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Business Statistics A Decision Making Approach 8th Edition David F. Groebner, Patrick W. Shannon, Phillip C. Fry, Kent D. Smith - Solutions
The quality manager for a major automobile manufacturer is interested in estimating the mean number of paint defects in cars produced by the company. She wishes to have her estimate be within 0.10 of the true mean and wants 98% confidence in the estimate. The file called CarPaint contains data from
The Future-Vision Company is considering applying for a franchise to market satellite television dish systems in a Florida market area. As part of the company’s research into this opportunity, staff in the new acquisitions department conducted a survey of 548 homes selected at random in the
On its first day on the stock market, the Chinese Internet search engine, Baidu, increased its share price from $27.00 to $122.54, an increase of 354%. This was larger than any other Chinese initial public offering(IPO) and the second biggest for a foreign IPO.However, of the nine other biggest
In an article entitled “Airport Screeners’ Strains, Sprains Highest among Workers,” Thomas Frank reported that the injury rate for airport screeners was 29%, far exceeding the 4.5% injury rate for the rest of the federal workforce. The 48,000 full- and part-time screeners were reported to
A random sample of 25 sport utility vehicles (SUVs)of the same year and model revealed the following miles per gallon (mpg) values:12.4 13.0 12.6 12.1 13.1 13.0 12.0 13.1 11.4 12.6 9.5 13.25 12.4 10.7 11.7 10.0 14.0 10.9 9.9 10.2 11.0 11.9 9.9 12.0 11.3 Assume that the population for mpg for this
Arco Manufacturing makes electronic pagers. As part of its quality efforts, the company wishes to estimate the mean number of days the pager is used before repair is needed. A pilot sample of 40 pagers indicates a sample standard deviation of 200 days. The company wishes its estimate to have a
According to an investigative reporter (Jim Drinkard,“Legislators Want to Ground ‘Fact-Finding’ Trips,”USA Today, January 19, 2006), members of Congress are coming under scrutiny for “fact-finding” trips.Since 2000, members of Congress have made 6,666 trips paid for by private
A random sample of 441 shoppers revealed that 76% made at least one purchase at a discount store last month.a. Based on this sample information, what is the 90%confidence interval for the population proportion of shoppers who made at least one discount store purchase last month?b. The city of San
Examine the equation for the margin of error when estimating a population meanIndicate the effect on the margin of error resulting from an increase in each of the following items:a. confidence levelb. z-valuec. standard deviationd. sample sizee. standard error e= e 2- n
An insurance company in Iowa recently conducted a survey of its automobile policy customers to estimate the mean miles these customers commute to work each day. The result based on a random sample of 300 policyholders indicated the population mean was between 3.5 and 6.7 miles. This interval
When we need to estimate the population mean, and the population standard deviation is unknown, we are hit with a “double whammy” when it comes to the margin of error. Explain what the “double whammy”is and why it occurs. (Hint: Consider the sources of variation in the margin of error.)
Explain why the critical value for a given confidence level when the population variance is not known is always greater than the critical value for the same confidence level when the population variance is known.
The Emerging Workforce Study conducted by Harris Interactive on behalf of Spherion, a leader in providing value-added staffing, recruiting, and workforce solutions, utilized a random sample of 502 senior human resources executives. The survey asked which methods the executives felt led them to find
A survey by Frank N. Magid Associates Inc. concluded that men, of any age, are twice as likely as women to play console video games. The survey was based on a sample of men and women ages 12 and older. A file entitled Gameboys contains responses that would result in the findings obtained by Magid
Neverslip, Inc., produces belts for industrial use. As part of its continuous process improvement program, Neverslip has decided to monitor on-time shipments of its products. Suppose a random sample of 140 shipments was taken from shipping records for the last quarter and the shipment was recorded
A study by the Investment Company Institute (ICI), which randomly surveyed 3,500 households and drew on information from the Internal Revenue Service, found that 72% of households have conducted at least one IRA rollover from an employer-sponsored retirement plan
According to the Employee Benefit Research Institute(www.ebri.org) 34% of workers between the ages of 35 and 44 owned a 401(k)-type retirement plan. Suppose a recent survey was conducted by the Atlanta Chamber of Commerce to determine the participation rate of 35-to 44-year-old working adults in
