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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
Given the following null and alternative hypothesesand the following sample informationa. If a 0.05, state the decision rule for the hypothesis.b. Test the hypothesis and indicate whether the null hypothesis should be rejected. H>
The Fillmore Institute has established a service designed to help charities increase the amount of money they collect from their direct-mail solicitations.Its consulting is aimed at increasing the mean dollar amount returned from each giver and also at reducing the variation in amount contributed
Canidae Corporation, based in San Luis Obispo, California, is a producer of pet food. One of its products is Felidae cat food. The Chicken and Rice Cat and Kitten Formula is a dry cat food that comes in various sizes. Canidae guarantees that 32% of this cat food is crude protein. In the 6.6-pound
Due to the sharp rise in oil prices, the cost of heating a home rose sharply in the winter of 2008. The average cost was $1,044, which was an increase of 33% above that in 2007. In addition to concern over the increase in average heating costs was the possibility of a sharp increase in the
The U.S. Bureau of Labor Statistics’ most current figures indicate the average wage for construction workers was about $19.50 an hour. Its survey suggests that construction wages can vary widely. Hartford, Connecticut, wages are approximately 38% larger and Brownsville, Texas, wages are about 30%
A corporation makes CV joints for automobiles. An integral part of CV joints is the bearings that allow the joints to rotate differentially. One application utilizes six bearings in a CV joint that have an average diameter of 2.5 centimeters. The consistency of the diameters is vital to the
A software design firm has recently developed a prototype educational computer game for children.One of the important factors in the success of a game like this is the time it takes the child to play the game.Two factors are important: the mean time it takes to play and the variability in time
Airlines face the challenging task of keeping their planes on schedule. One key measure is the number of minutes a plane deviates from the targeted arrival time.Ideally, the measure for each arrival will be zero minutes, indicating that the plane arrived exactly on time. However, experience
The Flicks is a small, independent theater that shows foreign and limited-release films. One attraction of the Flicks is that it sells beer and wine as well as premium coffee and pastries at its snack bar. Friday and Saturday nights are the busiest nights at the Flicks, and the owners of the
The consulting firm of Winston & Associates has been retained by an electronic component assembly company in Phoenix to design and program a computer simulation model of its operations. Winston &Associates plan to construct the model using ProModel software (see www.Promodel.com). This software
In an effort to increase public acceptance of a light rail system, the manager for City Transit Services in Seattle is interested in estimating the standard deviation for the time it takes a bus to travel between the University of Washington and the downtown bus terminal. To develop an estimate for
Examine the sample obtained from a normally distributed population:5.2 10.4 5.1 2.1 4.8 15.5 10.2 8.7 2.8 4.9 4.7 13.4 15.6 14.5a. Calculate the variance.b. Calculate the probability that a randomly chosen sample would produce a sample variance at least as large as that produced in part a if the
Historical data indicate that the standard deviation of a process is 6.3. A recent sample of sizea. 28 produced a variance of 66.2. Test to determine if the variance has increased using a significance level of 0.05.b. 8 produced a variance of 9.02. Test to determine if the variance has decreased
Suppose a random sample of 22 items produces a sample standard deviation of 16.a. Use the sample results to develop a 90% confidence interval estimate for the population variance.b. Use the sample results to develop a 95% confidence interval estimate for the population variance.
Given the following null and alternative hypotheses H0: s2 50 HA: s2 50a. Test when n 12, s 9, and a 0.10. Be certain to state the decision rule.b. Test when n 19, s 6, and a 0.05. Be certain to state the decision rule.
The following sample data have been collected for the purpose of testing whether a population standard deviation is equal to 40. Conduct the appropriate hypothesis test using a 0.05.318 255 323 325 334 354 266 308 321 297 316 272 346 266 309
A manager is interested in determining if the population standard deviation has dropped below 130.Based on a sample of n 20 items selected randomly from the population, conduct the appropriate hypothesis test at a 0.05 significance level. The sample standard deviation is 105.
