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Business Statistics Contemporary Decision Making 6th Edition Ken Black - Solutions
Determine the sample size necessary under the following conditions.a. To estimate with = 44, E = 3, and 95% confidenceb. To estimate with a range of values from 20 to 88 with E = 2 and 90% confidencec. To estimate p with p unknown, E = .04, and 98%confidenced. To estimate p with E = .03, 95%
Use the following data to construct 90% and 95% confidence intervals to estimate the population variance.Assume the data come from a normally distributed population.212 229 217 216 223 219 208 214 232 219
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 , with 90% confidencec. n = 1250 and , with 95% confidenced. n = 457 and x = 270, with 98% confidence
Construct 90%, 95%, and 99% confidence intervals to estimate from the following data. State the point estimate.Assume the data come from a normally distributed population.12.3 11.6 11.9 12.8 12.5 11.4 12.0 11.7 11.8 12.3
Use the following data to construct 80%, 94%, and 98%confidence intervals to estimate . Assume that is 7.75. State the point estimate.44 37 49 30 56 48 53 42 51 38 39 45 47 52 59 50 46 34 39 46 27 35 52 51 46 45 58 51 37 45 52 51 54 39 48
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 you take? Assume you have no idea what proportion of all shoppers actually make a large-ticket purchase.
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 you take if you want to be 95% confident of the results and you want the error of the confidence
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 supplier. She believes the proportion defective is no more than .20 and wants to be within .02 of the true
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. They decide to sample some fast-food restaurants currently operating to estimate the monthly cost of
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 reports for these years. However, you do not want to average all the daily prices over 10 years
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. How large a sample should he take to be within $200 of the actual average with 99% confidence? He
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 level is 95%c. E is to be within 5%, p is approximately 55%, and confidence level is 90%d. E is to be
Determine the sample size necessary to estimate for the following information.a. = 36 and E = 5 at 95% confidenceb. = 4.13 and E = 1 at 99% confidencec. Values range from 80 to 500, error is to be within 10, and the confidence level is 90%d. Values range from 50 to 108, error is to be within 3, and
Suppose a random sample of 14 people 30–39 years of age produced the household incomes shown here. Use these data to determine a point estimate for the population variance of household incomes for people 30–39 years of age and construct a 95%confidence interval. Assume household income is
A manufacturing plant produces steel rods. During one production run of 20,000 such rods, the specifications called for rods that were 46 centimeters in length and 3.8 centimeters in width. Fifteen of these rods comprising a random sample were measured for length; the resulting measurements are
The Interstate Conference of Employment Security Agencies says the average workweek in the United States is down to only 35 hours, largely because of a rise in part-time workers. Suppose this figure was obtained from a random sample of 20 workers and that the standard deviation of the sample was
Use the following sample data to estimate the population variance. Produce a point estimate and a 98% confidence interval. Assume the data come from a normally distributed population.27 40 32 41 45 29 33 39 30 28 36 32 42 40 38 46
For each of the following sample results, construct the requested confidence interval.Assume the data come from normally distributed populations. a. n = 12, x = 28.4, s = 44.9; 99% confidence for b. n 7, 4.37, s=1.24; 95% confidence for or c. n=20, x = 105, s= 32; 90% confidence for o d. n=17, s
Suppose a survey of 275 executives is taken in an effort to determine what qualities are most important for an effective CEO to possess. The survey participants are offered several qualities as options, one of which is “communication.” One hundred twenty-one of the surveyed respondents select
According to Runzheimer International, in a survey of relocation administrators 63% of all workers who rejected relocation offers did so for family considerations.Suppose this figure was obtained by using a random sample of the files of 672 workers who had rejected relocation offers. Use this
What proportion of commercial airline pilots are more than 40 years of age?Suppose a researcher has access to a list of all pilots who are members of the Commercial Airline Pilots Association. If this list is used as a frame for the study, she can randomly select a sample of pilots, contact them,
The highway department wants to estimate the proportion of vehicles on Interstate 25 between the hours of midnight and 5:00 A.M. that are 18-wheel tractor trailers.The estimate will be used to determine highway repair and construction considerations and in highway patrol planning. Suppose
What proportion of pizza restaurants that are primarily for walk-in business have a salad bar? Suppose that, in an effort to determine this figure, a random sample of 1,250 of these restaurants across the United States based on the Yellow Pages is called.If 997 of the restaurants sampled have a
According to the Stern Marketing Group, 9 out of 10 professional women say that financial planning is more important today than it was five years ago.Where do these women go for help in financial planning? Forty-seven percent use a financial advisor(broker, tax consultant, financial planner).
