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mathematics
introduction to business statistics
Introduction To Business Statistics 6th Edition Ronald M. Weiers - Solutions
Using the sample results in Exercise 11.14, construct and interpret the 90% confidence interval for the difference between the population means. Is the hypothesized difference (0.00) within the interval? Given the presence or absence of the 0.00 value within the interval, is this consistent with
The New York Stock Exchange has reported that the average number of stocks directly held by senior citizens is 4.3, compared to 2.0 stocks for “Baby Boomers.” Assume that data file XR11014 contains the number of stocks held by persons sampled from each age group. Based on the results of a
In Los Angeles, doctors carried out an experiment in which 105 sedentary people whose arteries were photographed were given a photograph of the inside of their arteries to carry around. Another 105 people for whom the same medical procedure was performed were not given a photograph to take with
In a study by WebCriteria, it took an average of 2.1 minutes to locate information and buy products on the Delta Airlines website, compared to an average of 2.7 minutes on the British Airways site. Assume that data file XR11012 contains the times (in minutes) required during visits to the two
When comparing two sample means, the t-test should be used only when the sample sizes are less than 30.” Comment.
Based on the sample results in Exercise 10.109, construct and interpret the 95% confidence interval for the population proportion. Is the hypothesized proportion (0.27) within the interval? Given the presence or absence of the 0.27 value within the interval, is this consistent with the findings of
According to the U.S. Department of Justice, 27% of violent crimes involve the use of a weapon. We will assume that data file XR10109 contains a sample of the crime information for a given city, with data for the 400 crimes coded as 1 = crime involved a weapon and 2 = crime did not involve a
During 2000, 3.2% of all U.S. households were burglary victims. For a simple random sample of 300 households from a certain region, suppose that 18 households were victimized by burglary during that year. Apply an appropriate hypothesis test and the 0.05 level of significance in determining whether
The average U.S. household has $178,600 in life insurance. A local insurance agent would like to see how households in his city compare to the national average, and selects a simple random sample of 30 households from the city. For households in the sample, the average amount of life insurance is
The average U.S. family includes 3.17 persons. To determine whether families in her city tend to be representative in size compared to those across the United States, a city council member selects a simple random sample of 40 families. She finds the average number of persons in a family to be 3.44,
A hypothesis test has been set up and is to be conducted at the α = 0.05 level of significance. If the sample size is doubled, what will be the effect on α? On β?
Using the sample results in Exercise 10.71, construct and interpret the 90% confidence interval for the population proportion. Is the hypothesized population proportion (0.09) within the interval? Given the presence or absence of the 0.09 value within the interval, is this consistent with the
According to the U.S. Bureau of Labor Statistics, 9.0% of working women who are 16 to 24 years old are being paid minimum wage or less. (Note that some workers in some industries are exempt from the minimum wage requirement of the Fair Labor Standards Act and, thus, could be legally earning less
Based on the sample results in Exercise 10.69, construct and interpret the 95% confidence interval for the population proportion. Is the hypothesized proportion (0.62) within the interval? Given the presence or absence of the 0.62 value within the interval, is this consistent with the findings of
According to the National Association of Home Builders, 62% of new single-family homes built during 1996 had a fireplace. Suppose a nationwide home builder has claimed that its homes are “a cross section of America,” but a simple random sample of 600 of its single-family homes built during that
Opinion Research has said that 49% of U.S. adults have purchased life insurance. Suppose that for a random sample of 50 adults from a given U.S. city, a researcher finds that only 38% of them have purchased life insurance. At the 0.05 level in a one-tail test, is this sample finding significantly
When carrying out a hypothesis test for a population proportion, under what conditions is it appropriate to use the normal distribution as an approximation to the (theoretically correct) binomial distribution?