Given the following null and alternative hypotheses H0: s2 100 HA: s2 100a. Test when n 27, s 9, and a 0.10. Be certain to state the decision rule.b. Test when n 17, s 6, and a 0.05. Be certain to state the decision rule.
A random sample of 20 values was selected from a population, and the sample standard deviation was computed to be 360. Based on this sample result, compute a 95% confidence interval estimate for the true population standard deviation.
Vintner Mortgage Company in Chicago, Illinois, markets residential and commercial loans to customers in the region. Although the company had generally tried to avoid the “sub-prime” loan market, recently the company’s board of directors asked whether the company had experienced a difference
One of the statistics that the College Board monitors is the rising tuition at private and public four-year colleges. The tuition and fees for private and public four-year colleges for the 1980–1981 academic year in 2005 dollars were $8,180 and $1,818, respectively. The file entitled College$
As part of a study on student loan debt, a national agency that underwrites student loans is examining the differences in student loan debt for undergraduate students. One question the agency would like to address specifically is whether the mean undergraduate debt of Hispanic students graduating
Reviewers from the Oregon Evidence-Based Practice Center at the Oregon Health and Science University investigated the effectiveness of prescription drugs in assisting people to fall asleep and stay asleep. The Oregon reviewers, led by Susan Carson, M.P.H., concluded that Sonata was better than
Surprisingly, injuries such as strains and sprains are higher among airport screeners than any other federal work group. A recent study found the injury rate for airport screeners was 29%, far exceeding the 4.5%injury rate for the rest of the federal workforce.Assume the sample sizes required to
Turbo-Tax and Tax-Cut are two of the best-selling tax preparation software packages. Recently, a consumer group conducted a test to estimate the difference in themean time it would take an individual to complete his or her federal income tax using these two products. To run the test, the group
Before the unprecedented decline in home sales that started in late 2008, the National Association of Realtors profile of home buyers and sellers indicated the percentage of home buyers who are single women has more than doubled since 1981, whereas the percentages of home buyers who are single men
The Eaton Company sells breakable china through a mail-order system that has been very profitable.One of its major problems is freight damage. It insures the items at shipping, but the inconvenience to the customer when a piece gets broken can cause the customer not to place another order in the
Allstate Insurance is one of the major automobile insurance companies in the country. Recently, the western region claims manager instructed an intern in her department to develop a confidence interval estimate of the difference between the mean years that male customers have been insured by
Bach Photographs is a photography business with studios in two locations. The owner is interested in monitoring business activity closely at the two locations. Among the factors in which he is interested is whether the mean customer orders per day for the two locations are the same. A random sample
A student group at a university located in the Midwest is conducting a study to determine whether there is a difference between textbook prices for new textbooks sold by the on-campus bookstore and an Internet retailer. A random sample of 10 textbooks was taken, and the campus price and the
Examine the following information:Sample 1 Sample 2 ni 15 10 –x i 12 7 si 3 4a. Construct a 95% confidence interval for m1 m2.b. Calculate the test statistic that would be used to determine if m1 m2 The upper confidence limit.Given this, what would the result of the test be if you wish to
Explain, in nontechnical terms, why pairing observations, if possible, is often a more effective tool than taking independent samples.
Why, when dealing with two independent samples where you cannot assume the population variances are equal, should the degrees of freedom be adjusted?
