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Complete Business Statistics 7th Edition Amir Aczel, Jayavel Sounderpandian - Solutions
According to the Wall Street Journal, the rising popularity of hedge funds and similar investment instruments has made splitting assets in cases of divorce much more difficult. If a random sample of 250 divorcing couples reveals that 53 of them have great difficulties in splitting their family
According to BusinessWeek, environmental groups are making headway on American campuses. In a survey of 570 schools, 130 were found to incorporate chapters of environmental organizations.18 Assume this is a random sample of universities and use the reported information to construct a 95% confidence
The service time in queues should not have a large variance; otherwise, the queue tends to build up. A bank regularly checks service time by its tellers to determine its variance. A random sample of 22 service times (in minutes) gives s2 = 8. Give a 95% confidence interval for the variance of
A sensitive measuring device should not have a large variance in the errors of measurements it makes. A random sample of 41 measurement errors gives s2 = 102.Give a 99% confidence interval for the variance of measurement errors.
A random sample of 60 accounts gives a sample variance of 1,228. Give a 95% confidence interval for the variance of all accounts.
In problem 6–21, give a 99% confidence interval for the variance of the number of miles that may be driven on a tire.In problem A tire manufacturer wants to estimate the average number of miles that may be driven on a tire of a certain type before the tire wears out. A random sample of 32 tires
In problem 6–25, give a 95% confidence interval for the variance of the population of billionaires’ worth in dollars.In problem The following is a random sample of the wealth, in billions of U.S. dollars, of individuals listed on the Forbes “Billionaires” list for 2007.82.1, 5.8, 7.3, 33.0,
In problem 6–26, give a 95% confidence interval for the variance of the caloric content of all 3-ounce cuts of top loin steak.In problem For advertising purposes, the Beef Industry Council needs to estimate the average caloric content of 3-ounce top loin steak cuts. A random sample of 400 pieces
In problem 6–27, give a 95% confidence interval for the variance of the transit time for all goods.In problem A transportation company wants to estimate the average length of time goods are in transit across the country. A random sample of 20 shipments gives x-bar = 2.6 days and s = 0.4 day.
What is the required sample size for determining the proportion of defective items in a production process if the proportion is to be known to within 0.05 with 90% confidence? No guess as to the value of the population proportion is available.
In problem 6-5, suppose that a 99% confidence interval is required. Compute the new interval, and compare it with the 95% confidence interval you computed in problem 6-5.In problem A real estate agent needs to estimate the average value of a residential property of a given size in a certain area.
How many test runs of the new Volvo S40 model are required for determining its average miles-per-gallon rating on the highway to within 2 miles per gallon with 95% confidence, if a guess is that the variance of the population of miles per gallon is about 100?
A company that conducts surveys of current jobs for executives wants to estimate the average salary of an executive at a given level to within $2,000 with 95% confidence. From previous surveys it is known that the variance of executive salaries is about 40,000,000. What is the minimum required
Find the minimum required sample size for estimating the average return on real estate investments to within 0.5% per year with 95% confidence. The standard deviation of returns is believed to be 2% per year.
A company believes its market share is about 14%. Find the minimum required sample size for estimating the actual market share to within 5% with 90% confidence.
Find the minimum required sample size for estimating the average number of designer shirts sold per day to within 10 units with 90% confidence if the standard deviation of the number of shirts sold per day is about 50.
Find the minimum required sample size of accounts of the Bechtel Corporation if the proportion of accounts in error is to be estimated to within 0.02 with 95% confidence. A rough guess of the proportion of accounts in error is 0.10.
Tradepoint, the electronic market set up to compete with the London Stock Exchange, is losing on average $32,000 per day. A potential long-term financial partner for Tradepoint needs a confidence interval for the actual (population) average daily loss, in order to decide whether future prospects
Landings and takeoffs at Schiphol, Holland, per month are (in 1,000s) as follows:26, 19, 27, 30, 18, 17, 21, 28, 18, 26, 19, 20, 23, 18, 25, 29, 30, 26, 24, 22, 31, 18, 30, 19Assume a random sample of months. Give a 95% confidence interval for the average monthly number of takeoffs and landings.
