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mathematics
statistics

Questions and Answers of Statistics

Determine the sample size necessary to estimate for the following information.a. σ = 36 and E = 5 at 95% confidenceb. σ = 4.13 and E = 1 at 99% confidencec. Values range from 80 to 500, error is to
Determine the sample size necessary to estimate p for the following information.a. E = .02, p is approximately .40, and confidence level is 96%b. E is to be within .04, p is unknown, and confidence
A group of investors wants to develop a chain of fast-food restaurants. In determining potential costs for each facility, they must consider, among other expenses, the average monthly electric bill.
Suppose a production facility purchases a particular component part in large lots from a supplier. The production manager wants to estimate the proportion of defective parts received from this
What proportion of secretaries of Fortune 500 companies has a personal computer at his or her workstation? You want to answer this question by conducting a random survey. How large a sample should
What proportion of shoppers at a large appliance store actually makes a large-ticket purchase? To estimate this proportion within 10% and be 95% confident of the results, how large a sample should
Use the following data to construct 80%, 94%, and 98% confidence intervals to estimate Âµ. Assume that Ïƒ is 7.75.State the pointestimate.
Construct 90%, 95%, and 99% confidence intervals toEstimate Âµ from the following data. State the point estimate. Assume the data come from a normally distributedpopulation.
Use the following information to compute the confidence interval for the population proportion.a. n = 715 and x = 329,with 95% confidenceb. n = 284 and p̂ with 90% confidencec. n = 1250 and p̂ with
Use the following data to construct 90% and 95% confidence intervals to estimate the population variance. Assume the data come from a normally distributedpopulation.
Determine the sample size necessary under the following conditions.a. To estimate µ with σ = 44,E = 3,and 95% confidenceb. To estimate µ with a range of values from 20 to 88 with E = 2 and 90%
In planning both market opportunity and production levels, being able to estimate the size of a market can be important. Suppose a diaper manufacturer wants to know how many diapers a one-month-old
Use the data in Problem 8.53 to construct a 99% confidence interval to estimate the population variance for the number of diapers used during a 24-hour period for one-month-olds. How could
What is the average length of a company’s policy book? Suppose policy books are sampled from 45 medium-sized companies. The average number of pages in the sample books is 213,and the population
A random sample of small-business managers was given a leadership style questionnaire. The results were scaled so that each manager received a score for initiative. Suppose the following data are a
Is the environment a major issue with Americans? To answer that question, a researcher conducts a survey of 1255 randomly selected Americans. Suppose 714 of the sampled people replied that the
According to a survey by Topaz Enterprises, a travel auditing company, the average error by travel agents is $128. Suppose this figure was obtained from a random sample of 41 travel agents and the
A national survey on telemarketing was undertaken. One of the questions asked was: How long has your organization had a telemarketing operation? Suppose the following data represent some of the
An entrepreneur wants to open an appliance repair shop. She would like to know about what the average home repair bill is, including the charge for the service call for appliance repair in the area.
A national survey of insurance offices was taken, resulting in a random sample of 245 companies. Of these 245 companies, 189 responded that they were going to purchase new software for their offices
A national survey of companies included a question that asked whether the company had at least one bilingual telephone operator. The sample results of 90 companies follow (Y denotes that the company
A movie theater has had a poor accounting system. The manager has no idea how many large containers of popcorn are sold per movie showing. She knows that the amounts vary by day of the week and hour
According to a survey by Runzheimer International, the average cost of a fast-food meal (quarter-pound cheese-burger, large fries, medium soft drink, excluding taxes) in Seattle is $4.82. Suppose
A survey of 77 commercial airline flights of under 2 hours resulted in a sample average late time for a flight of 2.48 minutes. The population standard deviation was 12 minutes. Construct a 95%
A regional survey of 560 companies asked the vice president of operations how satisfied he or she was with the software support received from the computer staff of the company. Suppose 33% of the 560
A national magazine marketing firm attempts to win subscribers with a mail campaign that involves a contest using magazine stickers. Often when people subscribe to magazines in this manner they sign
A national survey showed that Hillshire Farm Deli Select cold cuts were priced, on the average, at $5.20 per pound. Suppose a national survey of 23 retail outlets was taken and the price per pound of
A study of 1,000 adult Canadians was undertaken in an effort to obtain information about Canadian shopping habits. One of the results of this survey was that 23% often buy items that are not on their
A bank officer wants to determine the amount of the average total monthly deposits per customer at the bank. He believes an estimate of this average amount using a confidence interval is sufficient.