USA Today notes (Mary Beth Marklein, “College Gender Gap Widens: 57% Are Women”) that there are more men than women ages 18–24 in the United States—15 million versus 14.2 million. The male/female ratio in colleges today is 42.6/57.4.However, there is a discrepancy in the percentage of males
A marketing research firm is interested in determining whether there is a difference between the proportion of households in Chicago and the proportion of households in Milwaukee who purchase groceries online. The research firm decided to randomly sample households earning over $50,000 a year in
The Boston Consulting Group released a survey of 940 executives representing 68 countries. One of the questions on the survey examined if the executives ranked innovation as the top priority for the coming year. The responses from 400 executives in the United States and 300 in Asia are given in the
As part of a nationwide study on home Internet use, researchers randomly sampled 150 urban households and 150 rural households. Among the questions asked of the sampled households was whether they used the Internet to download computer games. The survey results for this question are contained in
The American College Health Association produced the National College Health Assessment (Andy Gardiner, “Surfacing from Depression,” February 6, 2006). The assessment indicates that the percentage of U.S. college students who report having been diagnosed with depression has risen from 2000. The
Suppose a random sample of 100 U.S. companies taken in 2005 showed that 21 offered high-deductible health insurance plans to their workers. A separate random sample of 120 firms taken in 2006 showed that 30 offered high-deductible health insurance plans to their workers. Based on the sample
Suppose as part of a national study of economic competitiveness a marketing research firm randomly sampled 200 adults between the ages of 27 and 35 living in metropolitan Seattle and 180 adults between the ages of 27 and 35 living in metropolitan Minneapolis. Each adult selected in the sample was
In an article entitled “Childhood Pastimes Are Increasingly Moving Indoors,” Dennis Cauchon asserts that there have been huge declines in spontaneous outdoor activities such as bike riding, swimming, and touch football. In the article, he cites separate studies by the national Sporting Goods
Independent random samples of size 50 and 75 are selected. The sampling results in 35 and 35 successes, respectively. Test the following hypotheses:a. H0: p1 p2 0 vs. HA: p1 p2 0.Use a 0.05.b. H0: p1 p2 0 vs. HA: p1 p2 0.Use a 0.05.c. H0: p1 p2 0 vs. HA: p1 p2 0.Use a
Given the following null and alternative hypotheses H0: p1 p2 0.0 HA: p1 p2 0.0 and the following sample information Sample 1 Sample 2 n1 60 n2 80 x1 30 x2 24a. Based on a 0.02 and the sample information, what should be concluded with respect to the null and alternative
Given the following null and alternative hypotheses and level of significance H0: p1 p2 HA: p1 p2 a 0.10 together with the sample information Sample 1 Sample 2 n1 120 n2 150 x1 42 x2 57 conduct the appropriate hypothesis test using the pvalue approach. What conclusion would be reached
Given the following sample information randomly selected from two populations Sample 1 Sample 2 n1 200 n2 150 x1 40 x2 27a. Determine if the sample sizes are large enough so that the sampling distribution for the difference between the sample proportions is approximately normally
In each of the following cases, determine if the sample sizes are large enough so that the sampling distribution of the differences in the sample proportions can be approximated with a normal distribution:a. n1 15, n2 20, x1 6, and x2 16b. n1 10, n2 30, p1 0.6, and x2 19c. n1 25,
As the number of air travelers with time on their hands increases, it would seem that spending on retail purchases in airports would increase as well.A study by Airport Revenue News addressed the per person spending at selected airports for merchandise, excluding food, gifts, and news items. A file
A treadmill manufacturer has developed a new machine with softer tread and better fans than its current model. The manufacturer believes these new features will enable runners to run for longer times than they can on its current machines. To determine whether the desired result is achieved, the
A prime factor in the economic troubles that started in 2008 was the end of the “housing bubble.” The file entitled House contains data for a sample showing the average and median housing prices for different areas in the country in November 2007 and November 2008.Assume the data can be viewed
An article in The American Statistician (M. L. R.Ernst, et al., “Scatterplots for Unordered Pairs,”50 (1996), pp. 260–265) Reports on the difference in the measurements by two evaluators of the cardiac output of 23 patients using Doppler echocardiography. Both observers took measurements from
An article on the PureEnergySystems.com Web site written by Louis LaPoint discusses a product called Acetone. The article stated that “Acetone (CH3COCH3)is a product that can be purchased inexpensively in most locations around the world, such as in common hardware, auto parts, or drug stores.
The United Way raises money for community charity activities. Recently, in one community, the fundraising committee was concerned about whether there is a difference in the proportion of employees who give to United Way depending on whether the employer is a private business or a government agency.