Using the sample data in Exercise 10.57, construct and interpret the 95% confidence interval for the population mean. Is the hypothesized population mean ($706) within the interval? Given the presence or absence of the $706 value within the interval, is this consistent with the findings of the
According to the Insurance Information Institute, the mean annual expenditure for automobile insurance for U.S. motorists is $706. Suppose that a government official in North Carolina has surveyed a simple random sample of 80 residents of her state, and that their auto insurance expenditures for
The International Council of Shopping Centers reports that the average teenager spends $39 during a shopping trip to the mall. The promotions director of a local mall has used a variety of strategies to attract area teens to his mall, including live bands and “teen appreciation days” that
Using the sample results in Exercise 10.49, construct and interpret the 95% confidence interval for the population mean. Is the hypothesized population mean ($183,000) within the interval? Given the presence or absence of the $183,000 value within the interval, is this consistent with the findings
According to the New York Stock Exchange, the mean portfolio value for U.S. senior citizens who are shareholders is $183,000. Suppose a simple random sample of 50 senior citizen shareholders in a certain region of the United States is found to have a mean portfolio value of $198,700, with a
During 2002, college work-study students earned a mean of $1252. Assume that a sample consisting of 45 of the work-study students at a large university was found to have earned a mean of $1277 during that year, with a standard deviation of $210. Would a one-tail test at the 0.05 level suggest the
The average length of a flight by regional airlines in the United States has been reported as 299 miles. If a simple random sample of 30 flights by regional airlines were to have x̅ =314.6 miles and s =42.8 miles, would this tend to cast doubt on the reported average of 299 miles? Use a two-tail
Under what circumstances should the t-statistic be used in carrying out a hypothesis test for the population mean?
According to Remodeling magazine, the average cost to convert an existing room into a home office with custom cabinetry and rewiring for electronic equipment is $5976. Assuming a population standard deviation of $1000 and the sample of home office conversion prices charged for 40 recent jobs
In the past, patrons of a cinema complex have spent an average of $2.50 for popcorn and other snacks, with a standard deviation of $0.90. The amounts of these expenditures have been normally distributed. Following an intensive publicity campaign by a local medical society, the mean expenditure for
A hypothesis test is carried out using the α = 0.01 level of significance, and H0 cannot be rejected. What is the most accurate statement we can make about the p-value for this test?
The p-value for a hypothesis test has been reported as 0.04. If the test result is interpreted using the α = 0.01 level of significance as a criterion, will H0 be rejected? Explain.
The p-value for a hypothesis test has been reported as 0.03. If the test result is interpreted using the α = 0.05 level of significance as a criterion, will H0 be rejected? Explain.
If the population standard deviation is known, but the sample size is less than 30, what assumption is necessary to use the z-statistic in carrying out a hypothesis test for the population mean?
A researcher wants to carry out a hypothesis test involving the mean for a sample of size n = 18. She does not know the true value of the population standard deviation, but is reasonably sure that the underlying population is approximately normally distributed. Should she use a z-test or a t-test
Regarding the testing of pharmaceutical companies’ claims that their drugs are safe, a U.S. Food and Drug Administration official has said that it’s “better to turn down 1000 good drugs than to approve one that’s unsafe.” If the null hypothesis is H0: “The drug is not harmful,” what
In response to the assertion made in Exercise 10.8, suppose an insurance company executive were to claim the percentage of fraudulent auto theft reports to be “no more than 10%.” What null and alternative hypotheses would be appropriate in evaluating the executive’s statement?
On CNN and other news networks, guests often express their opinions in rather strong, persuasive, and sometimes frightening terms. For example, a scientist who strongly believes that global warming is taking place will warn us of the dire consequences (such as rising sea levels, coastal flooding,
For taxpayers having an adjusted gross income of $1 million or more, the Internal Revenue Service reports that the average deduction for gifts to charity was $144,700. Curious to see how his state compares, a legislator surveys a simple random sample of 200 taxpayers from his state who are in this
According to the National Restaurant Association, the average check for a sit-down dinner is $25. Such a finding could have been based on data like the 800 sample checks in file XR09109. Using the data in this file, construct and interpret the 95% confidence interval for the population mean.