Suppose you have been following a particular airline stock for many years. You are interested in determining the average daily price of this stock in a 10-year period and you have access to the stock
Suppose you want to estimate the proportion of cars that are sport utility vehicles (SUVs) being driven in Kansas City, Missouri, at rush hour by standing on the corner of I-70 and I-470 and counting
A national beauty spa chain wants to estimate the number of times per year a woman has her nails done at one of their spas if she uses one at least once a year. The chain’s researcher estimates
A research firm has been asked to determine the proportion of all restaurants in the state of Ohio that serve alcoholic beverages. The firm wants to be 98% confident of its results but has no idea of
The price of a head of iceberg lettuce varies greatly with the season and the geographic location of a store. During February a researcher contacts a random sample of 39 grocery stores across the
A soft drink company produces a cola in a 12-ounce can. Even though their machines are set to fill the cans with 12 ounces, variation due to calibration, operator error, and other things sometimes
A company has developed a new light bulb that seems to burn longer than most residential bulbs. To determine how long these bulbs burn, the company randomly selects a sample of these bulbs and burns
Suppose a researcher wants to estimate the average age of a person who is a first-time home buyer. A random sample of first-time home buyers is taken and their ages are ascertained. The Minitab
What proportion of all American workers drive their cars to work? Suppose a poll of American workers is taken in an effort to answer that question, and the Minitab output shown here is an analysis of
In the late 1970s, Kip Tindell (chairman and CEO), Garrett Boone (Chairman Emeritus), and John Mullen (architect) drew up plans for a first of a kind retail store specializing in storage solutions
Read each of the following statements. Assuming that statistical hypotheses are set up to test them, classify each as a one-tailed or a two-tailed test.a. Maritz Marketing Research reports that 42%
In each of the following scenarios, tell if the researcher has committed a Type I error, a Type II error, or made a correct decision. a. A researcher is testing to determine if .31 of all families
a. Use the data given to test the following hypotheses.b. Use the p-value to reach a statistical conclusion.c. Using the critical value method, what are the critical sample meanvalues?
Use the data given to test the following hypotheses. Assume the data are normally distributed in thepopulation.
a. Use the data given to test the following hypotheses.b. Use the p-value to obtain the results.c. Solve for the critical value required to reject themean.