Production engineers at Sinotron believe that a modified layout on its assembly lines might increase average worker productivity (measured in the number of units produced per hour). However, before the engineers are ready to install the revised layout officially across the entire firm’s
One of the advances that helped to diminish carpal tunnel syndrome is ergonomic keyboards. The ergonomic keyboards may also increase typing speed.Ten administrative assistants were chosen to type on both standard and ergonomic keyboards. The resulting word per minute typing speeds follow:Ergonomic:
Consider the following set of samples obtained from two normally distributed populations whose variances are equal:Sample 1: 11.2 11.2 7.4 8.7 8.5 13.5 4.5 11.9 Sample 2: 11.7 9.5 15.6 16.5 11.3 17.6 17.0 8.5a. Suppose that the samples were independent.Perform a test of hypothesis to determine if
The following samples are observations taken from the same elements at two different times:Unit Sample 1 Sample 2 1 15.1 4.8 2 12.3 5.7 3 14.9 6.2 4 17.5 9.4 5 18.1 2.3 6 18.4 4.7a. Assume that the populations are normally distributed and construct a 90% confidence interval for the difference in
A paired sample study has been conducted to determine whether two populations have equal means.Twenty paired samples were obtained with the following sample results:d 12.45 sd 11.0 Based on these sample data and a significance level of 0.05, what conclusion should be made about the population
The following sample data have been collected from a paired sample from two populations. The claim is that the first population mean will be at least as large as the mean of the second population. This claim will be assumed to be true unless the data strongly suggest otherwise.Sample 1 Sample 2
You are given the following results of a paireddifference test:d = 4-6 s = 0.25 n = 16a. Construct and interpret a 99% confidence interval estimate for the paired difference in mean values.b. Construct and interpret a 90% confidence interval estimate for the paired difference in mean values.
The following paired samples have been obtained from normally distributed populations. Construct a 90%confidence interval estimate for the mean paired difference between the two population means.Sample # Population 1 Population 2 1 3,693 4,635 2 3,679 4,262 3 3,921 4,293 4 4,106 4,197 5 3,808 4,536
The following dependent samples were randomly selected. Use the sample data to construct a 95%confidence interval estimate for the population mean paired difference.Sample 1 Sample 2 Sample 1 Sample 2 22 31 23 31 25 24 25 27 27 25 28 31 26 32 27 31 22 25 23 26 21 27
Airlines were severely affected by the oil price increases of 2008. Even Southwest lost money, the first time ever, during that time. Many airlines began charging for services that had previously been free, such as baggage and meals. One national airline had as an objective getting an additional $5
The Marriott Corporation operates the largest chain of hotel and motel properties in the world. The Fairfield Inn and the Residence Inn are just two of the hotel brands that Marriott owns. At a recent managers’meeting, a question was posed regarding whether the average length of stay was
A USA Today editorial addressed the growth of compensation for corporate CEOs. Quoting a study made by BusinessWeek, USA Today indicated that the pay packages for CEOs have increased almost sevenfold on average from 1994 to 2004. The file entitled CEODough contains the salaries of CEOs in 1994 and
Suppose a professional job-placement firm that monitors salaries in professional fields is interested in determining if the fluctuating price of oil and the outsourcing of computer-related jobs have had an effect on the starting salaries of chemical and electrical engineering graduates.
