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mathematics
statistics
Business Statistics For Contemporary Decision Making 8th Edition Black Ken - Solutions
Determine the sample size necessary to estimate for the following information.a. σ = 36 and E = 5 at 95% confidenceb. σ = 4.13 and E = 1 at 99% confidencec. Values range from 80 to 500, error is to be within 10, and the confidence level is 90%d. Values range from 50 to 108, error is to be within
Determine the sample size necessary to estimate p for the following information.a. E = .02, p is approximately .40, and confidence level is 96%b. E is to be within .04, p is unknown, and confidence level is 95%c. E is to be within 5%, p is approximately 55%, and confidence level is 90%d. E is to be
A group of investors wants to develop a chain of fast-food restaurants. In determining potential costs for each facility, they must consider, among other expenses, the average monthly electric bill. They decide to sample some fast-food restaurants currently operating to estimate the monthly cost of
Suppose a production facility purchases a particular component part in large lots from a supplier. The production manager wants to estimate the proportion of defective parts received from this supplier. She believes the proportion defective is no more than .20 and wants to be within .02 of the true
What proportion of secretaries of Fortune 500 companies has a personal computer at his or her workstation? You want to answer this question by conducting a random survey. How large a sample should you take if you want to be 95% confident of the results and you want the error of the confidence
What proportion of shoppers at a large appliance store actually makes a large-ticket purchase? To estimate this proportion within 10% and be 95% confident of the results, how large a sample should you take? Assume you have no idea what proportion of all shoppers actually make a large-ticket
Use the following data to construct 80%, 94%, and 98% confidence intervals to estimate µ. Assume that σ is 7.75.State the pointestimate.
Construct 90%, 95%, and 99% confidence intervals toEstimate µ from the following data. State the point estimate. Assume the data come from a normally distributedpopulation.
Use the following information to compute the confidence interval for the population proportion.a. n = 715 and x = 329,with 95% confidenceb. n = 284 and p̂ with 90% confidencec. n = 1250 and p̂ with 95% confidenced. n = 457 and x = 270,with 98% confidence
Use the following data to construct 90% and 95% confidence intervals to estimate the population variance. Assume the data come from a normally distributedpopulation.
Determine the sample size necessary under the following conditions.a. To estimate µ with σ = 44,E = 3,and 95% confidenceb. To estimate µ with a range of values from 20 to 88 with E = 2 and 90% confidencec. To estimate p with p unknown, E = .04, and 98% confidenced. To estimate p with E = .03,
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
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?
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 of48. Use this information to construct a 98% confidence interval to estimate the
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.Assuming σ is 3.891, use these data to construct a 90% confidence
Is the environment a major issue with Americans? To answer that question, a researcher conducts a survey of 1255 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
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
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
An entrepreneur wants to open an appliance 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 bills
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
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).Use this information to
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
According to a survey by Runzheimer International, the average cost of a fast-food meal (quarter-pound cheese-burger, 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 $0.37.
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
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 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 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 study of 1,000 adult Canadians was undertaken in an effort to obtain information about Canadian shopping habits. One of the results of this survey was that 23% often buy items that are not on their shopping list but catch their eye. Use this study result to estimate with an 80% level of
A bank officer wants to determine the amount of the average total monthly deposits per customer at the bank. He believes an estimate of this average amount using a confidence interval is sufficient. How large a sample should he take to be within $200 of the actual average with 99% confidence? He
Suppose you have been following a particular airline stock for many years. You are interested in determining the average daily price of this stock in a 10-year period and you have access to the stock reports for these years. However, you do not want to average all the daily prices over 10 years
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.Ifyou want the error of the confidence interval
A national beauty spa chain wants to estimate the number of times per year a woman has her nails done at one of their spas if she uses one at least once a year. The chain’s researcher estimates that, of those women who use a beauty spa at least once a year to get their nails done, the standard
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 large
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 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
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.
