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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
Suppose we are told the sampling distribution developed from a sample of size 400 has a mean of 56.78 and a standard error of 9.6. If the population is known to be normally distributed, what are the population mean and population standard deviation?Discuss how these values relate to the values for
If a population is known to be normally distributed, what size sample is required to ensure that the sampling distribution of is normally distributed?
Consider the standard error of a sample proportion obtained from a sample of size 100.a. Determine the standard error obtained from a population with p 0.1.b. Repeat part a for a population proportion equal to(1) 0.5 and (2) 0.9.c. Which population proportion results in the largest standard
A researcher has collected all possible samples of a size of 150 from a population and listed the sample means for each of these samples.a. If the average of the sample means is 450.55, what would be the numerical value of the true population mean? Discuss.b. If the standard deviation of the sample
Discuss the similarities and differences between a standard deviation and a standard error.
Discuss why the sampling distribution will be less variable than the population distribution. Give a short example to illustrate your answer.
A sample of size 30 is obtained from a population that has a proportion of 0.34. Determine the range of sampling errors possible when the sample proportion is used to estimate the population proportion.(Hint: Review the Empirical Rule.)
Under what conditions should the finite population correction factor be used in determining the standard error of a sampling distribution?
A study conducted by Watson Wyatt Worldwide, a human resources consulting firm, revealed that 13%of Fortune 1000 companies either terminated or froze their defined-benefit pension plans. As part of a study to evaluate how well its benefits package compares to other Fortune 1000 companies, a retail
Driven, a recently released magazine targeted to young professionals, states that 65% of its subscribers have an annual income greater than $100,000. The sales staff at Driven uses this high proportion of subscribers earning more than $100,000 as a selling point when trying to get companies to
The Bureau of Labor Statistics, U.S. Office of Personnel Management, indicated that the average hourly compensation (salary plus benefits) for federal workers (not including military or postal service employees) was $44.82. The rates for private industry and state and local government workers are
The Bureau of Transportation Statistics releases information concerning the monthly percentage of U.S.airline flights that land no later than 15 minutes after scheduled arrival. The average of these percentages for the 12 months in 2004 was 78.08%. These data become available as soon as feasible.
Procter & Gamble (P&G) merged with Gillette in 2005. One of the concerns the new, larger company has is the increasing burden of retirement expenditures.An effort is being made to encourage employees to participate in 401(k) accounts. Nationwide, 66% of eligible workers participate in these
Airgistics provides air consolidation and freightforwarding services for companies that ship their products internationally. As a part of its commitment to continuous process improvement, Airgistics monitors the performance of its partner carriers to ensure that high standards of on-time delivery
TransUnion is a leading global provider of business intelligence services. Transunion reported that 33% of the mortgages in the year previous to the sub-prime mortgage crisis were adjustable-rate mortgages(ARMs).a. In samples of mortgages of size 75, what proportion of the samples would you expect
According to the most recent Labor Department data, 10.5% of engineers (electrical, mechanical, civil, and industrial) were women. Suppose a random sample of 50 engineers is selected.a. How likely is it that the random sample of 50 engineers will contain 8 or more women in these positions?b. How
The National Association of Realtors released a survey indicating that a surprising 43% of first-time home buyers purchased their homes with no-money-down loans during 2005. The fear is that house prices will decline and leave homeowners owing more than their homes are worth. PMI Mortgage Insurance
The J R Simplot Company is one of the world’s largest privately held agricultural companies, employing over 10,000 people in the United States, Canada, China, Mexico, and Australia. More information can be found at the company’s Web site: www.Simplot.com. One of its major products is french
United Manufacturing and Supply makes sprinkler valves for use in residential sprinkler systems. United supplies these valves to major companies such as Rain Bird and Nelson, who in turn sell sprinkler products to retailers. United recently entered into a contract to supply 40,000 sprinkler valves.
A survey is conducted from a population of people of whom 40% have a college degree. The following sample data were recorded for a question asked of each person sampled, “Do you have a college degree?”YES NO NO YES YES YES YES YES YES YES YES NO NO NO YES NO YES YES NO NO NO YES YES YES NO YES
A random sample of size 100 is to be taken from a population that has a proportion equal to 0.35. The sample proportion will be used to estimate the population proportion.a. Calculate the probability that the sample proportion will be within 0.05 of the population proportion.b. Calculate the
Given a population where the probability of a success is p 0.40, if a sample of 1,000 is taken,a. Calculate the probability the proportion of successes in the sample will be less than 0.42.b. What is the probability the proportion of successes in the sample will be greater than 0.44?