A report released by the College Board asserted the percentage of students who took and passed Advanced Placement (AP) courses in all subjects has increased in every state and the District of Columbia since 2000.Among public school students, 14.1% earned a passing grade on at least one AP exam, the
The MainStay Investments of New York Life Investment Management survey of respondents between the ages of 26 to 82 indicated that 66% of seniors, 61%of baby boomers, and 58% of Generation X expect IRAs to be their primary source of income in retirement.The margin of error was given as 5 percentage
A survey of 777 teenagers between the ages of 13 and 18 conducted by JA Worldwide/Deloitte & Touche USA LLP found that 69% agree that people who practice good business ethics are more successful than those who do not.a. Calculate the 90% confidence interval estimate for the true population
A multinational corporation employing several thousand workers at its campus in a large city in the southwestern United States would like to estimate the proportion of its employees who commute to work by any means other than an automobile. The company hopes to use the information to develop a
An Associated Press article written by Rukmini Callimachi pointed out that Nike, the world’s largest maker of athletic shoes, has started to feature female models who are not the traditional rail-thin women who have graced billboards and magazine covers for the last 20–25 years. These new
Suppose the Akron Chamber of Commerce has decided to conduct a survey to estimate the proportion of adults between the ages of 25 and 35 living in the metropolitan area who have a college degree in a high-technology field. The chamber hopes to use the survey’s results to attract more
Most major airlines allow passengers to carry two pieces of luggage (of a certain maximum size) onto the plane. However, their studies show that the more carry-on baggage passengers have, the longer it takes to unload and load passengers. One regional airline is considering changing its policy to
The television landscape has certainly been changing in recent years as satellite and cable television providers compete for old-line television networks’viewers. In fact, prior to 2005, the networks had lost viewers in the 18–49 age group for over 10 consecutive years, according to a May 2005
A survey of 499 women for the American Orthopedic Foot and Ankle Society revealed that 38% wear flats to work.a. Use this sample information to develop a 99%confidence interval for the population proportion of women who wear flats to work.b. Suppose the society also wishes to estimate the
As the automobile accident rate increases, insurers are forced to increase their premium rates. Companies such as Allstate have recently been running a campaign they hope will result in fewer accidents by their policyholders. For each six-month period that a customer goes without an accident,
A random sample of 40 television viewers was asked if they had watched the current week’s Lost episode. The following data represent their responses:no no no yes no no no yes no yes no no no yes no no no no yes no yes no no no no yes no no no no no no no no no no no no no noa. Calculate the
A random sample of 200 items reveals that 144 of the items have the attribute of interest.a. What is the point estimate for the population proportion for all items having this attribute?b. Use the information from the random sample to develop a 95% confidence interval estimate for the population
A random sample of size 150 taken from a population yields a proportion equal to 0.35.a. Determine if the sample size is large enough so that the sampling distribution can be approximated by a normal distribution.b. Construct a 90% confidence interval for the population proportion.c. Interpret the
A magazine company is planning to survey customers to determine the proportion who will renew their subscription for the coming year. The magazine wants to estimate the population proportion with 95%confidence and a margin of error equal to 0.02.What sample size is required?
At issue is the proportion of people in a particular county who do not have health care insurance coverage.A simple random sample of 240 people was asked if they have insurance coverage, and 66 replied that they did not have coverage. Based on these sample data, determine the 95% confidence
A decision maker is interested in estimating a population proportion. A sample of size n 150 yields 115 successes. Based on these sample data, construct a 90% confidence interval estimate for the true population proportion.
A pilot sample of 75 items was taken, and the number of items with the attribute of interest was found to be 15.How many more items must be sampled to construct a 99% confidence interval estimate for p with a 0.025 margin of error?
Compute the 90% confidence interval estimate for the population proportion, p, based on a sample size of 100 when the sample proportion, p, is equal to 0.40.
