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Complete Business Statistics 7th Edition Amir Aczel, Jayavel Sounderpandian - Solutions

A company supplies pins in bulk to a customer. The company uses an automatic lathe to produce the pins. Due to many causes-vibrations, temperature, wear and tear, and the like-the lengths of the pins made by the machine are normally distributed with a mean of 1.012 inches and a standard deviation
A company sells precision grinding machines to four customers in four different countries. It has just signed a contract to sell, two months from now, a batch of these machines to each customer. The following table shows the number of machines (batch quantity) to be delivered to the four customers.
Suppose you need to sample the concentration of a chemical in a production process that goes on continuously 24 hours per day, 7 days per week. You need to generate a random sample of six observations of the process over a period of one week. Use a computer, a calculator, or a random number table
If the population mean is 1,247, the population variance is 10,000, and the sample size is 100, what is the probability that x̄ will be less than 1,230?
When sampling is from a population with standard deviation σ = 55, using a sample of size n = 150, what is the probability that will be at least 8 units away from the population mean µ?
An auditor selected a random sample of 12 accounts from all accounts receivable of a given firm. The amounts of the accounts, in dollars, are as follows: 87.50, 123.10, 45.30, 52.22, 213.00, 155.00, 39.00, 76.05, 49.80, 99.99, 132.00, 102.11. Compute an estimate of the mean amount of all accounts
The Colosseum, once the most popular monument in Rome, dates from about AD 70. Since then, earthquakes have caused considerable damage to the huge structure, and engineers are currently trying to make sure the building will survive future shocks. The Colosseum can be divided into several thousand
According to Money, in the year prior to March 2007, the average return for firms of the S&P 500 was 13.1%. Assume that the standard deviation of returns was 1.2%. If a random sample of 36 companies in the S&P 500 is selected, what is the probability that their average return for this
An economist wishes to estimate the average family income in a certain population. The population standard deviation is known to be $4,500, and the economist uses a random sample of size n = 225. What is the probability that the sample mean will fall within $800 of the population mean?
When sampling is done for the proportion of defective items in a large shipment, where the population proportion is 0.18 and the sample size is 200, what is the probability that the sample proportion will be at least 0.20?
A study of the investment industry claims that 58% of all mutual funds outperformed the stock market as a whole last year. An analyst wants to test this claim and obtains a random sample of 250 mutual funds. The analyst finds that only 123 of the funds outperformed the market during the year.
According to a recent article in Worth, the average price of a house on Marco Island, Florida, is $2.6 million. Assume that the standard deviation of the prices is $400,000. A random sample of 75 houses is taken and the average price is computed.What is the probability that the sample mean exceeds
It has been suggested that an investment portfolio selected randomly by throwing darts at the stock market page of The Wall Street Journal may be a sound (and certainly well-diversified) investment. Suppose that you own such a portfolio of 16 stocks randomly selected from all stocks listed on the
An advertisement for Citicorp Insurance Services, Inc., claims "one person in seven will be hospitalized this year." Suppose you keep track of a random sample of 180 people over an entire year. Assuming Citicorp's advertisement is correct, what is the probability that fewer than 10% of the people
Shimano mountain bikes are displayed in chic clothing boutiques in Milan, Italy, and the average price for the bike in the city is $700. Suppose that the standard deviation of bike prices is $100. If a random sample of 60 boutiques is selected, what is the probability that the average price for a
A quality-control analyst wants to estimate the proportion of imperfect jeans in a large warehouse. The analyst plans to select a random sample of 500 pairs of jeans and note the proportion of imperfect pairs. If the actual proportion in the entire warehouse is 0.35, what is the probability that
Suppose that in a sampling survey to estimate the population variance, the biased estimator was used instead of the unbiased one. The sample size used was n = 100, and the estimate obtained was 1,287. Can you find the value of the unbiased estimate of the population variance?