The Colgate-Palmolive Company has 37,700 employees. If the company wishes to estimate, within 2 percentage points and with 99% confidence, the percentage of employees who are interested in participating in a new stock option benefits program, how large a simple random sample will be necessary?
There are 1733 machinery rebuilding and repairing companies in the United States. A tool manufacturer wishes to survey a simple random sample of these firms to find out what proportion of them are interested in a new tool design. If the tool manufacturer would like to be 95% confident that the
There are approximately 109 million television households in the United States. A ratings service would like to know, within 5 percentage points and with 95% confidence, the percentage of these households who tune in to the first episode of a network miniseries. How many television households must
As a rule of thumb, under what conditions should the finite population correction be employed in determining confidence intervals and calculating required sample sizes?
“If we want to cut the maximum likely error in half, we’ll have to double the sample size.” Is this statement correct? Why or why not?
A Pathfinder Research Group survey estimates that, of U.S. adults who have a favorite among The Three Stooges, Moe is the favorite of 31% of them. Assuming this finding to be based on a simple random sample of 800 Stooge fans who have a favorite Stooge, construct and interpret the 95% confidence
According to Keynote Systems, Wal-Mart’s website was available 95% of the time during a holiday shopping season. Assuming this finding to be based on a simple random sample of 200 attempts, construct and interpret the 90% confidence interval for the population proportion of the time the Wal-Mart
Based on its 1999 survey, Student Monitor reports that 20% of U.S. college students used the Internet for job hunting during the month preceding the survey. Assuming this finding to be based on a simple random sample of 1600 college students, construct and interpret the 90% confidence interval for
A study by the Society of Human Resource Management found 23% of U.S. business executives surveyed believe that an employer has no right to read employees’ e-mail. Assuming that the survey included a simple random sample of 1200 executives, construct a 90% confidence interval for π = the
Survey researchers estimate that 40% of U.S. women age 18–29 save in a 401(k) or individual retirement account. Assuming the persons surveyed to be a simple random sample of 1000 U.S. women in this age group, construct a 95% confidence interval for π = the population proportion of U.S. women in
Under what conditions is it appropriate to use the normal approximation to the binomial distribution in constructing the confidence interval for the population proportion?
Automotive researchers have reported that building the Ford Mustang required an average of 22.3 labor hours. Under the assumption that this finding was based on the sample data in file XR09041, construct and interpret the 95% confidence interval for the population mean number of labor hours
In an article published in a British medical journal, Japanese researchers found that adults who were videotaped in a relaxed setting blinked an average of 15.0 times per minute. Under the assumption that this finding was based on the sample data in file XR09040, construct and interpret the 99%
According to Nielsen//Net Ratings, the average visitor to the American Greetings website spends 11.85 minutes at the site. Assuming this finding to be based on a simple random sample of 20 visitors to the site, with a sample standard deviation of s = 3.0 minutes, and from a population of visiting
Researchers have estimated that office workers in Germany receive an average of 15.0 fax messages per day. Assuming this finding to be based on a simple random sample of 80 German office workers, with a sample standard deviation of s = 3.5 messages, construct and interpret the 95% confidence
In using the t distribution table, what value of t would correspond to an upper-tail area of 0.10 for 28 degrees of freedom?
In using the t distribution table, what value of t would correspond to an upper-tail area of 0.025 for 19 degrees of freedom?
Why are the t values listed in the df = infinity row of the t distribution table identical to the z values that correspond to the same right-tail areas of the standard normal distribution? What does this indicate about the relationship between the t and standard normal distributions?
When the t distribution is used in constructing a confidence interval based on a sample size of less than 30, what assumption must be made about the shape of the underlying population?
For one of the tasks in a manufacturing process, the mean time for task completion has historically been 35.0 minutes, with a standard deviation of 2.5 minutes. Workers have recently complained that the machinery used in the task is wearing out and slowing down. In response to the complaints, plant
In Exercise 9.20, if the sample size had been n = 5 instead of n = 30, what assumption would have to be made about the population distribution of filling weights in order to use z values in constructing the confidence interval?