The Universal Music Group is the music industry leader worldwide in sales according to the company Web site. Suppose a researcher wants to determine what market share the company holds in the city of St. Louis by randomly selecting 1,003 people who purchased a CD last month. In addition, suppose
Suppose a random sample of 85 items has been taken from a population and 40 of the items contain the characteristic of interest. Use this information to calculate a 90% confidence interval to estimate the proportion of the population that has the characteristic of interest. Calculate a 95%
Use the following sample information to calculate the confidence interval to estimate the population proportion. Let x be the number of items in the sample having the characteristic of interest.a. n = 116 and x = 57, with 99% confidenceb. n = 800 and x = 479, with 97% confidencec. n = 240 and x =
Use the information about each of the following samples to compute the confidence interval to estimate p. a. n=44 and p = .51; compute a 90% confidence interval. b. n 300 and p = .82; compute a 95% confidence interval. c. n=1,150 and p = .48; compute a 90% confidence interval. d. n=95 and p = .32;
Cycle time in manufacturing can be viewed as the total time it takes to complete a product from the beginning of the production process. The concept of cycle time varies according to the industry and product or service being offered. Suppose a boat manufacturing company wants to estimate the mean
How much experience do supply-chain transportation managers have in their field? Suppose in an effort to estimate this, 41 supply-chain transportation managers are surveyed and asked how many years of managerial experience they have in transportation. Survey results (in years) are shown below. Use
Runzheimer International publishes results of studies on overseas business travel costs.Suppose as a part of one of these studies the following per diem travel accounts (in dollars) are obtained for 14 business travelers staying in Johannesburg, South Africa.Use these data to construct a 98%
The marketing director of a large department store wants to estimate the average number of customers who enter the store every five minutes. She randomly selects five-minute intervals and counts the number of arrivals at the store. She obtains the figures 58, 32, 41, 47, 56, 80, 45, 29, 32, and 78.
Some fast-food chains offer a lower-priced combination meal in an effort to attract budget-conscious customers. One chain test-marketed a burger, fries, and a drink combination for $1.71. The weekly sales volume for these meals was impressive.Suppose the chain wants to estimate the average amount
A valve manufacturer produces a butterfly valve composed of two semicircular plates on a common spindle that is used to permit flow in one direction only. The semicircular plates are supplied by a vendor with specifications that the plates be 2.37 millimeters thick and have a tensile strength of
According to Runzheimer International, the average cost of a domestic trip for business travelers in the financial industry is $1,250. Suppose another travel industry research company takes a random sample of 51 business travelers in the financial industry and determines that the sample average
Use the following data to construct a 99% confidence interval for .16.4 17.1 17.0 15.6 16.2 14.8 16.0 15.6 17.3 17.4 15.6 15.7 17.2 16.6 16.0 15.3 15.4 16.0 15.8 17.2 14.6 15.5 14.9 16.7 16.3 Assume x is normally distributed.What is the point estimate for ?
A random sample of 15 items is taken, producing a sample mean of 2.364 with a sample variance of .81. Assume x is normally distributed and construct a 90%confidence interval for the population mean.
If a random sample of 41 items produces and s = 20.6, what is the 98%confidence interval for ? Assume x is normally distributed for the population.What is the point estimate?
In a recent year, turkey prices increased because of a high rate of turkey deaths caused by a heat wave and a fatal illness that spread across North Carolina, the top turkey-producing state. Suppose a random sample of turkey prices is taken from across the nation in an effort to estimate the
According to the U.S. Census Bureau, the average travel time to work in Philadelphia is 27.4 minutes. Suppose a business researcher wants to estimate the average travel time to work in Cleveland using a 95% level of confidence. A random sample of 45 Cleveland commuters is taken and the travel time
A meat-processing company in the Midwest produces and markets a package of eight small sausage sandwiches. The product is nationally distributed, and the company is interested in knowing the average retail price charged for this item in stores across the country. The company cannot justify a
A community health association is interested in estimating the average number of maternity days women stay in the local hospital. A random sample is taken of 36 women who had babies in the hospital during the past year. The following numbers of maternity days each woman was in the hospital are
The average total dollar purchase at a convenience store is less than that at a supermarket. Despite smaller-ticket purchases, convenience stores can still be profitable because of the size of operation, volume of business, and the markup.A researcher is interested in estimating the average
A small lawnmower company produced 1,500 lawnmowers in 1998. In an effort to determine how maintenance-free these units were, the company decided to conduct a multiyear study of the 1998 lawnmowers. A sample of 200 owners of these lawnmowers was drawn randomly from company records and contacted.