Suppose that you have two biased estimators of the same population parameter. Estimator A has a bias equal to 1/n (that is, the mean of the estimator is 1/n unit away from the parameter it estimates), where n is the sample size used. Estimator B has a bias equal to 0.01 (the mean of the estimator
Three random samples of sizes, 30, 48, and 32, respectively, are collected, and the three sample means are computed. What is the total number of degrees of freedom for deviations from the means?
The data points in a sample of size 9 are 34, 51, 40, 38, 47, 50, 52, 44, 37.a. If you can take the deviations of these data from any number you select, and you want to minimize the sum of the squared deviations (SSD), what number would you select? What is the minimized SSD? How many degrees of
Your bank sends you a summary statement, giving the average amount of all checks you wrote during the month. You have a record of the amounts of 17 out of the 19 checks you wrote during the month. Using this and the information provided by the bank, can you figure out the amounts of the two missing
An article in the New York Times describes an interesting business phenomenon.The owners of small businesses tend to pay themselves much smaller salaries than they would earn had they been working for someone else. Suppose that a random sample of small business owners' monthly salaries, in dollars,
Suppose you are sampling from a population with mean µ = 1,065 and standard deviation σ = 500. The sample size is n = 100. What are the expected value and the variance of the sample mean µ?
Suppose you are sampling from a population with population variance σ2 = 1,000,000. You want the standard deviation of the sample mean to be at most 25. What is the minimum sample size you should use?
When sampling is from a population with mean 53 and standard deviation 10, using a sample of size 400, what are the expected value and the standard deviation of the sample mean?
When sampling is for a population proportion from a population with actual proportion p = 0.5, using a sample of size n = 120, what is the standard deviation of our estimator P-hat?
What are the expected value and the standard deviation of the sample proportion P-hat if the true population proportion is 0.2 and the sample size is n = 90?
For a fixed sample size, what is the value of the true population proportion p that maximizes the variance of the sample proportion P-hat?
The average value of $1.00 in euros in early 2007 was 0.76. If σ = 0.02 and n = 30, find P(0.72 < x̄ < 0.82).
In problem 5-41, what is the probability that the sample mean will be at least 1,000? Do you need to use the central limit theorem to answer this question? Explain.In problem 5-41Suppose you are sampling from a population with mean µ = 1,065 and standard deviation σ = 500. The sample size is n =
In problem 5-43, what is the probability that the sample mean will be between 52 and 54?In problem 5-43,When sampling is from a population with mean 53 and standard deviation 10, using a sample of size 400, what are the expected value and the standard deviation of the sample mean?
Starbucks regularly introduces new coffee drinks and attempts to evaluate how these drinks fare by estimating the price its franchises can charge for them and sell enough cups to justify marketing the drink. Suppose the following random sample of prices a new drink sells for in New York (in
In problem 5-44, what is the probability that the sample proportion will be at least 0.45?In problem 5-44When sampling is for a population proportion from a population with actual proportion p = 0.5, using a sample of size n = 120, what is the standard deviation of our estimator P-hat?
Searches at Switzerland's 406 commercial banks turned up only $3.3 million in accounts belonging to Zaire's deposed president, Mobutu Sese Seko. The Swiss banks had been asked to look a little harder after finding nothing at all the first time round.a. If President Mobutu's money was distributed in
The proportion of defective microcomputer disks of a certain kind is believed to be anywhere from 0.06 to 0.10. The manufacturer wants to draw a random sample and estimate the proportion of all defective disks. How large should the sample be to ensure that the standard deviation of the estimator is
Explain why we need to draw random samples and how such samples are drawn. What are the properties of a (simple) random sample?
Explain the idea of a bias and its ramifications.
Is the sample median a biased estimator of the population mean? Why do we usually prefer the sample mean to the sample median as an estimator for the population mean? If we use the sample median, what must we assume about the population? Compare the two estimators.
Residential real estate in New York rents for an average of $44 per square foot, for a certain segment of the market. If the population standard deviation is $7, and a random sample of 50 properties is chosen, what is the probability that the sample average will be below $35?
In problem 5-57, give 0.95 probability bounds on the value of the sample mean that would be obtained. Also give 0.90 probability bounds on the value of the sample mean.
