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Business Statistics Contemporary Decision Making 6th Edition Ken Black - Solutions
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 = .05 and assuming the populations have equal variances and x is approximately normally distributed,
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.b. Use these data to construct a 90% confidence interval to estimate Sample 1 - = 0 H-20 Sample 2 11 =20 = 20 x =
Use the data given and the eight-step process to test the following hypotheses.Use a 1% level of significance, and assume that x is normally distributed. Sample 1 111 Sample 2 11 = 11 n = 8 x = 24.56 = 12.4 $2 = 15.8 = 26.42 Ha 20
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
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
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
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 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
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
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
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 ( = .02).b. Construct a 98% confidence interval to estimate the difference in population means using these data. How does your result validate
Use the following sample information to construct a 90% confidence interval for the difference in the two population means. Sample 1 n = 32 = 70.4 = 5.76 Sample 2 11 = 31 x-68.7 = 6.1
a. Test the following hypotheses of the difference in population means by using the following data ( = .10) and the eight-step process. Ho = 0 Ha 20 Sample 1 x=51.3 Sample 2 53.2 = 52 = 60 n-32 11 = 31 b. Use the critical value method to find the critical difference in the mean values required to
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
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
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
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
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
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
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
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
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 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
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
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
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
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
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 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
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
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
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
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
Solve for the value of beta in each of the following problems. a. Ho 130 H >130 n = 75 o 12 a=.01. The alternative mean is actually 135. b. Ho: p = .44 H: p
Test the following hypotheses by using the information given and the HTAB system. Let alpha be .01. Assume the population is normally distributed. H: = 15.4 H: >15.4 n = 18 s = 29.6
For each of the following problems, test the hypotheses.Incorporate the HTAB system with its eight-step process. a. Hop .28 Hp> .28 b. Ho p.61 H: p.61 n=-783 x = 230 a=.10 n=401 = .56 a=.05
Use the information given and the HTAB system to test the hypotheses. Let Assume the population is normally distributed. H: a=7.82 Hip
Use the information given and the HTAB system to test the hypotheses. Let a = .01.
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
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
An alternative hypothesis is that To test this hypothesis, a random sample of size 360 is taken.What is the probability of committing a Type II error if and the alternative proportion is as follows? a. Pa = .60 b. Pa = .55 c. Pa = .50
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 if the population standard deviation is 7 and the alternative mean is 53? Use
For Problem 9.36, use a = .05 and solve for the probability of committing a Type II error for the following possible true alternative means. a. =98.5 b. a=98 c. a=97 d. =96 e. What happens to the probability of committing a Type II error as the alternative value of the mean gets farther from the
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 values, compute the probability of committing a Type II error if the population
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
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 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
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 to test the null hypothesis about the variance. Assume the measurements are
Test each of the following hypotheses by using the given information. Assume the populations are normally distributed. = a. Ho: = 20 H: > 20 a = .05, n = 15, s = 32
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
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
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 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
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
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
Suppose you are testing versus 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 had used the critical value
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
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,
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
