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theory of statistics

Basic Statistics For Business And Economics 6th Edition Douglas Lind, William Marchal, Samuel Wathen - Solutions

Most air travelers now use e-tickets. Electronic ticketing allows passengers to not worry about a paper ticket, and it costs the airline companies less to handle than paper ticketing. However, in recent times the airlines have received complaints from passengers regarding their e-tickets,
The Rocky Mountain district sales manager of Rath Publishing, Inc., a college textbook publishing company, claims that the sales representatives make an average of 40 sales calls per week. Several reps say that this estimate is too low. To investigate, a random sample of 28 sales representatives
Given the following hypothesis:For a random sample of 12 observations, the sample mean was 407 and the sample standard deviation 6. Using the .01 significance level:a. State the decision rule.b. Compute the value of the test statistic.c. What is your decision regarding the null hypothesis? Ho: u =
Given the following hypothesis:For a random sample of 10 observations, the sample mean was 12 and the sample standard deviation 3. Using the .05 significance level:a. State the decision rule.b. Compute the value of the test statistic.c. What is your decision regarding the null hypothesis? S H: > 10
The mean life of a battery used in a digital clock is 305 days. The lives of the batteries follow the normal distribution. The battery was recently modified to last longer. A sample of 20 of the modified batteries had a mean life of 311 days with a standard deviation of 12 days. Did the
The McFarland Insurance Company Claims Department reports the mean cost to process a claim is $60. An industry comparison showed this amount to be larger than most other insurance companies, so the company instituted cost-cutting measures. To evaluate the effect of the cost-cutting measures, the
At the time she was hired as a server at the Grumney Family Restaurant, Beth Brigden was told, “You can average more than $80 a day in tips.” Assume the standard deviation of the population distribution is $3.24. Over the first 35 days she was employed at the restaurant, the mean daily amount
A recent national survey found that high school students watched an average (mean) of 6.8 DVDs per month with a population standard deviation of 0.5 hours. A random sample of 36 college students revealed that the mean number of DVDs watched last month was 6.2.At the .05 significance level, can we
The MacBurger restaurant chain claims that the mean waiting time of customers is 3 minutes with a population standard deviation of 1 minute. The quality-assurance department found in a sample of 50 customers at the Warren Road MacBurger that the mean waiting time was 2.75 minutes. At the .05
The manufacturer of the X-15 steel-belted radial truck tire claims that the mean mileage the tire can be driven before the tread wears out is 60,000 miles. The population standard deviation of the mileage is 5,000 miles. Crosset Truck Company bought 48 tires and found that the mean mileage for its
A sample of 64 observations is selected from a normal population.The sample mean is 215, and the population standard deviation is 15.Conduct the following test of hypothesis using the .03 significance level.(a) Is this a one- or two-tailed test?(b) What is the decision rule? (c) What is the value
A sample of 36 observations is selected from a normal population.The sample mean is 21, and the population standard deviation is 5.Conduct the following test of hypothesis using the .05 significance level.(a) Is this a one- or two-tailed test?(b) What is the decision rule? (c) What is the value of
The following information is available.The sample mean is 12 for a sample of 36. The population standard deviation is 3. Use the .02 significance level.(a) Is this a one- or two-tailed test?(b) What is the decision rule? (c) What is the value of the test statistic? (d)What is your decision
The following information is available.The sample mean is 49, and the sample size is 36. The population standard deviation is 5. Use the .05 significance level.(a) Is this a one- or two-tailed test?(b) What is the decision rule? (c) What is the value of the test statistic? (d)What is your decision
Refer to Self-Review 10–1.(a) Suppose the next to the last sentence is changed to read: Does this evidence suggest that the mean amount dispensed is more than 16 ounces? State the null hypothesis and the alternate hypothesis under these conditions.(b) What is the decision rule under the new
Heinz, a manufacturer of ketchup, uses a particular machine to dispense 16 ounces of its ketchup into containers. From many years of experience with the particular dispensing machine, Heinz knows the amount of product in each container follows a normal distribution with a mean of 16 ounces and a
Jamestown Steel Company manufactures and assembles desks and other office equipment at several plants in western New York State. The weekly production of the Model A325 desk at the Fredonia Plant follows a normal probability distribution with a mean of 200 and a standard deviation of 16. Recently,
Distinguish between a one-tailed and a two-tailed test of hypothesis.
Describe the five-step hypothesis-testing procedure
Define a hypothesis and hypothesis testing.
Refer to the CIA data, which report demographic and economic information on 46 countries.a. Develop a 90 percent confidence interval for the mean percent of the population age 65 years or older.b. Develop a 90 percent confidence interval for the mean Gross Domestic Product (GDP) per
Refer to the Wage data, which report information on annual wages for a sample of 100 workers. Also included are variables relating to industry, years of education, and gender for each worker.a. Develop a 95 percent confidence interval for the mean wage of the workers. Is it reasonable to conclude
Refer to the Baseball 2006 data, which report information on the 30 Major League Baseball teams for the 2006 season.a. Develop a 95 percent confidence interval for the mean number of home runs per team.b. Develop a 95 percent confidence interval for the mean number of errors committed by each
Refer to the Real Estate data, which report information on the homes sold in Denver, Colorado, last year.a. Develop a 95 percent confidence interval for the mean selling price of the homes.b. Develop a 95 percent confidence interval for the mean distance the home is from the center of the city.c.