Thomas Stanley, who surveyed 200 millionaires in the United States for his book The Millionaire Mind, found that those in that bracket had an average net worth of $9.2 million. The sample variance was 1.3 million $. Assuming that the surveyed subjects are a random sample of U.S. millionaires, give
The Java computer language, developed by Sun Microsystems, has the advantage that its programs can run on types of hardware ranging from mainframe computers all the way down to handheld computing devices or even smart phones.A test of 100 randomly selected programmers revealed that 71 preferred
A car manufacturer wants to estimate the average miles-per-gallon highway rating for a new model. From experience with similar models, the manufacturer believes the miles-per-gallon standard deviation is 4.6. A random sample of 100 highway runs of the new model yields a sample mean of 32 miles per
According to an advertisement in Worth, in a survey of 68 multifamily office companies, the average client company had assets of $55.3 million. If this is a result of a random sample and the sample standard deviation was $21.6 million, give a 95% confidence interval for the population average asset
According to the Wall Street Journal, an average of 44 tons of carbon dioxide will be saved per year if new, more efficient lamps are used. Assume that this average is based on a random sample of 15 test runs of the new lamps and that the sample standard deviation was 18 tons. Give a 90% confidence
Finjan is a company that makes a new security product designed to protect software written in the Java programming language against hostile interference. The market for this program materialized recently when Princeton University experts showed that a hacker could write misleading applets that fool
Sony's new optical disk system prototype tested and claimed to be able to record an average of 1.2 hours of high-definition TV. Assume n = 10 trials and σ = 0.2 hour. Give a 90% confidence interval.
The average customer of the Halifax bank in Britain (of whom there are 7.6 million) received $3,600 when the institution changed from a building society to a bank. If this is based on a random sample of 500 customers with standard deviation = $800, give a 95% confidence interval for the average
Fin Aid is a new, free Web site that helps people obtain information on 180,000 college tuition aid awards. A random sample of 500 such awards revealed that 368 were granted for reasons other than financial need. They were based on the applicant's qualifications, interests, and other variables.
In May 2007, a banker was arrested and charged with insider trading after government investigators had secretly looked at a sample of nine of his many trades and found that on these trades he had made a total of $7.5 million. Compute the average earning per trade. Assume also that the sample
A small British computer-game firm, Eidos Interactive PLC, stunned the U.S.- and Japan-dominated market for computer games when it introduced Lara Croft, an Indiana Jones-like adventuress. The successful product took two years to develop. One problem was whether Lara should have a swinging
In a survey, Fortune rated companies on a 0 to 10 scale. A random sample of 10 firms and their scores is as follows. FedEx 8.94, Walt Disney 8.76, CHS 8.67, McDonald's 7.82, CVS 6.80, Safeway 6.57, Starbucks 8.09, Sysco 7.42, Staples 6.45, HNI 7.29.Construct a 95% confidence interval for the
According to a survey published in the Financial Times, 56% of executives at Britain's top 500 companies are less willing than they had been five years ago to sacrifice their family lifestyle for their career. If the survey consisted of a random sample of 40 executives, give a 95% confidence
Fifty years after the birth of duty-free shopping at international airports and border-crossing facilities, the European commission announced plans to end this form of business. A study by Cranfield University was carried out to estimate the average percentage rise in airline landing charges that
When NYSE, NASDAQ, and the British government bonds market were planning to change prices of shares and bonds from powers of 2, such as 1/2, 1/4, 1/8, 1/16, 1/32, to decimals (hence 1/32 = 0.03125), they decided to run a test. If the test run of trading rooms using the new system revealed that 80%
A survey of 5,250 business travelers worldwide conducted by OAG Business Travel Lifestyle indicated that 91% of business travelers consider legroom the most important in-flight feature. (Angle of seat recline and food service were second and third, respectively.) Give a 95% confidence interval for
Use the following random sample of suitcase prices to construct a 90% confidence interval for the average suitcase price.$285, 110, 495, 119, 450, 125, 250, 320
According to Money, 60% of men have significant balding by age 50.24 If this finding is based on a random sample of 1,000 men of age 50, give a 95% confidence interval for the population of men of 50 who show some balding.
An estimate of the average length of pins produced by an automatic lathe is wanted to within 0.002 inch with a 95% confidence level. σ is guessed to be 0.015 inch.a. What is the minimum sample size?b. If the value of σ may be anywhere between 0.010 and 0.020 inch, tabulate the minimum sample size
Wells Fargo Bank, based in San Francisco, offered the option of applying for a loan over the Internet. If a random sample of 200 test runs of the service reveal an average of 8 minutes to fill in the electronic application and standard deviation = 3 minutes, construct a 75% confidence interval for
An estimate of the percentage defective in a lot of pins supplied by a vendor is desired to within 1% with a 90% confidence level. The actual percentage defective is guessed to be 4%.a. What is the minimum sample size?b. If the actual percentage defective may be anywhere between 3% and 6%, tabulate
The lengths of pins produced by an automatic lathe are normally distributed. A random sample of 20 pins gives a sample mean of 0.992 inch and a sample standard deviation of 0.013 inch.a. Give a 95% confidence interval for the average lengths of all pins produced.b. Give a 99% confidence interval
A wine importer needs to report the average percentage of alcohol in bottles of French wine. From experience with previous kinds of wine, the importer believes the population standard deviation is 1.2%. The importer randomly samples 60 bottles of the new wine and obtains a sample mean x-bar = 9.3%.