According to Money, the average U.S. government bond fund earned 3.9% over the 12 months ending in February 2007. Assume a standard deviation of 0.5%. What is the probability that the average earning in a random sample of 25 bonds exceeded 3.0%?
Thirty-eight percent of all shoppers at a large department store are holders of the store's charge card. If a random sample of 100 shoppers is taken, what is the probability that at least 30 of them will be found to be holders of the card?
When sampling is from a normal population with an unknown variance, is the sampling distribution of the sample mean normal? Explain.
Which of the following estimators are unbiased estimators of the appropriate population parameters: x̄, P-hat, S2, S? Explain.
Three independent random samples are collected, and three sample means are computed. The total size of the combined sample is 124. How many degrees of freedom are associated with the deviations from the sample means in the combined data set? Explain.
Use a random number table to find identification numbers of elements to be used in a random sample of size n = 25 from a population of 950 elements.
Suppose that you are given a new sample statistic to serve as an estimator of some population parameter. You are unable to assume any theoretical results such as the central limit theorem. Discuss how you would empirically determine the sampling distribution of the new statistic.
A new kind of alkaline battery is believed to last an average of 25 hours of continuous use (in a given kind of flashlight). Assume that the population standard deviation is 2 hours. If a random sample of 100 batteries is selected and tested, is it likely that the average battery in the sample will
Häagen-Dazs ice cream produces a frozen yogurt aimed at health-conscious ice cream lovers. Before marketing the product in 2007, the company wanted to estimate the proportion of grocery stores currently selling Häagen-Dazs ice cream that would sell the new product. If 60% of the grocery stores
Japan's birthrate is believed to be 1.57 per woman. Assume that the population standard deviation is 0.4. If a random sample of 200 women is selected, what is the probability that the sample mean will fall between 1.52 and 1.62?
The Toyota Prius uses both gasoline and electric power. Toyota claims its mileage per gallon is 52. A random sample of 40 cars is taken and each sampled car is tested for its fuel efficiency. Assuming that 52 miles per gallon is the population mean and 2.4 miles per gallon is the population
A bank that employs many part-time tellers is concerned about the increasing number of errors made by the tellers. To estimate the proportion of errors made in a day, a random sample of 400 transactions on a particular day was checked. The proportion of the transactions with errors was computed. If
The daily number of visitors to a Web site follows a normal distribution with mean 15,830 and standard deviation 458. The average number of visitors on 10 randomly chosen days is computed. What is the probability that the estimated average exceeds 16,000?
According to Business Week, profits in the energy sector have been rising, with one company averaging $3.42 monthly per share. Assume this is an average from a population with standard deviation of $1.5. If a random sample of 30 months is selected, what is the probability that its average will
Find five random numbers from 0 to 5,600.
Assume that you have a frame of 40 million voters (something the Literary Digest should have had for an unbiased polling). Randomly generate the numbers of five sampled voters.
A company supplies pins in bulk to a customer. The company uses an automatic lathe to produce the pins. Factors such as vibration, temperature, and wear and tear affect the pins, so that the lengths of the pins made by the machine are normally distributed with a mean of 1.008 inches and a standard
British Petroleum has recently been investing in oil fields in the former Soviet Union.4 Before deciding whether to buy an oilfield, the company wants to estimate the number of barrels of oil that the oilfield can supply. For a given well, the company is interested in a purchase if it can determine
Recently, three new airlines, MAXjet, L'Avion, and Eos, began operations selling business or first-class-only service. These airlines need to estimate the highest fare a business-class traveler would pay on a New York to Paris route, roundtrip. Suppose that one of these airlines will institute its
According to Money, the average price of a home in Albuquerque is $165,000. Suppose that the reported figure is a sample estimate based on 80 randomly chosen homes in this city, and that the population standard deviation was known to be $55,000. Give an 80% confidence interval for the population
A mining company needs to estimate the average amount of copper ore per ton mined. A random sample of 50 tons gives a sample mean of 146.75 pounds. The population standard deviation is assumed to be 35.2 pounds. Give a 95% confidence interval for the average amount of copper in the "population" of
A new low-calorie pizza introduced by Pizza Hut has an average of 150 calories per slice. If this number is based on a random sample of 100 slices, and the population standard deviation is 30 calories, give a 90% confidence interval for the population mean.