Although not all students have debt after graduating from college, more than half do. The College Board’s 2008 Trends in Student Aid addresses, among other topics, the difference in the average college debt accumulated by undergraduate bachelor of arts degree recipients by type of college for the
The Washington Post Weekly Edition quoted an Urban Institute study that stated that about 80% of the estimated $200 billion of federal housing subsidies consisted of tax breaks (mainly deductions for mortgage interest payments). Samples indicated that the federal housing benefits average was $8,268
Albertsons was once one of the largest grocery chains in the United States with over 1,100 grocery stores, but in the early 2000s the company began to feel the competitive pinch from companies like Wal-Mart and Costco. In January 2006, the company announced that it would be sold to SuperValu, Inc.,
Sherwin-Williams is a major paint manufacturer.Recently, the research and development (R&D)department came out with a new paint product designed to be used in areas that are particularly prone to periodic moisture and hot sun. They believe that this new paint will be superior to anything that
The marketing manager for a major retail grocery chain is wondering about the location of the stores’dairy products. She believes that the mean amount spent by customers on dairy products per visit is higher in stores where the dairy section is in the central part of the store compared with
The management of the Seaside Golf Club regularly monitors the golfers on its course for speed of play.Suppose a random sample of golfers was taken in 2005 and another random sample of golfers was selected in 2006. The results of the two samples are as follows 2005 2006 –x 1 225 –x 2 219 s1
Descent, Inc., produces a variety of climbing and mountaineering equipment. One of its products is a traditional three-strand climbing rope. An important characteristic of any climbing rope is its tensile strength. Descent produces the three-strand rope on two separate production lines: one in
Consider the following two independently chosen samples whose population variances are not equal to each other.Sample 1 Sample 2 12.1 10.5 13.4 9.5 11.7 8.2 10.7 7.8 14.0 11.1a. Using a significance level of 0.025, test the null hypothesis that m1 m2 0.b. Calculate the p-value.
Given the following null and alternative hypotheses H0: m1 m2 0 HA: m1 m2 0 and the following sample information Sample 1 Sample 2 n1 125 n2 120 s1 31 s2 38 –x 1 130 –x 2 105a. Develop the appropriate decision rule, assuming a significance level of 0.05 is to be used.b. Test
The following statistics were obtained from independent samples from populations that have normal distributions:1 2 ni 41 51 –x i 25.4 33.2 si 5.6 7.4a. Use these statistics to conduct a test of hypothesis if the alternative hypothesis is m1 m2 4. Use a significance level of 0.01.b. Determine
Given the following null and alternative hypotheses, conduct a hypothesis test using an alpha equal to 0.05.(Note: The population standard deviations are assumed to be known.)H0: m1 m2 HA: m1 m2 The sample means for the two populations are shown as follows:x–1 144 x–2 129 s1 11 s2
Given the following null and alternative hypotheses H0: m1 m2 HA: m1 m2 together with the following sample information Sample 1 Sample 2 n1 14 n2 18 –x 1 565 –x 2 578 s1 28.9 s2 26.3a. Assuming that the populations are normally distributed with equal variances, test at the 0.10
The following null and alternative hypotheses have been stated:H0: m1 m2 0 HA: m1 m2 0 Sample from Population 1 Sample from Population 2 33 29 35 46 43 42 39 39 41 46 44 47 25 33 38 50 43 39 Test the null hypothesis using an alpha level equal to 0.05.
A decision maker wishes to test the following null and alternative hypotheses using an alpha level equal to 0.05:H0: m1 m2 0 HA: m1 m2 0 The population standard deviations are assumed to be known. After collecting the sample data, the test statistic is computed to be z 1.78a. Using the
The Federal Reserve reported in its comprehensive Survey of Consumer Finances, released every three years, that the average income of families in the United States declined from 2001 to 2004. This was the first decline since 1989–1992. A sample of incomes was taken in 2001 and repeated in 2004.