You take a random sample of 100 pins from the lot supplied by the vendor and test them. You find 8 of them defective. What is the 95% confidence interval for percentage defective in the lot?
A statistician estimates the 90% confidence interval for the mean of a normally distributed population as 172.58 ± 3.74 at the end of a sampling experiment, assuming a known population standard deviation. What is the 95% confidence interval?
A confidence interval for a population mean is to be estimated. The population standard deviation is guessed to be anywhere from 14 to 24. The half-width B desired could be anywhere from 2 to 7.a. Tabulate the minimum sample size needed for the given ranges of σ and B.b. If the fixed cost of
A marketing manager wishes to estimate the proportion of customers who prefer a new packaging of a product to the old. He guesses that 60% of the customers would prefer the new packaging. The manager wishes to estimate the proportion to within 2% with 90% confidence. What is the minimum required
According to Money, a survey of 1,700 executives revealed that 51% of them would likely choose a different field if they could start over. Construct a 95% confidence interval for the proportion of all executives who would like to start over, assuming the sample used was random and representative of
According to Shape, on the average, 1/2 cup of edamame beans contains 6 grams of protein. If this conclusion is based on a random sample of 50 half-cups of edamames and the sample standard deviation is 3 grams, construct a 95% confidence interval for the average amount of protein in 1/2 cup of
1. What is the required minimum sample size?2. The project manager assigned to the survey is not sure about the actual proportion or about the 2% error limit. The proportion may be anywhere from 40% to 60%. Construct a table for the minimum sample size required with half-width ranging from 1% to 3%
1. What is the minimum sample size (of attempts) if the proportion is to be estimated within ± 2% with 95% confidence? What is the associated total cost?2. What is the minimum sample size if the proportion is to be estimated within ±1% with 95% confidence? What is the associated total cost?3.
A company orders bolts in bulk from a vendor. The contract specifies that a shipment of bolts will be accepted by testing the null hypothesis that the percentage defective in the shipment is not more than 3% at an α of 5% using random sampling from the shipment. The company further wishes that any
According to Money, "3 in 5 executives said they anticipate making a major career change." Suppose a random sample of 1,000 executives shows that 55% said they anticipate making a major career change. Can you reject the claim made by the magazine? What is the p-value?
Consider the use of metal detectors in airports to test people for concealed weapons. In essence, this is a form of hypothesis testing. a. What are the null and alternative hypotheses? b. What are type I and type II errors in this case? c. Which type of error is more costly? d. Based on your answer
1. To help the manufacturer get a clear picture of type I and type II error probabilities, draw a β versus α chart for sample sizes of 30, 40, 60, and 80. If β is to be at most 1% with α = 5%, which sample size among these four values is suitable?2. Calculate the exact sample size required for
For each one of the following null hypotheses, determine if it is a left-tailed, a right-tailed, or a two-tailed test. a. μ ≥ 10. b. p ≤ 0.5. c. μ is at least 100. d. μ ≤ = – 20. e. p is exactly 0.22. f. μ is at most 50. g. σ2 = 140.
The calculated z for a hypothesis test is – 1.75. What is the p-value if the test is (a) Left-tailed, (b) Right-tailed, (c) Two-tailed?
In which direction of will the p-value decrease for the null hypotheses? (a) μ ≥ 10, (b) μ ≤ 10, (c) μ = 10?