"Small-fry" funds trade at an average of 20% discount to net asset value. If σ = 8% and n = 36, give the 95% confidence interval for average population percentage.
Suppose you have a confidence interval based on a sample of size n. Using the same level of confidence, how large a sample is required to produce an interval of one-half the width?
The width of a 95% confidence interval for μ is 10 units. If everything else stays the same, how wide would a 90% confidence interval be for μ?
A telephone company wants to estimate the average length of long-distance calls during weekends. A random sample of 50 calls gives a mean x-bar = 14.5 minutes and standard deviation s = 5.6 minutes. Give a 95% confidence interval and a 90% confidence interval for the average length of a
An insurance company handling malpractice cases is interested in estimating the average amount of claims against physicians of a certain specialty. The company obtains a random sample of 165 claims and finds x-bar = $16,530 and s = $5,542. Give a 95% confidence interval and a 99% confidence
The manufacturer of batteries used in small electric appliances wants to estimate the average life of a battery. A random sample of 12 batteries yields x-bar = 34.2 hours and s = 5.9 hours. Give a 95% confidence interval for the average life of a battery.
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 is chosen; the tires are driven on until they wear out, and the number of miles driven on each tire is recorded. The data, in
Digital media have recently begun to take over from print outlets. A newspaper owners' association wants to estimate the average number of times a week people buy a newspaper on the street. A random sample of 100 people reveals that the sample average is 3.2 and the sample standard deviation is
Pier 1 Imports is a nationwide retail outlet selling imported furniture and other home items. From time to time, the company surveys its regular customers by obtaining random samples based on customer zip codes. In one mailing, customers were asked to rate a new table from Thailand on a scale of 0
An executive placement service needs to estimate the average salary of executives placed in a given industry. A random sample of 40 executives gives x-bar = $42,539 and s = $11,690. Give a 90% confidence interval for the average salary of an executive placed in this industry.
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, 2.0, 8.4, 11.0, 18.4, 4.3, 4.5, 6.0, 13.3, 12.8, 3.6, 2.4, 1.0Construct a 90% confidence interval for the average wealth in $
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 gives a sample mean of 212 calories and a sample standard deviation of 38 calories. Give a 95% confidence interval for the average caloric
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. Give a 99% confidence interval for the average transit time.
To aid in planning the development of a tourist shopping area, a state agency wants to estimate the average dollar amount spent by a tourist in an existing shopping area. A random sample of 56 tourists gives x-bar = $258 and s = $85.Give a 95% confidence interval for the average amount spent by a
According to Money, the average home in Ventura County, California, sells for $647,000.9 Assume that this sample mean was obtained from a random sample of 200 homes in this county, and that the sample standard deviation was $140,000. Give a 95% confidence interval for the average value of a home in
Explain how the postsampling confidence level is derived from a presampling probability.
Citibank Visa gives its cardholders "bonus dollars," which may be spent in partial payment for gifts purchased with the Visa card. The company wants to estimate the average amount of bonus dollars that will be spent by a cardholder enrolled in the program during a year. A trial run of the program
An accountant wants to estimate the average amount of an account of a service company. A random sample of 46 accounts yields x-bar = $16.50 and s = $2.20. Give a 95% confidence interval for the average amount of an account.