A candy company fills a 20-ounce package of Halloween candy with individually wrapped pieces of candy. The number of pieces of candy per package varies because the package is sold by weight. The company wants to estimate the number of pieces per package. Inspectors randomly sample 120 packages of
A random sample of size 39 is taken from a population of 200 members. The sample mean is 66 and the population standard deviation is 11. Construct a 96% confidence interval to estimate the population mean.What is the point estimate of the population mean?
A random sample of size 70 is taken from a population that has a variance of 49. The sample mean is 90.4 What is the point estimate of ? Construct a 94% confidence interval for .
Use the following information to construct the confidence intervals specified to estimate . a. 95% confidence for x = b. 98% confidence for x = c. 90% confidence for x = 25, = 3.5, and n = 60 119.6, = 23.89, and n = 75 3.419, = 0.974, and n=32 d. 80% confidence for x = 56.7, = 12.1, N=500, and
According to Runzheimer International, a typical business traveler spends an average of $281 per day in Chicago. This cost includes hotel, meals, car rental, and incidentals. A survey of 65 randomly selected business travelers who have been to Chicago on business recently is taken. For the
Give a variable that could be used to stratify the population for each of the following studies. List at least four subcategories for each variable.a. A political party wants to conduct a poll prior to an election for the office of U.S. senator in Minnesota.b. A soft drink company wants to take a
The U.S. Bureau of Labor Statistics released hourly wage figures for various countries for workers in the manufacturing sector. The hourly wage was $30.67 for Switzerland,$20.20 for Japan, and $23.82 for the U.S.Assume that in all three countries, the standard deviation of hourly labor rates is
In a particular area of the Northeast, an estimated 75%of the homes use heating oil as the principal heating fuel during the winter. A random telephone survey of 150 homes is taken in an attempt to determine whether this figure is correct. Suppose 120 of the 150 homes surveyed use heating oil as
Suppose you work for a large firm that has 20,000 employees. The CEO calls you in and asks you to determine employee attitudes toward the company. She is willing to commit $100,000 to this project.What are the advantages of taking a sample versus conducting a census?What are the trade-offs?
According to the U.S. Bureau of Labor Statistics, 20% of all people 16 years of age or older do volunteer work. In this age group, women volunteer slightly more than men, with 22% of women volunteering and 19% of men volunteering.What is the probability of randomly sampling 140 women 16 years of
Direct marketing companies are turning to the Internet for new opportunities. A recent study by Gruppo, Levey,& Co. showed that 73% of all direct marketers conduct transactions on the Internet. Suppose a random sample of 300 direct marketing companies is taken.a. What is the probability that
Use Table A.1 to select 20 three-digit random numbers.Did any of the numbers occur more than once? How is it possible for a number to occur more than once? Make a stem-and-leaf plot of the numbers with the stem being the left digit. Do the numbers seem to be equally distributed, or are they bunched
The Aluminum Association reports that the average American uses 56.8 pounds of aluminum in a year. A random sample of 51 households is monitored for one year to determine aluminum usage. If the population standard deviation of annual usage is 12.3 pounds, what is the probability that the sample
The average cost of a one-bedroom apartment in a town is $550 per month.What is the probability of randomly selecting a sample of 50 one-bedroom apartments in this town and getting a sample mean of less than $530 if the population standard deviation is $100?
In an effort to cut costs and improve profits, many U.S.companies have been turning to outsourcing. In fact, according to Purchasing magazine, 54% of companies surveyed outsourced some part of their manufacturing process in the past two to three years. Suppose 565 of these companies are
A directory of personal computer retail outlets in the United States contains 12,080 alphabetized entries.Explain how systematic sampling could be used to select a sample of 300 outlets.