A machine that stuffs a cheese-filled snack product can be adjusted for the amount of cheese injected into each unit. A simple random sample of 30 units is selected, and the average amount of cheese injected is found to be x̅ 3.5 grams. If the process standard deviation is known to be σ = 0.25
An assembly process includes a torque wrench device that automatically tightens compressor housing bolts; the device has a known process standard deviation of σ = 3 lb-ft in the torque applied. A simple random sample of 35 nuts is selected, and the average torque to which they have been tightened
In testing the heat resistance of electrical components, safety engineers for an appliance manufacturer routinely subject wiring connectors to a temperature of 450 degrees Fahrenheit, then record the amount of time it takes for the connector to melt and cause a short circuit. Past experience has
The administrator of a physical therapy facility has found that postoperative performance scores on a knee flexibility test have tended to follow a normal distribution with a standard deviation of 4. For a simple random sample of ten patients who have recently had knee surgery, the scores are as
A simple random sample of 25 has been collected from a normally distributed population for which it is known that σ =17.0. The sample mean has been calculated as 342.0, and the sample standard deviation is s = 14.9. Construct and interpret the 95% and 99% confidence intervals for the population
A simple random sample of 30 has been collected from a population for which it is known that σ =10.0. The sample mean has been calculated as 240.0. Construct and interpret the 90% and 95% confidence intervals for the population mean.
The following data values are a simple random sample from a population that is normally distributed, with σ2 = 25.0: 47, 43, 33, 42, 34, and 41. Construct and interpret the 95% and 99% confidence intervals for the population mean.
In using the standard normal distribution to construct a confidence interval for the population mean, what two assumptions are necessary if the sample size is less than 30?
What role does the central limit theorem play in the construction of a confidence interval for the population mean?
Exactly what is meant by the accuracy of a point estimate?
The average annual U.S. per capita consumption of iceberg lettuce has been estimated as 24.3 pounds. The annual per capita consumption 2 years earlier had been estimated as 21.6 pounds. Could either or both of these consumption figures be considered a point estimate? Could the difference between
A simple random sample of 8 employees is selected from a large firm. For the 8 employees, the number of days each was absent during the past month was found to be 0, 2, 4, 2, 1, 7, 3, and 2, respectively.a. What is the point estimate for µ, the mean number of days absent for the firm’s
During the month of July, an auto manufacturer gives its production employees a vacation period so it can tool up for the new model run. In surveying a simple random sample of 200 production workers, the personnel director finds that 38% of them plan to vacation out of state for at least one week
When calculating the sample variance, what procedure is necessary to ensure that s2 will be an unbiased estimator of σ2? Will s be an unbiased estimator of σ?
What is meant when a sample statistic is said to be an unbiased estimator?
What is necessary for an interval estimate to be a confidence interval?
What is meant by inferential statistics, and what role does it play in estimation?
The overall pass rate for law school graduates taking the Maryland bar exam has been reported as 75%. Assume that a certain Maryland law school has had 400 of its most recent graduates take the Maryland bar exam, but only 60% passed. When asked about these results, the dean of this university’s
Employees at a corporate headquarters own an average of 240 shares of the company’s common stock, with a standard deviation of 40 shares. For a simple random sample consisting of 5 employees, what assumption would be required if we are to use the standard normal distribution in determining P(x̅
In 1999, the average fee paid by H&R Block tax preparation customers in Canada was $55.93. Assume that the standard deviation of fees was $20 but that we have no idea regarding the shape of the population distribution.a. What additional assumption about the population would be needed in order
Of the 235 airports available for public use in Michigan, 128 are paved and lighted. For a simple random sample of n = 50, what is the probability that at least 20 of the airports in the sample will be paved and lighted?
Compared to the situation in which the population is either extremely large or infinite in size, what effect does the use of the finite population term tend to have on the resulting value of the standard error?
Under what circumstances is it desirable to use the finite population correction factor in describing the sampling distribution of a mean or a proportion?