Given a population where the proportion of items with a desired attribute is p 0.50, if a sample of 200 is taken,a. Find the probability the proportion of successes in the sample will be between 0.47 and 0.51.b. Referring to parta, what would the probability be if the sample size were 100?
Given a population in which the probability of success is p 0.20, if a sample of 500 items is taken, thena. Calculate the probability the proportion of successes in the sample will be between 0.18 and 0.23.b. Calculate the probability the proportion of successes in the sample will be between 0.18
Given a population where the proportion of items with a desired attribute is p 0.25, if a sample of 400 is taken,a. What is the standard deviation of the sampling distribution of p?b. What is the probability the proportion of successes in the sample will be greater than 0.22?
The proportion of items in a population that possess a specific attribute is known to be 0.70.a. If a simple random sample of size n 100 is selected and the proportion of items in the sample that contain the attribute of interest is 0.65, what is the sampling error?b. Referring to parta, what is
If a random sample of 200 items is taken from a population in which the proportion of items having a desired attribute is p 0.30, what is the probability that the proportion of successes in the sample will be less than or equal to 0.27?
A population has a proportion equal to 0.30. Calculate the following probabilities with n 100:a. P(p 0.35)b. P(p 0.40)c. P(0.25 p 0.40)d. P(p 0.27).
The file Salaries contains the annual salary for all faculty at a small state college in the Midwest. Assume that these faculty salaries represent the population of interest.a. Compute the population mean and population standard deviation.b. Develop a frequency distribution of these data using 10
The data file called CEO Compensation contains data for the CEOs of 496 of the nation’s top 500 companies in 2005. These data are published by the Forbes organization and are available on its Web site (www.forbes.com/2005/04/20/05ceoland.html).a. Treating these data as the population of interest,
The highly respected financial magazine Forbes publishes data on CEO salaries each year. At the end of 2005, Forbes posted CEO compensation data to its Web site (www.forbes.com/2005/04/20/05ceoland.html). These data reflect the total compensation for CEOs for 496 of the nation’s 500 largest
Bruce Leichtman is president of Leichtman Research Group, Inc. (LRG), which specializes in research and consulting on broadband, media, and entertainment industries. In a recent survey, the company determined the cost of extra high-definition (HD) gear needed to watch television in HD. The costs
Acee Bottling and Distributing bottles and markets Pepsi-Cola products in southwestern Montana. The average fill volume for Pepsi cans is supposed to be 12 ounces. The filling machine has a known standard deviation of 0.05 ounces. Each week, the company selects a simple random sample of 60 cans and
One of the top-selling video games continues to be Madden NFL 09 published by Electronic Arts. While prices vary widely depending on store, the suggested retail price for this video game is $46. The file entitled Madden contains a random sample of the retail prices paid for Madden NFL 09.a.
ACNielsen is a New York–based corporation and a member of the modern marketing research industry.One of the items that ACNielsen tracks is the expenditure on over-the-counter (OTC) cough medicines. ACNielsen recently indicated that consumers spent $620 million on OTC cough medicines in the United
Airlines have recently toughened their standards for the weight of checked baggage, limiting the weight of a bag to 50 pounds on domestic U.S. flights. Heavier bags will be carried but at an additional fee. Suppose that one major airline has stated in an internal memo to employees that the mean
In an article entitled “Fuel Economy Calculations to Be Altered,” James R. Healey indicated that the government planned to change how it calculates fuel economy for new cars and trucks. This is the first modification since 1985. It is expected to lower average mileage for city driving in
The branch manager for United Savings and Loan in Seaside, Virginia, has worked with her employees in an effort to reduce the waiting time for customers at the bank. Recently, she and the team concluded that average waiting time is now down to 3.5 minutes with a standard deviation equal to 1.0
Sands, Inc., makes particleboard for the building industry. Particleboard is built by mixing wood chips and resins together and pressing the sheets under extreme heat and pressure to form a 4-feet 8-feet sheet that is used as a substitute for plywood.The strength of the particleboards is tied to
Suppose the life of a particular brand of calculator battery is approximately normally distributed with a mean of 75 hours and a standard deviation of 10 hours.a. What is the probability that a single battery randomly selected from the population will have a life between 70 and 80 hours?b. What is
SeaFair Fashions relies on its sales force of 220 to do an initial screening of all new fashions. The company is currently bringing out a new line of swimwear and has invited 40 salespeople to its Orlando home office.An issue of constant concern to the SeaFair sales office is the volume of orders
Many Happy Returns is a tax preparation service with offices located throughout the western United States.Suppose the average number of returns processed by employees of Many Happy Returns during tax season is 12 per day with a standard deviation of 3 per day.A random sample of 36 employees taken
SeeClear Windows makes windows for use in homes and commercial buildings. The standards for glass thickness call for the glass to average 0.375 inches with a standard deviation equal to 0.050 inches.Suppose a random sample of n 50 windows yields a sample mean of 0.392 inches.a. What is the
Consider a normal distribution with mean 12 and standard deviation 90. Calculate for each of the following sample sizes:a. n 1b. n 9c. n 16d. n 25
Given a distribution that has a mean of 40 and a standard deviation of 13, calculate the probability that a sample of 49 has a sample mean that isa. greater than 37b. at most 43c. between 37 and 43d. between 43 and 45e. no more than 35
A random sample of 100 items is selected from a population of size 350. What is the probability that the sample mean will exceed 200 if the population mean is 195 and the population standard deviation equals 20? (Hint: Use the finite correction factor since the sample size is more than 5% of the
Suppose nine items are randomly sampled from a normally distributed population with a mean of 100 and a standard deviation of 20. The nine randomly sampled values are 125 95 66 116 99 91 102 51 110 Calculate the probability of getting a sample mean that is smaller than the sample mean for these
If a population is known to be normally distributed with m 250 and s 40, what will be the characteristics of the sampling distribution for based on a random sample of size 25 selected from the population?