An automobile manufacturer substitutes a different engine in cars that were known to have an average miles-per-gallon rating of 31.5 on the highway. The manufacturer wants to test whether the new engine changes the miles-per-gallon rating of the automobile model. A random sample of 100 trial runs
In controlling the quality of a new drug, a dose of medicine is supposed to contain an average of 247 parts per million (ppm) of a certain chemical. If the concentration is higher than 247 ppm, the drug may cause some side effects; and if the concentration is below 247 ppm, the drug may be
The Boston Transit Authority wants to determine whether there is any need for changes in the frequency of service over certain bus routes. The transit authority needs to know whether the frequency of service should increase, decrease, or remain the same.The transit authority determined that if the
Many recent changes have affected the real estate market. A study was undertaken to determine customer satisfaction from real estate deals. Suppose that before the changes, the average customer satisfaction rating, on a scale of 0 to 100, was 77. A survey questionnaire was sent to a random sample
According to Money, the average appreciation, in percent, for stocks has been 4.3% for the five-year period ending in May 2007. An analyst tests this claim by looking at a random sample of 50 stocks and finds a sample mean of 3.8% and a sample standard deviation of 1.1%. Using α = 0.05, does the
A certain commodity is known to have a price that is stable through time and does not change according to any known trend. Price, however, does change from day to day in a random fashion. If the price is at a certain level one day, it is as likely to be at any level the next day within some
Average total daily sales at a small food store are known to be $452.80. The store's management recently implemented some changes in displays of goods, order within aisles, and other changes, and it now wants to know whether average sales volume has changed. A random sample of 12 days shows x-bar =
New software companies that create programs for World Wide Web applications believe that average staff age at these companies is 27. To test this two-tailed hypothesis, a random sample is collected:41, 18, 25, 36, 26, 35, 24, 30, 28, 19, 22, 22, 26, 23, 24, 31, 22, 22, 23, 26, 27, 26, 29, 28, 23,
A study was undertaken to evaluate how stocks are affected by being listed in the Standard & Poor's 500 Index. The aim of the study was to assess average excess returns for these stocks, above returns on the market as a whole. The average excess return on any stock is zero because the "average"
A new chemical process is introduced by Duracell in the production of lithium-ion batteries. For batteries produced by the old process, the average life of a battery is 102.5 hours. To determine whether the new process affects the average life of the batteries, the manufacturer collects a random
Average soap consumption in a certain country is believed to be 2.5 bars per person per month. The standard deviation of the population is known to be σ = 0.8. While the standard deviation is not believed to have changed (and this may be substantiated by several studies), the mean consumption may
According to Money, which not only looked at stocks (as in problem 7-20) but also compared them with real estate, the average appreciation for all real estate sold in the five years ending May 2007 was 12.4% per year. To test this claim, an analyst looks at a random sample of 100 real estate deals
Suppose that the Goodyear Tire Company has historically held 42% of the market for automobile tires in the United States. Recent changes in company operations, especially its diversification to other areas of business, as well as changes in competing firms' operations, prompt the firm to test the
The manufacturer of electronic components needs to inform its buyers of the proportion of defective components in its shipments. The company has been stating that the percentage of defectives is 12%. The company wants to test whether the proportion of all components that are defective is as
According to BusinessWeek, the average market value of a biotech company is less than $250 million. Suppose that this indeed is the alternative hypothesis you want to prove. A sample of 30 firms reveals an average of $235 million and a standard deviation of $85 million. Conduct the test at α =
A company's market share is very sensitive to both its level of advertising and the levels of its competitors' advertising. A firm known to have a 56% market share wants to test whether this value is still valid in view of recent advertising campaigns of its competitors and its own increased level
According to a financial planner, individuals should in theory save 7% to 10% of their income over their working life, if they desire a reasonably comfortable retirement. An agency wants to test whether this actually happens with people in the United States, suspecting the overall savings rate may
The theory of finance allows for the computation of "excess" returns, either above or below the current stock market average. An analyst wants to determine whether stocks in a certain industry group earn either above or below the market average at a certain time period. The null hypothesis is that
According to Fortune, on February 27, 2007, the average stock in all U.S. exchanges fell by 3.3%. If a random sample of 120 stocks reveals a drop of 2.8% on that day and a standard deviation of 1.7%, are there grounds to reject the magazine's claim?