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 itsimplication.
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.
In the late 1970s, Kip Tindell (chairman and CEO), Garrett Boone (Chairman Emeritus), and John Mullen (architect) drew up plans for a first of a kind retail store specializing in storage solutions for both the home and the office. The vision that they created was realized when on July 1, 1978, the
Read each of the following statements. Assuming that statistical hypotheses are set up to test them, classify each as a one-tailed or a two-tailed test.a. Maritz Marketing Research reports that 42% of all adults seek advice from others in selecting a lawyer. A business researcher wants to test this
In each of the following scenarios, tell if the researcher has committed a Type I error, a Type II error, or made a correct decision. a. A researcher is testing to determine if .31 of all families own more than one car. His null hypothesis is that the population proportion is .31.He randomly
a. Use the data given to test the following hypotheses.b. Use the p-value to reach a statistical conclusion.c. Using the critical value method, what are the critical sample meanvalues?
Use the data given to test the following hypotheses. Assume the data are normally distributed in thepopulation.
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 themean.
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
According to the U.S. Bureau of Labor Statistics, the average weekly earnings of a production worker in July 2011 were $657.49.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
According to a study several years ago by the Personal Communications Industry Association, the average cell phone user earns $62,600 per year. Suppose a researcher believes that the average annual earnings of a cell phone user are lower now, and he sets up a study in an attempt to prove his
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 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 few years later, business
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 it operates, the average price for this service is higher. To test this
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 this is so. They randomly select a sample of Americans and
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 α = .05 to test the following hypotheses.H0: µ = 16 Ha: µ ≠ 16
A random sample of 51 items is taken, with x̄ = 58.42 and s2 = 25.68. 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.H0: µ = 60 Ha: µ < 60
The following data were gathered from a random sample of 11 items.Use these data and a 5% level of significance to test the following hypotheses, assuming that the data come from a normally distributed population.H0: µ = 1160 Ha: µ >1160
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.Use these data and α = .01 to test the hypothesis that the parts average 8.3pounds.
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
Suppose a study reports that the average price for a gallon of self-serve regular unleaded gasoline is $3.76.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
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
Major cities around the world compete with each other 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 structure, the
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 $1,135 annually on dental procedures. Suppose further that a regional dental association wants to test to determine if
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 p̂ = .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, 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
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. H0: σ2 = 45Ha: σ2 > 45α = .01, n = 8, s2 = 4.12d. H0: σ2 =
Previous experience shows the variance of a given process to be 14.Researchers is 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 9.38, use and solve for the probability of committing a Type II error for the following possible true alternative means.a. µa = 98.5b. µa = 98c. µa = 97d. µa = 96e. What happens to the probability of committing a Type II error as the alternative value of the mean gets farther from
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.
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 = .60b. pa = .55c. 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 eight-step approach to test the hypotheses. Let α = .01.H0:µ = 36Ha: µ ≠ 36n = 63x̄ = 38.4σ =5.93
Use the information given and the eight-step approach to test the hypotheses. Let α =.05.Assume that the population is normally distributed.H0:µ = 7.82Ha: µ < 7.82n = 17x̄ = 7.01s = 1.69
For each of the following problems, use the eight-step approach to test the hypotheses.a. H0:p = 36Ha: p > 36n = 783x̄ = 230α = .10.b. H0:p = 36Ha: p ≠ 36n = 401p̂ = .56α = .05.
Test the following hypotheses by using the information given and the eight-step approach. Let alpha be .01. Assume the population is normally distributed.H0: σ2 = 15.4Ha: σ2 > 15.4n = 18s2 = 29.6.
Solve for the value of beta in each of the following problems.a. H0:µ = 130Ha: µ > 130n = 75σ = 12α = .01.The alternative mean is actually 135.b. H0:µ = .44Ha: p < .44n = 1095α = .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 mini computers 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 medium-sized 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 16.0%. 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
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