A researcher is conducting a study of a Fortune 500 company that has factories, distribution centers, and retail outlets across the country. How can she use cluster or area sampling to take a random sample of employees of this firm?
Suppose you are sending out questionnaires to a randomly selected sample of 100 managers. The frame for this study is the membership list of the American Managers Association. The questionnaire contains demographic questions about the company and its top manager. In addition, it asks questions
A survey of 2,645 consumers by DDB Needham Worldwide of Chicago for public relations agency Porter/Novelli showed that how a company handles a crisis when at fault is one of the top influences in consumer buying decisions,with 73% claiming it is an influence. Quality of product was the number one
Suppose the average client charge per hour for out-ofcourt work by lawyers in the state of Iowa is $125. Suppose further that a random telephone sample of 32 lawyers in Iowa is taken and that the sample average charge per hour for out-of-court work is $110. If the population variance is $525, what
A company has 1,250 employees, and you want to take a simple random sample of n = 60 employees. Explain how you would go about selecting this sample by using the table of random numbers. Are there numbers that you cannot use? Explain.
A particular automobile costs an average of $17,755 in the Pacific Northwest. The standard deviation of prices is $650. Suppose a random sample of 30 dealerships in Washington and Oregon is taken, and their managers are asked what they charge for this automobile.What is the probability of getting a
Determine a possible frame for conducting random sampling in each of the following studies.a. The average amount of overtime per week for production workers in a plastics company in Pennsylvaniab. The average number of employees in all Alpha/Beta supermarkets in Californiac. A survey of commercial
Candidate Jones believes she will receive .55 of the total votes cast in her county. However, in an attempt to validate this figure, her pollster contacts a random sample of 600 registered voters in the county. The poll results show that 298 of the voters say they are committed to voting for her.
Suppose the age distribution in a city is as follows.Under 18 22%18–25 18%26–50 36%51–65 10%Over 65 14%A researcher is conducting proportionate stratified random sampling with a sample size of 250. Approximately how many people should he sample from each stratum?
Forty-six percent of a population possesses a particular characteristic. Random samples are taken from this population.Determine the probability of each of the following occurrences.a. The sample size is 60 and the sample proportion is between .41 and .53.b. The sample size is 458 and the sample
The mean of a population is 76 and the standard deviation is 14. The shape of the population is unknown.Determine the probability of each of the following occurring from this population.a. A random sample of size 35 yielding a sample mean of 79 or moreb. A random sample of size 140 yielding a
A Travel Weekly International Air Transport Association survey asked business travelers about the purpose for their most recent business trip. Nineteen percent responded that it was for an internal company visit. Suppose 950 business travelers are randomly selected.a. What is the probability that
According to a survey by Accountemps, 48% of executives believe that employees are most productive on Tuesdays. Suppose 200 executives are randomly surveyed.a. What is the probability that fewer than 90 of the executives believe employees are most productive on Tuesdays?b. What is the probability
According to a study by Decision Analyst, 21% of the people who have credit cards are very close to the total limit on the card(s). Suppose a random sample of 600 credit card users is taken.What is the probability that more than 150 credit card users are very close to the total limit on their
If a population proportion is .28 and if the sample size is 140, 30% of the time the sample proportion will be less than what value if you are taking random samples?
Suppose a population proportion is .40, and 80% of the time when you draw a random sample from this population you get a sample proportion of .35 or more.How large a sample were you taking?
A population proportion is .58. Suppose a random sample of 660 items is sampled randomly from this population.a. What is the probability that the sample proportion is greater than .60?b. What is the probability that the sample proportion is between .55 and .65?c. What is the probability that the
A given population proportion is .25. For the given value of n, what is the probability of getting each of the following sample proportions?a. n = 110 and pn … .21b. n = 33 and pn 7 .24c. n = 59 and .24 … pn 6 .27d. n = 80 and pn 6 .30e. n = 800 and pn 6 .30
According to Nielsen Media Research, the average number of hours of TV viewing per household per week in the United States is 50.4 hours. Suppose the standard deviation is 11.8 hours and a random sample of 42 U.S. households is taken.a. What is the probability that the sample average is more than
Suppose the average checkout tab at a large supermarket is $65.12, with a standard deviation of $21.45. Twenty-three percent of the time when a random sample of 45 customer tabs is examined, the sample average should exceed what value?