The Environmental Protection Agency releases figures on urban air soot in selected cities in the United States. For the city of St. Louis, the EPA claims that the average number of micrograms of
According to the U.S. Bureau of Labor Statistics, the average weekly earnings of a production worker in July 2011 were $657.49.Suppose a labor researcher wants to test to determine whether this
According to a study several years ago by the Personal Communications Industry Association, the average cell phone user earns $62,600 per year. Suppose a researcher believes that the average annual
A manufacturing company produces valves in various sizes and shapes. One particular valve plate is supposed to have a tensile strength of 5 pounds per millimeter (lbs/mm).The company tests a random
According to a report released by CIBC entitled “Women Entrepreneurs: Leading the Charge, “the average age for Canadian businesswomen in 2008 was 41.In the report, there was some indication that
According to HowtoAdvice.com, the average price charged to a customer to have a 12' by 18' wall-to-wall carpet shampoo cleaned is about $50.Suppose that a start-up carpet-cleaning company believes
The American Water Works Association estimates that the average person in the United States uses 123 gallons of water per day. Suppose some researchers believe that more water is being used now and
A random sample of size 20 is taken, resulting in a sample mean of 16.45 and a sample standard deviation of 3.59.Assume x is normally distributed and use this information and α = .05 to test the
A random sample of 51 items is taken, with x̄ = 58.42 and s2 = 25.68. Use these data to test the following hypotheses, assuming you want to take only a 1% risk of committing a Type I error and that
The following data were gathered from a random sample of 11 items.Use these data and a 5% level of significance to test the following hypotheses, assuming that the data come from a normally
The following data (in pounds),which were selected randomly from a normally distributed population of values, represent measurements of a machine part that is supposed to weigh, on average, 8.3
A hole-punch machine is set to punch a hole 1.84 centimeters in diameter in a strip of sheet metal in a manufacturing process. The strip of metal is then creased and sent on to the next phase of
Suppose a study reports that the average price for a gallon of self-serve regular unleaded gasoline is $3.76.You believe that the figure is higher in your area of the country. You decide to test this
Suppose that in past years the average price per square foot for warehouses in the United States has been $32.28.A national real estate investor wants to determine whether that figure has changed
Major cities around the world compete with each other to attract new businesses. Some of the criteria that businesses use to judge cities as potential locations for their headquarters might include
Based on population figures and other general information on the U.S. population, suppose it has been estimated that, on average, a family of four in the United States spends about $1,135 annually on
According to data released by the World Bank, the mean PM10 (particulate matter) concentration for the city of Kabul, Afghanistan, in 1999 was 46.Suppose that because of efforts to improve air
According to a National Public Transportation survey, the average commuting time for people who commute to a city with a population of 1 to 3 million is 19.0 minutes. Suppose a researcher lives in a
Suppose you are testing H0: p = .45 versus Ha: p > .45.A random sample of 310 people produces a value of p̂ = .465. Use α = .05 to test this hypothesis.
Suppose you are testing H0: p = .63 versus Ha: p = .63 .For a random sample of 100 people, where x denotes the number in the sample that have the characteristic of interest. Use a .01 level of
Suppose you are testing H0: p = .29 versus Ha: p ≠ .29 A random sample of 740 items shows that 207 have this characteristic. With a .05 probability of committing a Type I error, test the
The Independent Insurance Agents of America conducted a survey of insurance consumers and discovered that 48% of them always reread their insurance policies, 29% sometimes do, 16% rarely do, and 7%
A study by Hewitt Associates showed that 79% of companies offer employees flexible scheduling. Suppose a researcher believes that in accounting firms this figure is lower. The researcher randomly
A survey was undertaken by Bruskin/Goldring Research for Quicken to determine how people plan to meet their financial goals in the next year. Respondents were allowed to select more than one way to
Eighteen percent of U.S.-based multinational companies provide an allowance for personal long-distance calls for executives living overseas, according to the Institute for International Human
A large manufacturing company investigated the service it received from suppliers and discovered that, in the past, 32% of all materials shipments were received late. However, the company recently
Where do CFOs get their money news? According to Robert Half International, 47% get their money news from newspapers, 15% get it from communication/colleagues, 12% get it from television,11% from the
Test each of the following hypotheses by using the given information. Assume the populations are normally distributed.a. H0: σ2 = 20Ha: σ2 > 20α = .05, n = 15, s2 = 32b. H0: σ2 = 8.5Ha: σ2