The online edition of the Information Please Almanac is a valuable source of business information. Go to the website at www.infoplease.com. On the left, click on Business. Then in the Almanac section, click on Taxes, then on State Taxes on Individuals. The result is a listing of the 50 states and
Yahoo is an excellent source of business information. It includes daily summaries as well as information about various industries and specific companies. Go to the site http://finance.yahoo.com. About halfway down the page on the left side, click on Industries and then select Chemicals—Major
The Tennessee Tourism Institute (TTI) plans to sample information center visitors entering the state to learn the fraction of visitors who plan to camp in the state. Current estimates are that 35 percent of visitors are campers. How large a sample would you take to estimate at a 95 percent
Huntington National Bank, like most other large banks, found that using automatic teller machines (ATMs) reduces the cost of routine bank transactions. Huntington installed an ATM in the corporate offices of Fun Toy Company. The ATM is for the exclusive use of Fun’s 605 employees. After several
You plan to conduct a survey to find what proportion of the workforce has two or more jobs. You decide on the 95 percent confidence level and state that the estimated proportion must be within 2 percent of the population proportion. A pilot survey reveals that 5 of the 50 sampled hold two or more
A film alliance used a random sample of 50 U.S. citizens to estimate that the typical American spent 78 hours watching videos and DVDs last year. The standard deviation of this sample was 9 hours.a. Develop a 95 percent confidence interval for the population mean number of hours spent watching
A random sample of 25 people employed by the Florida Department of Transportation earned an average wage (including benefits) of$65.00 per hour. The sample standard deviation was $6.25 per hour.a. What is the population mean? What is the best estimate of the population mean?b. Develop a 99 percent
Passenger comfort is influenced by the amount of pressurization in an airline cabin. Higher pressurization permits a closer-to-normal environment and a more relaxed flight. A study by an airline user group recorded the corresponding air pressure on 30 randomly chosen flights. The study revealed a
Families USA, a monthly magazine that discusses issues related to health and health costs, surveyed 20 of its subscribers. It found that the mean annual health insurance premium for a family with coverage through an employer was $10,979. The standard deviation of the sample was $1,000.a. Based on
You need to estimate the mean number of travel days per year for pharmaceutical sales representatives. The mean of a small pilot study was 150 days, with a standard deviation of 14 days. If you must estimate the population mean within 2 days, how many sales representative in the pharmaceutical
Police Chief Edward Wilkin of River City reports 500 traffic citations were issued last month. A sample of 35 of these citations showed the mean amount of the fine was $54, with a standard deviation of $4.50. Construct a 95 percent confidence interval for the mean amount of a citation in River City.
Dr. Susan Benner is an industrial psychologist. She is currently studying stress among executives of Internet companies. She has developed a questionnaire that she believes measures stress. A score above 80 indicates stress at a dangerous level. A random sample of 15 executives revealed the
Warren County Telephone Company claims in its annual report that“the typical customer spends $60 per month on local and longdistance service.” A sample of 12 subscribers revealed the following amounts spent last month.a. What is the point estimate of the population mean?b. Develop a 90 percent
The National Collegiate Athletic Association (NCAA) reported that the mean number of hours spent per week on coaching and recruiting by college football assistant coaches during the season was 70. A random sample of 50 assistant coaches showed the sample mean to be 68.6 hours, with a standard
A recent study of 50 self-service gasoline stations in the Greater Cincinnati–Northern Kentucky metropolitan area revealed that the mean price of unleaded gas was $2.799 per gallon. The sample standard deviation was $0.03 per gallon.a. Determine a 99 percent confidence interval for the population
Past surveys reveal that 30 percent of tourists going to Las Vegas to gamble during a weekend spend more than $1,000. Management wants to update this percentage.a. The new study is to use the 90 percent confidence level. The estimate is to be within 1 percent of the population proportion. What is
Suppose the U.S. president wants an estimate of the proportion of the population who support his current policy toward revisions in the Social Security system. The president wants the estimate to be within.04 of the true proportion. Assume a 95 percent level of confidence.The president’s
A processor of carrots cuts the green top off each carrot, washes the carrots, and inserts six to a package. Twenty packages are inserted in a box for shipment. To test the weight of the boxes, a few were checked. The mean weight was 20.4 pounds, the standard deviation 0.5 pounds. How many boxes
Will you assist the college registrar in determining how many transcripts to study? The registrar wants to estimate the arithmetic mean grade point average (GPA) of all graduating seniors during the past 10 years. GPAs range between 2.0 and 4.0. The mean GPA is to be estimated within plus or minus
The study in the previous example also estimates the proportion of cities that have private refuse collectors. The student wants the margin of error to be within .10 of the population proportion, the desired level of confidence is 90 percent, and no estimate is available for the population
There are 300 welders employed at Maine Shipyards Corporation. A sample of 30 welders revealed that 18 graduated from a registered welding course. Construct the 95 percent confidence interval for the proportion of all welders who graduated from a registered welding course.
