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statistics

Questions and Answers of Statistics

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
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
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
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,
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
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
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.
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
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
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
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.
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.
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 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
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
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
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
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.
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
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
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
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
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
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,
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
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
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,
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
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
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
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
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
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
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
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
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.
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
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
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
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
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
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
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
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
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
"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.
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
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
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
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
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
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%
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,
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 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%
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
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
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
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
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
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
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
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,
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
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,
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
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
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
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
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
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.
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,
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
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
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
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
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
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
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

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