Phone Solutions, Inc., specializes in providing call center services for companies that wish to outsource their call center activities. There are two main ways that Phone Solutions has historically billed its clients:by the call or by the minute. Phone Solutions is currently negotiating with a new
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
Suppose a random sample of 137 households in Detroit was selected to determine the average annual household spending on food at home for Detroit residents. The sample results are contained in the file Detroit Eats.a. Using the sample standard deviation as an estimate for the population standard
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
A regional chain of fast-food restaurants would like to estimate the mean time required to serve its drive-thru customers. Because speed of service is a critical factor in the success of its restaurants, the chain wants to have as accurate an estimate of the mean service time as possible.a. If the
Business Week reports that film production companies are gravitating toward Eastern Europe. Studios there have a reputation of skilled technical work at a relatively low cost. But Bulgaria is even cheaper, with costs below those of Hollywood. As an example, weekly soundstage rental prices are
The Federal Communications Commission released a report (Leslie Cauley, USA Today, “Study: A la Carte Cable Would Be Cheaper,” February 10, 2006) refuting an earlier report released in 2004 by the Federal Communications Commission (FCC) under the prior chairman, Michael Powell. The 2006 report
The Longmont Computer Leasing Company leases computers and peripherals like laser printers. The printers have a counter that keeps track of the number of pages printed. The company wishes to estimate the mean number of pages that will be printed in a month on its leased printers. The plan is to
An Associated Press article by Eileen Alt Powell discussed the changes that banks are making to the way they calculate the minimum payment due on credit card balances. The changes are being pushed by federal regulators. In the past, minimum payments were set at about 2% of the outstanding balance.
The Northwest Pacific Phone Company wishes to estimate the average number of minutes its customers spend on long-distance calls per month. The company wants the estimate made with 99% confidence and a margin of error of no more than 5 minutes.a. A previous study indicated that the standard
With the high cost of fuel and intense competition, the major airline companies have had a very difficult time financially in recent years. Many carriers are now charging for checked bags. One carrier is considering charging a two-tiered rate based on the weight of checked bags. Before deciding at
A public policy research group is conducting a study of health care plans and would like to estimate the average dollars contributed annually to health savings accounts by participating employees. A pilot study conducted a few months earlier indicated that the standard deviation of annual
A production process that fills 12-ounce cereal boxes is known to have a population standard deviation of 0.009 ounces. If a consumer protection agency would like to estimate the mean fill, in ounces, for 12-ounce cereal boxes with a confidence level of 92% and a margin of error of 0.001, what size
A decision maker is interested in estimating the mean of a population based on a random sample. She wants the confidence level to be 90% and the margin of error to be 0.30. She does not know what the population standard deviation is, so she has selected the following pilot sample:8.80 4.89 10.98
Calculate the smallest sample size required to estimate the population mean under the following specifications:a. confidence level 95%, s 16, and e 4b. confidence level 90%, s 23, and e 0.5c. confidence level 99%, s 0.5, and e 1d. confidence level 98%, s 1.5, and e 0.2e. confidence
Determine the smallest sample size required to estimate the population mean under the following specifications:a. e 2.4, confidence level 80%, data between 50 and 150b. e 2.4, confidence level 90%, data between 50 and 150c. e 1.2, confidence level 90%, data between 50 and 150d. e 1.2
Suppose a study estimated the population mean for a variable of interest using a 99% confidence interval.If the width of the estimated confidence interval (the difference between the upper limit and the lower limit)is 600 and the sample size used in estimating the mean is 1,000, what is the
A sample size must be determined for estimating a population mean given that the confidence level is 90%and the desired margin of error is 0.30. The largest value in the population is thought to be 15 and the smallest value is thought to be 5.a. Calculate the sample size required to estimate the
A manager wishes to estimate a population mean using a 95% confidence interval estimate that has a margin of error of 44.0. If the population standard deviation is thought to be 680, what is the required sample size?
An advertising company wishes to estimate the mean household income for all single working professionals who own a foreign automobile. If the advertising company wants a 90% confidence interval estimate with a margin of error of $2,500, what sample size is needed if the population standard
What sample size is needed to estimate a population mean within 50 of the true mean value using a confidence level of 95%, if the true population variance is known to be 122,500?
The per capita consumption of chicken has risen from 28 pounds in 1960 to 90.6 pounds in 2007, according to the U.S. Department of Agriculture. That constitutes an average increase of approximately 1.33 pounds per capita per year. To determine if this trend has continued, in 2008 a random sample of
The Transportation Security Administration (TSA) has examined the possibility of a Registered Traveler program. This program is intended to be a way to shorten security lines for “trusted travelers.” In a study run at Orlando International Airport, 13,000 people paid an annual $80 fee to
The manager at a new tire and repair shop in Hartford, Connecticut, wants to establish guidelines for the time it should take to put new brakes on vehicles. In particular, he is interested in estimating the mean installation time for brakes for passenger cars and SUVs made by three different
The file German Coffee contains a random sample of 144 German coffee drinkers and measures the annual coffee consumption in kilograms for each sampled coffee drinker. A marketing research firm wants to use this information to develop an advertising campaign to increase German coffee consumption.a.
