to test the following hypotheses (α = .02).b. Construct a 98% confidence interval to estimate the difference in population means using these data. How does your result
The Trade Show Bureau conducted a survey to determine why people go to trade shows. The respondents were asked to rate a series of reasons on a scale from 1 to 5, with 1 representing little importance and 5 representing great importance. One of the reasons suggested was general curiosity. The
Suppose you own a plumbing repair business and employ 15 plumbers. You are interested in estimating the difference in the average number of calls completed per day between two of the plumbers. A random sample of 40 days of plumber A's work results in a sample average of 5.3 calls, with a population
The Bureau of Labor Statistics shows that the average insurance cost to a company per employee per hour is $1.84 for managers and $1.99 for professional specialty workers. Suppose these figures were obtained from 14 managers and 15 professional specialty workers and that their respective population
A company's auditor believes the per diem cost in Nashville, Tennessee, rose significantly between 1999 and 2009. To test this belief, the auditor samples 51 business trips from the company's records for 1999; the sample average was $190 per day, with a population standard deviation of $18.50. The
Suppose a market analyst wants to determine the difference in the average price of a gallon of whole milk in Seattle and Atlanta. To do so, he takes a telephone survey of 21 randomly selected consumers in Seattle who have purchased a gallon of milk and asks how much they paid for it. The analyst
Employee suggestions can provide useful and insightful ideas for management. Some companies solicit and receive employee suggestions more than others, and company culture influences the use of employee suggestions. Suppose a study is conducted to determine whether there is a significant difference
Two processes in a manufacturing line are performed manually: operation A and operation B. A random sample of 50 different assemblies using operation A shows that the sample average time per assembly is 8.05 minutes, with a population standard deviation of 1.36 minutes. A random sample of 38
Use the data given and the eight-step process to test the following hypotheses.H0: µ1 – µ2 = 0 Ha: µ1 – µ2Use a 1% level of significance, and assume that x is normallydistributed.
a. Use the following data and = .10 to test the stated hypotheses. Assume x is normally distributed in the populations and the variances of the populations are approximately equal.H0: µ1 – µ2 = 0 Ha: µ1 – µ2 ≠0b. Use these data to construct a 90% confidence
Suppose that for years the mean of population 1 has been accepted to be the same as the mean of population 2, but that now population 1 is believed to have a greater mean than population 2. Letting α = .05 and assuming the populations have equal variances and x is approximately normally
a. Suppose you want to determine whether the average values for populations 1 and 2 are different, and you randomly gather the following data.Test your conjecture, using a probability of committing a Type I error of .01. Assume the population variances are the same and x is normally distributed in
Suppose a Realtor is interested in comparing the asking prices of midrange homes in Peoria, Illinois, and Evansville, Indiana. The Realtor conducts a small telephone survey in the two cities, asking the prices of midrange homes. A random sample of 21 listings in Peoria resulted in a sample average
According to an Experiential Education Survey published at JobWeb.com, the average hourly wage of a college student working as a co-op is $15.64 an hour and the average hourly wage of an intern is $15.44. Assume that such wages are normally distributed in the population and that the population
Based on an indication that mean daily car rental rates may be higher for Boston than for Dallas, a survey of eight car rental companies in Boston is taken and the sample mean car rental rate is $47, with a standard deviation of $3. Further, suppose a survey of nine car rental companies in Dallas
What is the difference in average daily hotel room rates between Minneapolis and New Orleans? Suppose we want to estimate this difference by taking hotel rate samples from each city and using a 98% confidence level. The data for such a study follow. Use these data to produce a point estimate for
A study was made to compare the costs of supporting a family of four Americans for a year in different foreign cities. The lifestyle of living in the United States on an annual income of $75,000 was the standard against which living in foreign cities was compared. A comparable living standard in
Some studies have shown that in the United States, men spend more than women buying gifts and cards on Valentine's Day. Suppose a researcher wants to test this hypothesis by randomly sampling nine men and 10 women with comparable demographic characteristics from various large cities across the
Use the data given and a 1% level of significance to test the following hypotheses. Assume the differences are normally distributed in the population.H0: D = 0 Ha: D >0
Use the data given to test the following hypotheses (α = .05). Assume the differences are normally distributed in the population. H0: D = 0 Ha: D ≠0
Construct a 98% confidence interval to estimate D from the following sample information. Assume the differences are normally distributed in the population.d = 40.56, sd = 26.58, n = 22
Construct a 90% confidence interval to estimate D from the following sample information. Assume the differences are normally distributed in thepopulation.