According to the Federal Trade Commission (FTC), about 3.6% of sale-priced items come up at the wrong price when scanned at the checkout counter. Freda Thompson, director of investigations for her state’s consumer affairs office, sets up a study in which she has undercover shoppers (sometimes
It has been estimated that 17.0% of mutual fund shareholders are retired persons. Assuming the population proportion π = 0.17 to be and that a simple random sample of 400 shareholders has been selected:a. What is the expected value of p = the proportion of those in the sample who are retired?b.
Of the 53,309 salaried U.S. employees of Ford Motor Company, 26.5% are females. For simple random samples of size n, with n > 30, describe the sampling distribution of p = the proportion of females in the sample.
According to the Pew Research Center for the People and the Press, persons in higher age groups tend to spend much more time reading the newspaper. For persons 65 or more years of age who read a newspaper, the average time has been reported as 33 minutes. Assuming a population standard deviation of
It has been reported that the average U.S. office worker receives 14 fax messages per day. For purposes of this exercise, we will assume that the daily number of fax messages is normally distributed with a standard deviation of 5.0 messages. For an office in which 10 workers are employed, and
In a simple random sample of 1000 households, 150 households happen to own a barbecue grill. Based on the characteristics of the population, the expected number of grill owners in the sample was 180. What are the values of π, p, and n?
Approximately 60% of Americans have some form of life insurance coverage. For a randomly selected sample of n = 20 individuals, and the discrete random variable x = the number of persons in the sample who are covered by life insurance: a. Calculate the mean and the standard deviation of
During fiscal 2002, the average daily volume for FedEx Corporation was 3,077,000 packages per day. Assuming a normal distribution and a standard deviation of 400,000 packages per day, on what proportion of the days was the volume between 3,000,000 and 3,200,000 packages?
The American Council of Life Insurance and the Life Insurance Marketing and Research Association have reported that insured households with heads 35 to 44 years old had an average of $186,100 of life insurance coverage. Assuming a normal distribution and a standard deviation of $40,000, what is the
The American Iron and Steel Institute reports the fatality rate for workers in this industry as 0.007 fatalities per 200,000 worker-hours of production. During 1998, the aggregate number of worker-hours spent on producing iron and steel products amounted to 243 million worker-hours. Assuming that
During 2004, U.S. general aviation pilots had 1.20 fatal crashes per 100,000 flying hours. Harriet Arnold is president of Arnold’s Flying Service, a company that operates a total of 50 sightseeing planes based in 20 regions of the United States. Altogether, the planes in this fleet are in the air
The main switchboard at the Home Shopping Network receives calls from customers. If the Poisson distribution were applied to this process, what would be an appropriate random variable? What would be the exponential- distribution counterpart to this random variable?
Every day, drivers arrive at a tollbooth. If the Poisson distribution were applied to this process, what would be an appropriate random variable? What would be the exponential-distribution counterpart to this random variable?
The Electronic Industries Association reports that about 54% of U.S. households have a camcorder. For a randomly selected sample of 800 U.S. households, use the normal approximation to the binomial distribution in determining the probability that at least 420 of thesehouseholds have a camcorder.
Of all individual tax returns filed in the United States during the 1999 tax filing season, 13.7% were prepared by H&R Block. For a randomly selected sample of 1000 tax returns filed during this period, use the normal approximation to the binomial distribution in determining the probability
About 30% of new single-family homes completed in the United States during 2004 were heated with electricity. For a randomly selected sample of 25 new single-family homes completed during that year and the discrete random variable, x = the number of homes in this group heated with
In a certain binomial distribution, π = 0.20 and n = 30. In using the normal approximation,a. What are the mean and standard deviation of the corresponding normal distribution?b. If x = the number of “successes” among the 30 observations, determine the following: P(x = 5), P(4 ≤ x≤
Under what circumstances is it permissible to use the normal distribution in approximating the binomial distribution?
For the normal distribution described in Exercise 7.12, what is the probability that a randomly selected tax preparation customer would have paid a feea. Between $70 and $80?b. Under $60? c. Over $90?
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