One of the reasons for multiple car accidents on highways is thought to be poor visibility. Recently, the National Transportation Agency (NTA) of the federal government sponsored a study of one rural section of highway in Idaho that had been the scene of several multiple car accidents. Two
Suppose a study of 196 randomly sampled privately insured adults with incomes over 200% of the current poverty level is to be used to measure out-of-pocket medical expenses for prescription drugs for this income class. The sample data are in the file Drug Expenses.a. Based on the sample data,
The concession managers for the Arkansas Travelers(a minor league baseball team located in Little Rock)are interested in estimating the average amount spent on food by fans attending the team’s Friday night home games. Suppose a random sample of 36 receipts for food orders was taken from last
Nielsen Media Research reported that the average American home watched more television in 2007 than in any previous season. From September 2006 to September 2007 (the official start and end of television season in the United States), the average time spent by U.S. households tuned into television
A regional U.S. commercial bank issues both Visa credit cards and MasterCard credit cards. As a part of its annual review of the profitability of each type of credit card, the bank randomly samples 36 customers to measure the average annual charges per card. It has completed its analysis of the
In a study conducted by American Express, corporate clients were surveyed to determine the extent to which hotel room rates quoted by central reservation systems differ from the rates negotiated by the companies. The study found that the mean overcharge by hotels was$11.35 per night. Suppose a
XtraNet, an Internet service provider (ISP), has experienced rapid growth in the past five years. As a part of its marketing strategy, XtraNet promises fast connections and dependable service. To achieve its objectives, XtraNet constantly evaluates the capacity of its servers. One component of its
According to USA Today, customers are not settling for automobiles straight off the production lines. As an example, those who purchase a $355,000 Rolls-Royce typically add $25,000 in accessories. One of the affordable automobiles to receive additions is BMW’s Mini Cooper. A sample of 179 recent
Even before the record gas prices during the summer of 2008, an article written by Will Lester of the Associated Press reported on a poll in which 80% of those surveyed say that Americans who currently own a SUV (sport utility vehicle) should switch to a more fuel-efficient vehicle to ease
The BelSante Company operates retail pharmacies in 10 Eastern states. Recently, the company’s internal audit department selected a random sample of 300 prescriptions issued throughout the system. The objective of the sampling was to estimate the average dollar value of all prescriptions issued by
Allante Pizza delivers pizzas throughout its local market area at no charge to the customer. However, customers often tip the driver. The owner is interested in estimating the mean tip income per delivery. To do this, she has selected a simple random sample of 12 deliveries and has recorded the
A random sample was selected from a population having a normal distribution. Calculate a 90%confidence interval estimate for m for each of the following situations:a. x 134, n 10, s 3.1b. x 3,744, n 120, s 8.2c. x 40.5, n 9, s 2.9d. x 585.9, x2 15,472.37, n 27 (Hint:
A random sample of n 9 values taken from a normally distributed population with a population variance of 25 resulted in the following sample values:53 46 55 45 44 52 46 60 49 Use the sample values to construct a 90% confidence interval estimate for the population mean.
A random sample of n 12 values taken from a normally distributed population resulted in the following sample values:107 109 99 91 103 105 105 94 107 94 97 113 Use the sample information to construct a 95%confidence interval estimate for the population mean.
A random sample of size 20 yields and s2 1.45. Calculate a confidence interval for the population mean whose confidence level is as follows:a. 0.99b. 0.98c. 0.95d. 0.90e. 0.80f. What assumptions were necessary to establish the validity of the confidence intervals calculated in parts a through e?
The following sample data have been collected based on a simple random sample from a normally distributed population:2 8 0 2 3 5 3 1 4 2a. Compute a 90% confidence interval estimate for the population mean.b. Show what the impact would be if the confidence level is increased to 95%. Discuss why
Determine the margin of error for a confidence interval estimate for the population mean of a normal distribution given the following information:a. confidence level 0.98, n 13, s 15.68b. confidence level 0.99, n 25, s 3.47c. confidence level 0.98, standard error 2.356
Determine the 90% confidence interval estimate for the population mean of a normal distribution given n 100, s 121, and x 1,200.