Suppose a subdivision on the southwest side of Denver, Colorado, contains 1,500 houses. The subdivision was built in 1983. A sample of 100 houses is selected randomly and evaluated by an appraiser. If the mean appraised value of a house in this subdivision for all houses is $177,000, with a
The Statistical Abstract of the United States published by the U.S. Census Bureau reports that the average annual consumption of fresh fruit per person is 99.9 pounds.The standard deviation of fresh fruit consumption is about 30 pounds. Suppose a researcher took a random sample of 38 people and had
Find the probability in each case. a. N=1000, n=60, = 75, and = 6; P(x < 76.5) = ? b. N=90, n=36, = 108, and = 3.46; P(107 < x < 107.7) = ? c. N=250, n=100, = 35.6, and o=4.89; P(x36) = ? d. N=5000, n=60, p = 125, and = 13.4; P(x 123) = ?
A random sample of size 81 is drawn from a population with a standard deviation of 12. If only 18% of the time a sample mean greater than 300 is obtained, what is the mean of the population?
Suppose a random sample of size 36 is drawn from a population with a mean of 278.If 86% of the time the sample mean is less than 280, what is the population standard deviation?
A population is normally distributed, with a mean of 23.45 and a standard deviation of 3.8.What is the probability of each of the following?a. Taking a sample of size 10 and obtaining a sample mean of 22 or moreb. Taking a sample of size 4 and getting a sample mean of more than 26
A population has a mean of 50 and a standard deviation of 10. If a random sample of 64 is taken, what is the probability that the sample mean is each of the following?a. Greater than 52b. Less than 51c. Less than 47d. Between 48.5 and 52.4e. Between 50.6 and 51.3
Give an example of how convenience sampling could be used in a study of Fortune 500 executives to measure corporate attitude toward paternity leave for employees.
Give an example of how judgment sampling could be used in a study to determine how district attorneys feel about attorneys advertising on television.
For each of the following research projects, list at least one area or cluster that could be used in obtaining the sample.a. A study of road conditions in the state of Missourib. A study of U.S. offshore oil wellsc. A study of the environmental effects of petrochemical plants west of the
If a company employs 3,500 people and if a random sample of 175 of these employees has been taken by systematic sampling, what is the value of k? The researcher would start the sample selection between what two values? Where could the researcher obtain a frame for this study?
If every 11th item is systematically sampled to produce a sample size of 75 items, approximately how large is the population?
A city’s telephone book lists 100,000 people. If the telephone book is the frame for a study, how large would the sample size be if systematic sampling were done on every 200th person?
In each of the following cases, the variable represents one way that a sample can be stratified in a study. For each variable, list some strata into which the variable can be divided.a. Age of respondent (person)b. Size of company (sales volume)c. Size of retail outlet (square feet)d. Geographic
For each of the following research projects, list three variables for stratification of the sample.a. A nationwide study of motels and hotels is being conducted. An attempt will be made to determine the extent of the availability of online links for customers. A sample of motels and hotels will be
Use the random numbers in Table A.1 of Appendix A to select 10 of the companies from the 30 companies listed in Table 7.2. Compare the types of companies in your sample with the types in the population. How representative of the population is your sample?
Make a list of 20 people you know. Include men and women, various ages, various educational levels, and so on. Number the list and then use the random number list in Table 7.1 to select six people randomly from your list. How representative of the population is the sample? Find the proportion of
Develop a frame for the population of each of the following research projects.a. Measuring the job satisfaction of all union employees in a companyb. Conducting a telephone survey in Utica, New York, to determine the level of interest in opening a new hunting and fishing specialty store in the
A restaurant averages 4.51 customers per 10 minutes during the summer in the late afternoon. Shown here are Excel and Minitab output for this restaurant. Discuss the type of distribution used to analyze the data and the meaning of the probabilities. Exponential Distribution x Value 0.1 Probability
Suppose the Minitab output shown here represents the analysis of the length of home-use cell phone calls in terms of minutes. Describe the distribution of cell phone call lengths and interpret the meaning of the probability statements. CUMULATIVE DISTRIBUTION FUNCTION Normal with mean = 2.35 and
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