Major cities around the world compete with each other in an effort to attract new businesses. Some of the criteria that businesses use to judge cities as potential locations for their headquarters might include the labor pool; the environment, including work, governmental, and living; the tax
Suppose that in past years the average price per square foot for warehouses in the United States has been $32.28. A national real estate investor wants to determine whether that figure has changed now. The investor hires a researcher who randomly samples 49 warehouses that are for sale across the
Suppose a study reports that the average price for a gallon of self-serve regular unleaded gasoline is $3.16. You believe that the figure is higher in your area of the country. You decide to test this claim for your part of the United States by randomly calling gasoline stations. Your random survey
A hole-punch machine is set to punch a hole 1.84 centimeters in diameter in a strip of sheet metal in a manufacturing process. The strip of metal is then creased and sent on to the next phase of production, where a metal rod is slipped through the hole. It is important that the hole be punched to
The following data (in pounds), which were selected randomly from a normally distributed population of values, represent measurements of a machine part that is supposed to weigh, on average, 8.3 pounds.8.1 8.4 8.3 8.2 8.5 8.6 8.4 8.3 8.4 8.2 8.8 8.2 8.2 8.3 8.1 8.3 8.4 8.5 8.5 8.7 Use these data
The following data were gathered from a random sample of 11 items.1200 1175 1080 1275 1201 1387 1090 1280 1400 1287 1225 Use these data and a 5% level of significance to test the following hypotheses, assuming that the data come from a normally distributed population. Ho: 1160 H: 1160
A random sample of 51 items is taken, with and Use these data to test the following hypotheses, assuming you want to take only a 1% risk of committing a Type I error and that x is normally distributed. Ho: =60 H:
A random sample of size 20 is taken, resulting in a sample mean of 16.45 and a sample standard deviation of 3.59. Assume x is normally distributed and use this information and to test the following hypotheses. H: = 16 H: 16
The American Water Works Association estimates that the average person in the United States uses 123 gallons of water per day. Suppose some researchers believe that more water is being used now and want to test to determine whether it is so.They randomly select a sample of Americans and carefully
According to HowtoAdvice.com, the average price charged to a customer to have a 12 by 18 wall-to-wall carpet shampoo cleaned is about $50. Suppose that a start-up carpet-cleaning company believes that in the region in which they operate, the average price for this service is higher. To test this
According to a report released by CIBC entitled “Women Entrepreneurs: Leading the Charge,” the average age for Canadian businesswomen in 2008 was 41. In the report, there was some indication that researchers believed that this mean age will increase. Suppose now, a couple of years later,
A manufacturing company produces valves in various sizes and shapes. One particular valve plate is supposed to have a tensile strength of 5 pounds per millimeter(lbs/mm). The company tests a random sample of 42 such valve plates from a lot of 650 valve plates. The sample mean is a tensile strength
According to a study several years ago by the Personal Communications Industry Association, the average wireless phone user earns $62,600 per year. Suppose a researcher believes that the average annual earnings of a wireless phone user are lower now, and he sets up a study in an attempt to prove
According to the U.S. Bureau of Labor Statistics, the average weekly earnings of a production worker in 1997 were $424.20. Suppose a labor researcher wants to test to determine whether this figure is still accurate today. The researcher randomly selects 54 production workers from across the United
The Environmental Protection Agency releases figures on urban air soot in selected cities in the United States. For the city of St. Louis, the EPA claims that the average number of micrograms of suspended particles per cubic meter of air is 82. Suppose St. Louis officials have been working with
a. Use the data given to test the following hypotheses.b. Use the p-value to obtain the results.c. Solve for the critical value required to reject the mean. == : = 1200 H: > 1200 x=1215, n 113, == 100, a .10
a. Use the data given to test the following hypotheses.b. Use the p-value to reach a statistical conclusionc. Using the critical value method, what are the critical sample mean values? Ho: =25 H: 25 28.1, n = 57, = 8.46, a = .01 x=28.1,
What proportion of all American workers drive their cars to work? Suppose a poll of American workers is taken in an effort to answer that question, and the Minitab output shown here is an analysis of the data from the poll. Explain the meaning of the output in light of the question. Test and CI for
Suppose a researcher wants to estimate the average age of a person who is a first-time home buyer. A random sample of first-time home buyers is taken and their ages are ascertained. The Minitab output shown here is an analysis of that data. Study the output and explain its implication. One-Sample T
A company has developed a new light bulb that seems to burn longer than most residential bulbs. To determine how long these bulbs burn, the company randomly selects a sample of these bulbs and burns them in the laboratory. The Excel output shown here is a portion of the analysis from this effort.