According to Money, the average amount of money that a typical person in the United States would need to make him or her feel rich is $1.5 million. A researcher wants to test this claim. A random sample of 100 people in the United States reveals that their mean "amount to feel rich" is $2.3 million
The U.S. Department of Commerce estimates that 17% of all automobiles on the road in the United States at a certain time are made in Japan. An organization that wants to limit imports believes that the proportion of Japanese cars on the road during the period in question is higher than 17% and
Airplane tires are sensitive to the heat produced when the plane taxis along runways. A certain type of airplane tire used by Boeing is guaranteed to perform well at temperatures as high as 125°F. From time to time, Boeing performs quality control checks to determine whether the average maximum
An advertisement for Qualcomm appearing in various business publications in fall 2003 said: "The average lunch meeting starts seven minutes late." A research firm tested this claim to see whether it is true. Using a random sample of 100 business meetings, the researchers found that the average
A study of top executives' midlife crises indicates that 45% of all top executives suffer from some form of mental crisis in the years following corporate success. An executive who had undergone a midlife crisis opened a clinic providing counseling for top executives in the hope of reducing the
The unemployment rate in Britain during a certain period was believed to have been 11%. At the end of the period in question, the government embarked on a series of projects to reduce unemployment. The government was interested in determining whether the average unemployment rate in the country had
Certain eggs are stated to have reduced cholesterol content, with an average of only 2.5% cholesterol. A concerned health group wants to test whether the claim is true. The group believes that more cholesterol may be found, on the average, in the eggs. A random sample of 100 eggs reveals a sample
An ad for flights to Palm Springs, California, claims that "the average temperature (in Fahrenheit) on Christmas Day in Palm Springs is 56º." Suppose you think this ad exaggerates the temperature upwards, and you look at a random sample of 30 Christmas days and find an average of 50º and standard
An article in Active Trader claims that using the Adaptive Renko trading system seems to give a 75% chance of beating the market. Suppose that in a random simulation of 100 trades using this system, the trading rule beat the market only 61 times. Conduct the test at the 0.05 level of significance.
Several U.S. airlines carry passengers from the United States to countries in the Pacific region, and the competition in these flight routes is keen. One of the leverage factors for United Airlines in Pacific routes is that, whereas most other airlines fly to Pacific destinations two or three times
An advertisement for the Audi TT model lists the following performance specifications: standing start, 0-50 miles per hour in an average of 5.28 seconds; braking, 60 miles per hour to 0 in 3.10 seconds on the average. An independent testing service hired by a competing manufacturer of
Borg-Warner manufactures hydroelectric miniturbines that generate low-cost, clean electric power from the energy in small rivers and streams. One of the models was known to produce an average of 25.2 kilowatts of electricity. Recently the model's design was improved, and the company wanted to test
Recent near misses in the air, as well as several fatal accidents, have brought air traffic controllers under close scrutiny. As a result of a high-level inquiry into the accuracy of speed and distance determinations through radar sightings of airplanes, a statistical test was proposed to check the
According to the New York Times, the Martha Stewart Living Omni media Company concentrates mostly on food. An analyst wants to disprove a claim that 60% of the company's public statements have been related to food products in favor of a left-tailed alternative. A random sample of 60 public
According to the Wall Street Journal, the average American jockey makes only $25,000 a year. Suppose you try to disprove this claim against a right-tailed alternative and your random sample of 100 U.S. jockeys gives you a sample mean of $45,600 and sample standard deviation of $20,000. What is your
A large manufacturing firm believes that its market share is 45%. From time to time, a statistical hypothesis test is carried out to check whether the assertion is true. The test consists of gathering a random sample of 500 products sold nationally and finding what percentage of the sample
The engine of the Volvo model S70 T-5 is stated to provide 246 horsepower.To test this claim, believing it is too high, a competitor runs the engine n = 60 times, randomly chosen, and gets a sample mean of 239 horsepower and standard deviation of 20 horsepower. Conduct the test, using α = 0.01.
According to BusinessWeek, the Standard & Poor's 500 Index posted an average gain of 13% for 2006.12 If a random sample of 50 stocks from this index reveals an average gain of 11% and standard deviation of 6%, can you reject the magazine's claim in a two-tailed test? What is your p-value?
A recent marketing and promotion campaign by Charles of the Ritz more than doubled the sales of the suntan lotion Bain de Soleil, which has become the nation's number 2 suntan product. At the end of the promotional campaign, the company wanted to test the hypothesis that the market share of its
Efforts are under way to make the U.S. automobile industry more efficient and competitive so that it will be able to survive intense competition from foreign automakers. An industry analyst is quoted as saying, "GM is sized for 60% of the market, and they only have 43%." General Motors needs to
According to Money, the average house owner stays with the property for 6 years. Suppose that a random sample of 120 house owners reveals that the average ownership period until the property is sold was 7.2 years and the standard deviation was 3.5 years. Conduct a two-tailed hypothesis test using
Before a beach is declared safe for swimming, a test of the bacteria count in the water is conducted with the null and alternative hypotheses formulated as H0: Bacteria count is less than or equal to the specified upper limit for safety H1: Bacteria count is more than the specified upper limit
The p-value obtained in a hypothesis test for population mean is 8%. Select the most precise statement about what it implies. Explain why the other statements are not precise, or are false. a. If H0 is rejected based on the evidence that has been obtained, the probability of type I error would be
Explain the difference between the p-value and the significance level α.
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