Because of uncertainty in real estate markets, many homeowners are considering remodeling and constructing additions rather than selling. Probably the most expensive room in the house to remodel is the kitchen, with an average cost of about $23,400. In terms of resale value, is remodeling the
The vice president of marketing brought to the attention of sales managers that most of the company's manufacturer representatives contacted clients and maintained client relationships in a disorganized, haphazard way. The sales managers brought the reps in for a three-day seminar and training
Eleven employees were put under the care of the company nurse because of high cholesterol readings. The nurse lectured them on the dangers of this condition and put them on a new diet. Shown are the cholesterol readings of the 11 employees both before the new diet and one month after use of the
Lawrence and Glover published the results of a study in the Journal of Managerial Issues in which they examined the effects of accounting firm mergers on auditing delay. Auditing delay is the time between a company’s fiscal year-end and the date of the auditor’s report. The hypothesis is that
A nationally known supermarket decided to promote its own brand of soft drinks on TV for two weeks. Before the ad campaign, the company randomly selected 21 of its stores across the United States to be part of a study to measure the campaign’s effectiveness. During a specified half-hour period on
Is there a significant difference in the gasoline mileage of a car for regular unleaded and premium unleaded? To test this question, a researcher randomly selected 15 drivers for a study. They were to drive their cars for one month on regular unleaded and for one month on premium unleaded gasoline.
Using the given sample information, test the following hypotheses.a. H0: p1 - p2 = 0Ha: p1 - p2 ≠0Note that x is the number in the sample having the characteristic of interest.b. H0: p1 - p2 = 0Ha: p1 - p2 >0
In each of the following cases, calculate a confidence interval to estimate p1 – p2.a. n1 = 85, n2 = 90, p1 = .75, p2 = .67, ; level of confidence = 90%.b. n1 = 1100, n2 = 1300, p1 = .19, p2 = .17; level of confidence = 95%.c. n1 = 430, n2 = 399, x1 = 275, x2 = 275; level of confidence = 85%.d.
According to a study conducted for Gateway Computers, 59% of men and 70% of women say that weight is an extremely/very important factor in purchasing a laptop computer. Suppose this survey was conducted using 374 men and 481 women. Do these data show enough evidence to declare that a significantly
Does age make a difference in the amount of savings a worker feels is needed to be secure at retirement? A study by CommSciences for Transamerica Asset Management found that .24 of workers in the 25-33 age category feel that $250,000 to $500,000 is enough to be secure at retirement. However, .35 of
Companies that recently developed new products were asked to rate which activities are most difficult to accomplish with new products. Options included such activities as assessing market potential, market testing, finalizing the design, developing a business plan, and the like. A researcher wants
A large production facility uses two machines to produce a key part for its main product. Inspectors have expressed concern about the quality of the finished product. Quality control investigation has revealed that the key part made by the two machines is defective at times. The inspectors randomly
According to a CCH Unscheduled Absence survey, 9% of small businesses use telecommuting of workers in an effort to reduce unscheduled absenteeism. This proportion compares to 6% for all businesses. Is there really a significant difference between small businesses and all businesses on this issue?
Many Americans spend time worrying about paying their bills. A survey by Fleishman-Hilliard Research for MassMutual discovered that 60% of Americans with kids say that paying bills is a major concern. This proportion compares to 52% of Americans without kids. Suppose 850 Americans with kids and 910
Test the following hypotheses by using the given sample information and α = .01. Assume the populations are normally distributed.H0: σ21 = σ22Ha: σ21 < σ22n1 = 10, n2 = 12, s21 = 562, s22 = 1013
Test the following hypotheses by using the given sample information and Assume the populations are normally distributed.H0: σ21 = σ22Ha: σ21 ≠ σ22n1 = 5, n2 = 19, s1 = 4.68, s2 = 2.78
Suppose the data shown here are the results of a survey to investigate gasoline prices. Ten service stations were selected randomly in each of two cities and the figures represent the prices of a gallon of unleaded regular gasoline on a given day. Use the F test to determine whether there is a
How long are resale houses on the market? One survey by the Houston Association of Realtors reported that in Houston, resale houses are on the market an average of 112 days. Of course, the length of time varies by market. Suppose random samples of 13 houses in Houston and 11 houses in Chicago that
One recent study showed that the average annual amount spent by an East Coast household on frankfurters was $23.84 compared with an average of $19.83 for West Coast households. Suppose a random sample of 12 East Coast households showed that the standard deviation of these purchases (frankfurters)
According to the General Accounting Office of the U.S. government, the average age of a male federal worker is 43.6 years and that of a male worker in the nonfederal sector is 37.3 years. Is there any difference in the variation of ages of men in the federal sector and men in the nonfederal sector?
Test the following hypotheses with the data given. Let σ = .10.H0: µ1 – µ2 = 0 Ha: µ1 – µ2 ≠0
Use the following data to construct a 98% confidence interval to estimate the difference between µ1 andµ2.
The following data come from independent samples drawn from normally distributed populations. Use these data to test the following hypotheses. Let the Type I error rate be .05.H0: µ1 – µ2 = 0Ha: µ1 – µ2 >0
Construct a 95% confidence interval to estimate µ1 - µ2 by using the following data. Assume the populations are normallydistributed.
The following data have been gathered from two related samples. The differences are assumed to be normally distributed in the population. Use these data and alpha of .01 to test the following hypotheses.H0: D = 0Ha: D < 0n = 21, d = – 1.16, sd = 1.01
Use the following data to construct a 99% confidence interval to estimate D. Assume the differences are normally distributed in thepopulation.
Test the following hypotheses by using the given data and alpha equal to.05.
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