A normally distributed population has a mean of 500 and a standard deviation of 60.a. Determine the probability that a random sample of size 16 selected from this population will have a sample mean less than 475.b. Determine the probability that a random sample of size 25 selected from the
Suppose that a population is known to be normally distributed with m 2,000 and s 230. If a random sample of size n 8 is selected, calculate the probability that the sample mean will exceed 2,100.
A population with a mean of 1,250 and a standard deviation of 400 is known to be highly skewed to the right. If a random sample of 64 items is selected from the population, what is the probability that the sample mean will be less than 1,325?
The Badke Foundation was set up by the Fred Badke family following his death in 2001. Fred had been a very successful heart surgeon and real estate investor in San Diego, and the family wanted to set up an organization that could be used to help less fortunate people. However, one of the concepts
Maher, Barney, and White LLC is a legal firm with 40 employees. All of the firm’s employees are eligible to participate in the company’s 401(k) plan, and the firm is proud of its 100% participation rate. The file MBW 401 contains the most recent year-end 401(k) account balance for each of the
Welco Lumber Company is based in Shelton, Washington, and is a privately held company that makes cedar siding, cedar lumber, and cedar fencing products for sale and distribution throughout North America. The major cost of production is the cedar logs that are the raw material necessary to make the
The Dow-Jones Industrial Average (DJIA) Index is a well-known stock index. The index was originally developed in 1884 and has been in place ever since as a gauge of how the U.S. stock market is performing. The file Dow Jones contains date, open, high, low, close, and volume for the DJIA for the
The file entitled Clothing contains the monthly retail sales ($millions) of U.S. women’s clothing stores for 70 months. A sample taken from this population to estimate the average sales in this time period follows:2,942 2,574 2,760 2,939 2,642 2,905 2,568 2,677 2,572 3,119 2,697 2,884 2,632 2,742
USA Today reports salaries for National Football League (NFL) teams. The file Jaguars contains the salaries for the 2007 Jacksonville Jaguars.a. Calculate the average total salary for the Jacksonville Jaguars for 2007.b. Calculate the smallest sample mean for total salary and the largest sample
A computer lab at a small college has 25 computers.Twice during the day a full scan for viruses is performed on each computer. Because of differences in the configuration of the computers, the times required to complete the scan are different for each machine.Records for the scans are kept and
An investment advisor has worked with 24 clients for the past five years. Following are the percentage rates of average five-year returns that these 24 clients experienced over this time frame on their investments:11.2 11.2 15.9 2.7 4.6 7.6 15.6 1.3 3.3 4.8 12.8 14.9 10.1 10.9 4.9 2.1 12.5 3.7 7.6
Princess Cruises recently offered a 16-day voyage from Beijing to Bangkok during the time period from May to August. The announced price, excluding airfare, for a room with an ocean view or a balcony was listed as $3,475. Cruise fares usually are quite variable due to discounting by the cruise line
The administrator at Saint Frances Hospital is concerned about the amount of overtime the nursing staff is incurring and wonders whether so much overtime is really necessary. The hospital employs 60 nurses. Following is the number of hours of overtime reported by each nurse last week. These data
The Anasazi Real Estate Company has 20 listings for homes in Santa Fe, New Mexico. The number of days each house has been on the market without selling is as follows:26 45 16 77 33 50 19 23 55 107 88 15 7 19 30 60 80 66 31 17a. Considering these 20 values to be the population of interest, what is
An Internet service provider states that the average number of hours its customers are online each day is 3.75. Suppose a random sample of 14 of the company’s customers is selected and the average number of hours that they are online each day is measured. The sample results are 3.11 1.97 3.52
A previous report from the Centers for Disease Control and Prevention (CDC) indicates that smokers, on average, miss 6.16 days of work per year due to sickness(including smoking-related acute and chronic conditions).Nonsmokers miss an average of 3.86 days of work per year. If two years later the
Hillman Management Services manages apartment complexes in Tulsa, Oklahoma. They currently have 30 units available for rent. The monthly rental prices(in dollars) for this population of 30 units are 455 690 450 495 550 780 800 395 500 405 675 550 490 495 700 995 650 550 400 750 600 780 650 905 415