Platinum Billiards, Inc., based in Jacksonville, Florida, is a retailer of billiard supplies. It stands out among billiard suppliers because of the research it does to assure its products are top-notch. One experiment was conducted to measure the speed attained by a cue ball struck by various
The owner of the A.J. Fitness Center is interested in estimating the difference in mean years that female members have been with the club compared with male members. He wishes to develop a 95% confidence interval estimate. Sample data are in the file called AJ Fitness. Assuming that the sample data
Logston Enterprises operates a variety of businesses in and around the St. Paul, Minnesota, area. Recently, the company was notified by the law firm representing several female employees that a lawsuit was going to be filed claiming that males were given preferential treatment when it came to pay
The Graduate Management Admission Council reported a shift in the job-hunting strategies among second-year masters of business administration (MBA)candidates. Even though their prospective base salary has increased from $81,900 to $93,770 from 2002 to 2005, it appears that MBA candidates are
A working paper (Mark Aguiar and Erik Hurst,“Measuring Trends in Leisure: The Allocation of Time over Five Decades,” 2006) for the Federal Reserve Bank of Boston concluded that average leisure time spent per week by women in 2003 was 33.80 hours and 37.56 hours for men. The sample standard
Wilson Construction and Concrete Company is known as a very progressive company that is willing to try new ideas to improve its products and service. One of the key factors of importance in concrete work is the time it takes for the concrete to “set up.” The company is considering a new
Two companies that manufacture batteries for electronics products have submitted their products to an independent testing agency. The agency tested 200 of each company’s batteries and recorded the length of time the batteries lasted before failure.The following results were determined:Company A
A pet food producer manufactures and then fills 25-pound bags of dog food on two different production lines located in separate cities. In an effort to determine whether differences exist between the average fill rates for the two lines, a random sample of 19 bags from line 1 and a random sample of
A credit card company operates two customer service centers: one in Boise and one in Richmond. Callers to the service centers dial a single number, and a computer program routs callers to the center having the fewest calls waiting. As part of a customer service review program, the credit card
Amax Industries operates two manufacturing facilities that specialize in doing custom manufacturing work for the semiconductor industry. The facility in Denton, Texas, is highly automated, whereas the facility in Lincoln, Nebraska, has more manual functions. For the past few months, both facilities
Two random samples were selected independently from populations having normal distributions. The following statistics were extracted from the samples:x 1 42.3 –x 2 32.4a. If s1 3 and s2 2 and the sample sizes are n1 50 and n2 50, calculate a 95% confidence interval for the difference
Construct a 95% percent confidence interval for the difference between two population means using the following sample data that have been selected from normally distributed populations with different population variances:Sample 1 Sample 2 473 386 406 379 349 359 346 395 346 438 391 328 398 401 411
Construct a 95% confidence interval estimate for the difference between two population means based on the following information:Population 1 Population 2 x _ 1 355 x _ 2 320 s1 34 s2 40 n1 50 n2 80
Construct a 90% confidence interval estimate for the difference between two population means given the following sample data selected from two normally distributed populations with equal variances:Sample 1 Sample 2 29 25 31 42 39 38 35 35 37 42 40 43 21 29 34 46 39 35
The following information is based on independent random samples taken from two normally distributed populations having equal variances:nl 24 n2 28 –x 1 130 –x 2 125 s1 19 s2 17.5 Based on the sample information, determine the 95%confidence interval estimate for the difference between
The following information is based on independent random samples taken from two normally distributed populations having equal variances:n1 15 n2 13 –x 1 50 –x 2 53 s1 5 s2 6 Based on the sample information, determine the 90%confidence interval estimate for the difference between the
TOMRA Systems ASA is a Norwegian company that manufactures reverse vending machines (RVMs). In most cases, RVMs are used in markets that have deposits on beverage containers, offering an efficient and convenient method of identifying the deposit amount of each container returned and providing a
At the annual meeting of the Golf Equipment Manufacturer’s Association, a speaker made the claim that over 30% of all golf clubs being used by nonprofessional United States Golf Association(USGA) members are “knock-offs.” These knock-offs are clubs that look very much like the more expensive
MBNA offers personal and business credit cards, loans, and savings products. It was bought by Bank of America in June 2005. One of the selling points for MBNA was its position relative to the rest of the credit card industry.MBNA’s customers’ average annual spending per active account before
The Inland Empire Food Store Company has stated in its advertising that the average shopper will save more than $5.00 per week by shopping at Inland stores.A consumer group has decided to test this assertion by sampling 50 shoppers who currently shop at other stores. It selects the customers and
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