An art dealer wants to estimate the average value of works of art of a certain period and type. A random sample of 20 works of art is appraised. The sample mean is found to be $5,139 and the sample standard deviation $640. Give a 95% confidence interval for the average value of all works of art of
A management consulting agency needs to estimate the average number of years of experience of executives in a given branch of management. A random sample of 28 executives gives x-bar = 6.7 years and s = 2.4 years. Give a 99% confidence interval for the average number of years of experience for all
The Food and Drug Administration (FDA) needs to estimate the average content of an additive in a given food product. A random sample of 75 portions of the product gives x-bar = 8.9 units and s = 0.5 unit. Give a 95% confidence interval for the average number of units of additive in any portion of
The management of a supermarket needs to make estimates of the average daily demand for milk. The following data are available (number of half-gallon containers sold per day): 48, 59, 45, 62, 50, 68, 57, 80, 65, 58, 79, 69. Assuming that this is a random sample of daily demand, give a 90%
According to an article in Travel & Leisure, an average plot of land in Spain's San Martin wine-producing region yields 600 bottles of wine each year. Assume this average is based on a random sample of 25 plots and that the sample standard deviation is 100 bottles. Give a 95% confidence
The data on the daily consumption of fuel by a delivery truck, in gallons, recorded during 25 randomly selected working days, are as follows:9.7, 8.9, 9.7, 10.9, 10.3, 10.1, 10.7, 10.6, 10.4, 10.6, 11.6, 11.7, 9.7, 9.7, 9.7, 9.8, 12, 10.4, 8.8, 8.9, 8.4, 9.7, 10.3, 10, 9.2Compute a 90% confidence
According to the Darvas Box stock trading system, a trader looks at a chart of stock prices over time and identifies box-shaped patterns. Then one buys the stock if it appears to be in the lower left corner of a box, and sells if in the upper right corner. In simulations with real data, using a
Refer to the Darvas Box trading model of problem 6-38. The average profit was 11.46%. If the sample standard deviation was 8.2%, give a 90% confidence interval for average profit using this trading system.In problem According to the Darvas Box stock trading system, a trader looks at a chart of
Suppose that you computed a 95% confidence interval for a population mean. The user of the statistics claims your interval is too wide to have any meaning in the specific use for which it is intended. Discuss and compare two methods of solving this problem.
A maker of portable exercise equipment, designed for health-conscious people who travel too frequently to use a regular athletic club, wants to estimate the proportion of traveling business people who may be interested in the product. A random sample of 120 traveling business people indicates that
The makers of a medicated facial skin cream are interested in determining the percentage of people in a given age group who may benefit from the ointment.A random sample of 68 people results in 42 successful treatments. Give a 99% confidence interval for the proportion of people in the given age
According to The Economist, 55% of all French people of voting age are opposed to the proposed European constitution. Assume that this percentage is based on a random sample of 800 French people. Give a 95% confidence interval for the population proportion in France that was against the European
According to BusinessWeek, many Japanese consider their cell phones toys rather than tools. If a random sample of 200 Japanese cell phone owners reveals that 80 of them consider their device a toy, calculate a 90% confidence interval for the population proportion of Japanese cell phone users who
A recent article describes the success of business schools in Europe and the demand on that continent for the MBA degree. The article reports that a survey of 280 European business positions resulted in the conclusion that only one-seventh of the positions for MBAs at European businesses are
According to Fortune, solar power now accounts for only 1% of total energy produced. If this number was obtained based on a random sample of 8,000 electricity users, give a 95% confidence interval for the proportion of users of solar energy.
Money magazine is on a search for the indestructible suitcase. If in a test of the Helium Fusion Expandable Suiter, 85 suitcases out of a sample of 100 randomly tested survived rough handling at the airport, give a 90% confidence interval for the population proportion of suitcases of this kind that
A machine produces safety devices for use in helicopters. A quality-control engineer regularly checks samples of the devices produced by the machine, and if too many of the devices are defective, the production process is stopped and the machine is readjusted. If a random sample of 52 devices
Before launching its Buyers' Assurance Program, American Express wanted to estimate the proportion of cardholders who would be interested in this automatic insurance coverage plan. A random sample of 250 American Express cardholders was selected and sent questionnaires. The results were that 121
An airline wants to estimate the proportion of business passengers on a new route from New York to San Francisco. A random sample of 347 passengers on this route is selected, and 201 are found to be business travelers. Give a 90% confidence interval for the proportion of business travelers on the
A real estate agent needs to estimate the average value of a residential property of a given size in a certain area. The real estate agent believes that the standard deviation of the property values is σ = $5,500.00 and that property values are approximately normally distributed. A random sample

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