Assume that the following represent a population of N 16 values.25 12 21 13 19 17 15 18 23 16 18 15 22 14 23 17a. Compute the population mean.b. If a random sample of n 9 includes the following values 12 18 13 17 23 14 16 25 15 compute the sample mean and calculate the sampling error for this
Assume that the following represent a population of N 24 values:10 14 32 9 34 19 31 24 33 11 14 30 6 27 33 32 28 30 10 31 19 13 6 35a. If a random sample of n 10 items includes the following values, compute the sampling error for the sample mean:32 19 6 11 10 19 28 9 13 33b. For a sample of
Consider the following population:18 26 32 17 34 17 17 22 29 24 24 35 13 29 38 The following sample was drawn from this population:35 18 24 17 24 32 17 29a. Determine the sampling error for the sample mean.b. Determine the largest possible sampling error for this sample of n 8.
The following population is provided:17 15 8 12 9 7 9 11 12 14 16 9 5 10 14 13 12 12 11 9 14 8 14 12 Further, a simple random sample from this population gives the following values:12 9 5 10 14 11 Compute the sampling error for the sample mean in this situation.
The following data are the 16 values in a population:10 5 19 20 10 8 10 2 14 18 7 8 14 2 3 10a. Compute the population mean.b. Suppose a simple random sample of 5 values from the population is selected with the following results:5 10 20 2 3 Compute the mean of this sample.c. Based on the results
A population has a mean of 125. If a random sample of 8 items from the population results in the following sampled values, what is the sampling error for the sample?103 123 99 107 121 100 100 99
Championship Billiards, owned by D & R Industries, in Lincolnwood, Illinois, provides some of the finest billiard fabrics, cushion rubber, and component parts in the industry. It sells billiard cloth in bolts and halfbolts.A half-bolt of billiard cloth has an average length of 35 yards with widths
The Future-Vision Cable TV Company recently surveyed its customers. A total of 548 responses were received. Among other things, the respondents were asked to indicate their household income. The data from the survey are found in a file named Future-Vision.a. Develop a frequency histogram for the
Team Marketing Report (TMR) produces the Fan Cost Index™ (FCI) survey, now in its 16th year, which tracks the cost of attendance for a family of four at National Football League (NFL) games. The FCI includes four average-price tickets, four small soft drinks, two small beers, four hot dogs, two
Midwest Fan Manufacturing Inc. was established in 1986 as a manufacturer and distributor of quality ventilation equipment. Midwest Fan’s products include the AXC range hood exhaust fans. The file entitled Fan Life contains the length of life of 125 randomly chosen AXC fans that were used in an
The Hydronics Company is in the business of developing health supplements. Recently, the company’s research and development department came up with two weight-loss products that included products produced by Hydronics. To determine whether these products are effective, the company has conducted a
The Cozine Corporation runs the landfill operation outside Little Rock, Arkansas. Each day, each of the company’s trucks makes several trips from the city to the landfill. On each entry the truck is weighed. The data file Cozine contains a sample of 200 truck weights. Determine the mean and
The personnel manager for a large company is interested in the distribution of sick-leave hours for employees of her company. A recent study revealed the distribution to be approximately normal, with a mean of 58 hours per year and a standard deviation of 14 hours.An office manager in one division
The St. Maries plywood plant is part of the Potlatch Corporation’s Northwest Division. The plywood superintendent organized a study of the tree diameters that are being shipped to the mill. After collecting a large amount of data on diameters, he concluded that the distribution is approximately
One of the products of Pittsburg Plate Glass Industries(PPG) is laminated safety glass. It is made up of two pieces of glass 0.125 inch thick, with a thin layer of vinyl sandwiched between them. The average thickness of the laminated safety glass is 0.25 inch. The thickness of the glass does not
The Sea Pines Golf Course is preparing for a major LPGA golf tournament. Since parking near the course is extremely limited (room for only 500 cars), the course officials have contracted with the local community to provide parking and a bus shuttle service. Sunday, the final day of the tournament,
An online article (http://beauty.about.com) by Julyne Derrick, “Shelf Lives: How Long Can You Keep Makeup,” suggests that eye shadow and eyeliner each have a shelf life of up to three years. Suppose the shelf lives of these two products are exponentially distributed with an average shelf life
A small private ambulance service in Kentucky has determined that the time between emergency calls is exponentially distributed with a mean of 41 minutes.When a unit goes on call, it is out of service for 60 minutes. If a unit is busy when an emergency call is received, the call is immediately