Construct a 98% confidence interval estimate for the population mean given the following values:s 20 n 50
Construct a 95% confidence interval estimate for the population mean given the following values:s 55 n 250
Construct a 90% confidence interval estimate for the population mean given the following values:x 70 s 15 n 65
Assuming the population of interest is approximately normally distributed, construct a 95% confidence interval estimate for the population mean given the following values:s 4.2 n 13
The data file Trucks contains data on a sample of 200 trucks that were weighed on two scales. The WIM(weigh-in-motion) scale weighs the trucks as they drive down the highway. The POE scale weighs the trucks while they are stopped at the port-of-entry station. The maker of the WIM scale believes
Covercraft manufactures covers to protect automobile interiors and finishes. Its Block-It 200 Series fabric has a limited two-year warranty. Periodic testing is done to determine if the warranty policy should be changed.One such study may have examined those covers that became unserviceable while
Analysis by American Express found high fuel prices and airline losses resulted in increasing fares for business travelers. The average fare paid for business travel rose during the second quarter of 2008 to $260, up from $236 in the second quarter of 2007. However, fuel prices started declining in
The file High Desert Banking contains information regarding consumer, real estate, and small commercial loans made last year by the bank. Use your computer software to do the following:a. Construct a frequency histogram using eight classes for dollar value of loans made last year. Does the
USA Today reported the results of a survey conducted by HarrisInteractive to determine the percentage of adults who use a computer to access the Internet (from work, home, or other locations). The newspaper indicated the survey revealed that 74% of adults use a computer to access the Internet. The
The Patients file contains information for a random sample of geriatric patients. During a meeting, one hospital administrator indicated that 70% of the geriatric patients are males.a. Based on the data contained in the Patients file, would you conclude the administrator’s assertion concerning
A major video rental chain recently decided to allow customers to rent movies for three nights rather than one. The marketing team that made this decision reasoned that at least 70% of the customers would return the movie by the second night anyway. A sample of 500 customers found 68% returned the
Dave Wilson, president of the Graduate Management Admissions Council (GMAC), reported the results of a recent GMAC survey of 5,829 MBA graduates. The average annual base salary increased to $88,626. The high annual base salary was set in 2001 at approximately $92,500 after adjusting for
MPC makes personal computers that are then sold directly over the phone and over the Internet. One of the most critical factors in the success of PC makers is how fast they can turn their inventory of parts. Faster inventory turns mean lower average inventory cost.Recently at a meeting, the vice
The Bendbo Corporation has a total of 300 employees in its two manufacturing locations and the headquarters office. A study conducted five years ago showed the average commuting distance to work for Bendbo employees was 6.2 miles with a standard deviation of 3 miles. Recently, a follow-up study
Frank N. Magid Associates conducted a telephone survey of 1,109 consumers to obtain the number of cell phones in houses. The survey obtained the following results:Cell phones 0 1 2 3 4 Percent 19 26 33 13 9a. Determine the sample proportion of households that own two or more cell phones.b. If the
Frito-Lay is one of the world’s largest makers of snack foods. One of the final steps in making products like Cheetos and Doritos is to package the product in sacks or other containers. Suppose Frito-Lay managers set the fill volume on Cheetos to an average volume of 16 ounces. The filling
The time it takes a mechanic to tune an engine is known to be normally distributed with a mean of 45 minutes and a standard deviation of 14 minutes.a. Determine the mean and standard error of a sampling distribution for a sample size of 20 tune-ups. Draw a picture of the sampling distribution.b.
A year-old study found that the service time for all drive-thru customers at the Stardust Coffee Shop is uniformly distributed between 3 and 6 minutes.Assuming the service time distribution has not changed, a random sample of 49 customers is taken and the service time for each is recorded.a.
Suppose at your university some administrators believe that the proportion of students preferring to take classes at night exceeds 0.30. The president is skeptical and so has an assistant take a simple random sample of 200 students. Of these, 66 indicate that they prefer night classes. What is the
An analysis performed by Hewitt Associates indicated the median amount saved in a 401(k) plan by people 50 to 59 years old was $53,440. The average saved is$115,260 for that age group. Assume the standard deviation is $75,000.a. Examining these statements, would it be possible to use a normal
When its ovens are working properly, the time required to bake fruit pies at Ellardo Bakeries is normally distributed with a mean of 45 minutes and a standard deviation of 5 minutes. Yesterday, a random sample of 16 pies had an average baking time of 50 minutes.a. If Ellardo’s ovens are working
The Baily Hill Bicycle Shop sells mountain bikes and offers a maintenance program to its customers. The manager has found the average repair bill during the maintenance program’s first year to be $15.30 with a standard deviation of $7.00.a. What is the probability a random sample of 40 customers
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