A soft drink company produces a cola in a 12-ounce can.Even though their machines are set to fill the cans with 12 ounces, variation due to calibration, operator error, and other things sometimes precludes the cans having the correct fill. To monitor the can fills, a quality team randomly selects
The price of a head of iceberg lettuce varies greatly with the season and the geographic location of a store.During February a researcher contacts a random sample of 39 grocery stores across the United States and asks the produce manager of each to state the current price charged for a head of
A national survey showed that Hillshire Farm Deli Select cold cuts were priced, on the average, at $5.20 per pound. Suppose a national survey of 23 retail outlets was taken and the price per pound of Hillshire Farm Deli Select cold cuts was ascertained. If the following data represent these prices,
A national magazine marketing firm attempts to win subscribers with a mail campaign that involves a contest using magazine stickers. Often when people subscribe to magazines in this manner they sign up for multiple magazine subscriptions. Suppose the marketing firm wants to estimate the average
A research firm has been asked to determine the proportion of all restaurants in the state of Ohio that serve alcoholic beverages. The firm wants to be 98% confident of its results but has no idea of what the actual proportion is. The firm would like to report an error of no more than .05. How
A regional survey of 560 companies asked the vice president of operations how satisfied he or she was with the software support received from the computer staff of the company. Suppose 33% of the 560 vice presidents said they were satisfied. Construct a 99% confidence interval for the proportion of
A survey of 77 commercial airline flights of under 2 hours resulted in a sample average late time for a flight of 2.48 minutes. The population standard deviation was 12 minutes. Construct a 95% confidence interval for the average time that a commercial flight of under 2 hours is late.What is the
According to a survey by Runzheimer International, the average cost of a fast-food meal (quarter-pound cheeseburger, large fries, medium soft drink, excluding taxes)in Seattle is $4.82. Suppose this figure was based on a sample of 27 different establishments and the standard deviation was
A movie theater has had a poor accounting system. The manager has no idea how many large containers of popcorn are sold per movie showing. She knows that the amounts vary by day of the week and hour of the day.However, she wants to estimate the overall average per movie showing. To do so, she
A national survey of companies included a question that asked whether the company had at least one bilingual telephone operator. The sample results of 90 companies follow (Y denotes that the company does have at least one bilingual operator; N denotes that it does not).N N N N Y N Y N N Y N N N Y Y
A national survey of insurance offices was taken, resulting in a random sample of 245 companies. Of these 245 companies, 189 responded that they were going to purchase new software for their offices in the next year.Construct a 90% confidence interval to estimate the population proportion of
An entrepreneur wants to open an appliance service repair shop. She would like to know about what the average home repair bill is, including the charge for the service call for appliance repair in the area. She wants the estimate to be within $20 of the actual figure. She believes the range of such
A national survey on telemarketing was undertaken. One of the questions asked was: How long has your organization had a telemarketing operation? Suppose the following data represent some of the answers received to this question. Suppose further that only 300 telemarketing firms comprised the
According to a survey by Topaz Enterprises, a travel auditing company, the average error by travel agents is$128. Suppose this figure was obtained from a random sample of 41 travel agents and the sample standard deviation is $21. What is the point estimate of the national average error for all
Is the environment a major issue with Americans? To answer that question, a researcher conducts a survey of 1,255 randomly selected Americans. Suppose 714 of the sampled people replied that the environment is a major issue with them. Construct a 95% confidence interval to estimate the proportion of
A national beauty salon chain wants to estimate the number of times per year a woman has her hair done at a beauty salon if she uses one at least once a year. The chain’s researcher estimates that, of those women who use a beauty salon at least once a year, the standard deviation of number of
A random sample of small-business managers was given a leadership style questionnaire. The results were scaled so that each manager received a score for initiative.Suppose the following data are a random sample of these scores.37 42 40 39 38 31 40 37 35 45 30 33 35 44 36 37 39 33 39 40 41 33 35 36
What is the average length of a company’s policy book?Suppose policy books are sampled from 45 medium-sized companies. The average number of pages in the sample books is 213, and the population standard deviation of 48. Use this information to construct a 98% confidence interval to estimate the
Use the data in Problem 8.53 to construct a 99% confidence interval to estimate the population variance for the number of diapers used during a 24-hour period for one-month-olds. How could information about the population variance be used by a manufacturer or marketer in planning?
Suppose you want to estimate the proportion of cars that are sport utility vehicles (SUVs) being driven in Kansas City, Missouri, at rush hour by standing on the corner of I-70 and I-470 and counting SUVs.You believe the figure is no higher than .40. If you want the error of the confidence interval
In planning both market opportunity and production levels, being able to estimate the size of a market can be important. Suppose a diaper manufacturer wants to know how many diapers a one-month-old baby uses during a 24-hour period. To determine this usage, the manufacturer’s analyst randomly
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