Two automatic dispensing machines are being considered for use in a fast-food chain. The first dispenses an amount of liquid that has a normal distribution with a mean of 11.9 ounces and a standard deviation of 0.07 ounces. The second dispenses an amount of liquid that has a normal distribution
The Three Sisters Lumber Company is considering buying a machine that planes lumber to the correct thickness. The machine is advertised to produce “6-inch lumber” having a thickness that is normally distributed, with a mean of 6 inches and a standard deviation of 0.1 inch.a. If building
The manager for Select-a-Seat, a company that sells tickets to athletic games, concerts, and other events, has determined that the number of people arriving at the Broadway location on a typical day is Poisson distributed with a mean of 12 per hour. It takes approximately four minutes to process a
Revisit Problem 6-55, but examine whether it would matter when you started monitoring the 911 calls if the time between occurrences had a uniform distribution with a mean of 2 and a range of 4.a. Calculate the probability that no call comes in during the first hour.b. Now suppose that you are
The exponential distribution has a characteristic that is called the “memoryless” property. This means P(X x) P(X x x0 X x0). To illustrate this, consider the calls coming into 911. Suppose that the distribution of the time between occurrences has an exponential distribution with a
Suppose you tell one of your fellow students that when working with a continuous distribution, it does not make sense to try to compute the probability of any specific value since it will be zero. She says that, when the experiment is performed some value must occur, the probability can’t be
The probability that a value from a normally distributed random variable will exceed the mean is 0.50. The same is true for the uniform distribution. Why is this not necessarily true for the exponential distribution?Discuss and show examples to illustrate your point.
Recall the Empirical Rule from Chapter 3. It states that if the data distribution is bell-shaped, then the interval m s contains approximately 68% of the values, m 2s contains approximately 95%, and m 3s contains virtually all of the data values. The bell-shaped distribution referenced is the
Discuss the difference between discrete and continuous probability distributions. Discuss two situations where a variable of interest may be considered either continuous or discrete.
The San Luis Obispo, California, Transit Program provides daily fixed-route transit service to the general public within the city limits and to Cal Poly State University’s staff and students. The most heavily traveled route schedules a city bus to arrive at Cal Poly at 8:54 A.M. The file entitled
Although some financial institutions do not charge fees for using ATMs, many do. A recent study found the average fee charged by banks to process an ATM transaction was $2.91. The file entitled ATM Fees contains a list of ATM fees that might be required by banks.a. Produce a relative frequency
Rolls-Royce PLC provides forecasts for the business jet market and covers the regional and major aircraft markets. In a recent release, Rolls-Royce indicated that in both North America and Europe the number of delayed departures has declined since a peak in 1999/2000. This is partly due to a
A corrugated container company is testing whether a computer decision model will improve the uptime of its box production line. Currently, knives used in the production process are checked manually and replaced when the operator believes the knives are dull. Knives are expensive, so operators are
The average amount spent on electronics each year in U.S. households is $1,250 according to an article in USA Today (Michelle Kessler, “Gadget Makers Make Mad Dash to Market,” January 4, 2006). Assume that the amount spent on electronics each year has an exponential distribution.a. Calculate
A delicatessen located in the heart of the business district of a large city serves a variety of customers.The delicatessen is open 24 hours a day every day of the week. In an effort to speed up take-out orders, the deli accepts orders by fax. If, on the average, 20 orders are received by fax every
The time to failure for a power supply unit used in a particular brand of personal computer (PC) is thought to be exponentially distributed with a mean of 4,000 hours as per the contract between the vendor and the PC maker. The PC manufacturer has just had a warranty return from a customer who had
The time required to prepare a dry cappuccino using whole milk at the Daily Grind Coffee House is uniformly distributed between 25 and 35 seconds.Assuming a customer has just ordered a whole-milk dry cappuccino,a. What is the probability that the preparation time will be more than 29 seconds?b.
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