Previous experience shows the variance of a given process to be 14.Researchers is testing to determine whether this value has changed. They gather the following dozen measurements of the process. Use
A manufacturing company produces bearings. One line of bearings is specified to be 1.64 centimeters (cm) in diameter. A major customer requires that the variance of the bearings be no more than .001
A savings and loan averages about $100,000 in deposits per week. However, because of the way pay periods fall, seasonality, and erratic fluctuations in the local economy, deposits are subject to a
A company produces industrial wiring. One batch of wiring is specified to be 2.16 centimeters (cm) thick. A company inspects the wiring in seven locations and determines that, on the average, the
Suppose a null hypothesis is that the population mean is greater than or equal to 100. Suppose further that a random sample of 48 items is taken and the population standard deviation is 14. For each
For Problem 9.38, use and solve for the probability of committing a Type II error for the following possible true alternative means.a. µa = 98.5b. µa = 98c. µa = 97d. µa = 96e. What happens to
Suppose a hypothesis states that the mean is exactly 50. If a random sample of 35 items is taken to test this hypothesis, what is the value of β if the population standard deviation is 7 and the
An alternative hypothesis is that p < .65. To test this hypothesis, a random sample of size 360 is taken. What is the probability of committing a Type II error if α = .05 and the alternative
The New York Stock Exchange recently reported that the average age of a female shareholder is 44 years. A broker in Chicago wants to know whether this figure is accurate for the female shareholders
A Harris poll was taken to determine which of 13 major industries are doing a good job of serving their customers. Among the industries rated most highly by Americans for serving their customers were
Use the information given and the eight-step approach to test the hypotheses. Let α = .01.H0:µ = 36Ha: µ ≠ 36n = 63x̄ = 38.4σ =5.93
Use the information given and the eight-step approach to test the hypotheses. Let α =.05.Assume that the population is normally distributed.H0:µ = 7.82Ha: µ < 7.82n = 17x̄ = 7.01s = 1.69
For each of the following problems, use the eight-step approach to test the hypotheses.a. H0:p = 36Ha: p > 36n = 783x̄ = 230α = .10.b. H0:p = 36Ha: p ≠ 36n = 401p̂ = .56α = .05.
Test the following hypotheses by using the information given and the eight-step approach. Let alpha be .01. Assume the population is normally distributed.H0: σ2 = 15.4Ha: σ2 > 15.4n = 18s2 =
Solve for the value of beta in each of the following problems.a. H0:µ = 130Ha: µ > 130n = 75σ = 12α = .01.The alternative mean is actually 135.b. H0:µ = .44Ha: p < .44n = 1095α = .05.The
According to one survey taken a few years ago, 32% of American households have attempted to reduce their long-distance phone bills by switching long-distance companies. Suppose that business
According to Zero Population Growth, the average urban U.S. resident consumes 3.3 pounds of food per day. Is this figure accurate for rural U.S. residents? Suppose 64 rural U.S. residents are
Brokers generally agree that bonds are a better investment during times of low interest rates than during times of high interest rates. A survey of executives during a time of low interest rates
Highway engineers in Ohio are painting white stripes on a highway. The stripes are supposed to be approximately 10 feet long. However, because of the machine, the operator, and the motion of the
A computer manufacturer estimates that its line of mini computers has, on average, 8.4 days of downtime per year. To test this claim, a researcher contacts seven companies that own one of these
Life insurance experts have been claiming that the average worker in the city of Cincinnati has no more than $25,000 of personal life insurance. An insurance researcher believes that this is not true
A financial analyst watched a particular stock for several months. The price of this stock remained fairly stable during this time. In fact, the financial analyst claims that the variance of the
A study of MBA graduates by Universum for the American Graduate Survey 1999 revealed that MBA graduates have several expectations of prospective employers beyond their base pay. In particular,
Suppose the number of beds filled per day in a medium-sized hospital is normally distributed. A hospital administrator tells the board of directors that, on the average, at least 185 beds are filled
According to Gartner Inc., the largest share of the worldwide PC market is held by Hewlett-Packard with 16.0%. Suppose that a market researcher believes that Hewlett-Packard holds a higher share of
A national publication reported that a college student living away from home spends, on average, no more than $15 per month on laundry. You believe this figure is too low and want to disprove this
A local company installs natural-gas grills. As part of the installation, a ditch is dug to lay a small natural-gas line from the grill to the main line. On the average, the depth of these lines
A study of pollutants showed that certain industrial emissions should not exceed 2.5 parts per million. You believe a particular company may be exceeding this average. To test this supposition, you

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