A student in public administration wants to determine the mean amount members of city councils in large cities earn per month as remuneration for being a council member. The error in estimating the mean is to be less than $100 with a 95 percent level of confidence. The student found a report by the
The same study of church contributions in Scandia revealed that 15 of the 40 families sampled attend church regularly. Construct the 95 percent confidence interval for the proportion of families attending church regularly. Should the finite-population correction factor be used? Why or why not
Thirty-six items are randomly selected from a population of 300 items. The sample mean is 35 and the sample standard deviation 5.Develop a 95 percent confidence interval for the population mea
There are 250 families in Scandia, Pennsylvania. A random sample of 40 of these families revealed the mean annual church contribution was $450 and the standard deviation of this was $75.Could the population mean be $445 or $425?1. What is the population mean? What is the best estimate of the
The Fox TV network is considering replacing one of its prime-time crime investigation shows with a new family-oriented comedy show.Before a final decision is made, network executives commission a sample of 400 viewers. After viewing the comedy, 250 indicated they would watch the new show and
Ms. Maria Wilson is considering running for mayor of the town of Bear Gulch, Montana. Before completing the petitions, she decides to conduct a survey of voters in Bear Gulch. A sample of 400 voters reveals that 300 would support her in the November election.a. Estimate the value of the population
The owner of the West End Kwick Fill Gas Station wishes to determine the proportion of customers who use a credit card or debit card to pay at the pump. He surveys 100 customers and finds that 80 paid with a credit card or a debit card at the pump.a. Estimate the value of the population
A market survey was conducted to estimate the proportion of homemakers who would recognize the brand name of a cleanser based on the shape and the color of the container. Of the 1,400 homemakers sampled, 420 were able to identify the brand by name.(a)Estimate the value of the population
The union representing the Bottle Blowers of America (BBA)is considering a proposal to merge with the Teamsters Union.According to BBA union bylaws, at least three-fourths of the union membership must approve any merger. A random sample of 2,000 current BBA members reveals 1,600 plan to vote for
The Greater Pittsburgh Area Chamber of Commerce wants to estimate the mean time workers who are employed in the downtown area spend getting to work. A sample of 15 workers reveals the following number of minutes spent traveling.Develop a 98 percent confidence interval for the population
Merrill Lynch Securities and Health Care Retirement, Inc., are two large employers in down-town Toledo, Ohio. They are considering jointly offering child care for their employees. As a part of the feasibility study, they wish to estimate the mean weekly child-care cost of their employees. A sample
Use Appendix B.2 to locate the value of t under the following conditions.a. The sample size is 15 and the level of confidence is 95 percent.b. The sample size is 24 and the level of confidence is 98 percent.c. The sample size is 12 and the level of confidence is 90 percent.
Use Appendix B.2 to locate the value of t under the following conditions.a. The sample size is 12 and the level of confidence is 95 percent.b. The sample size is 20 and the level of confidence is 90 percent.c. The sample size is 8 and the level of confidence is 99 percent.
The manager of the Inlet Square Mall, near Ft. Myers, Florida, wants to estimate the mean amount spent per shopping visit by customers. A sample of 20 customers reveals the following amounts spent.What is the best estimate of the population mean? Determine a 95 percent confidence interval.
A tire manufacturer wishes to investigate the tread life of its tires. A sample of 10 tires driven 50,000 miles revealed a sample mean of 0.32 inch of tread remaining with a standard deviation of 0.09 inch.Construct a 95 percent confidence interval for the population mean.Would it be reasonable for
Dottie Kleman is the “Cookie Lady.” She bakes and sells cookies at 50 different locations in the Philadelphia area. Ms. Kleman is concerned about absenteeism among her workers. The information below reports the number of days absent for a sample of 10 workers during the last two-week pay
Dr. Patton is a professor of English. Recently she counted the number of misspelled words in a group of student essays. She noted the distribution of misspelled words per essay followed the normal distribution with a standard deviation of 2.44 words per essay. For her 10 a.m. section of 40
Bob Nale is the owner of Nale’s Texaco GasTown. Bob would like to estimate the mean number of gallons of gasoline sold to his customers. Assume the number of gallons sold follows the normal distribution with a standard deviation of 2.30 gallons. From his records, he selects a random sample of 60
Refer to the previous exercise. Suppose that 64 smokers (instead of 49) were sampled. Assume the sample mean remained the same.a. What is the 95 percent confidence interval estimate of μ?b. Explain why this confidence interval is narrower than the one determined in the previous exercise.
A research firm conducted a survey to determine the mean amount steady smokers spend on cigarettes during a week. They found the distribution of amounts spent per week followed the normal distribution with a standard deviation of $5. A sample of 49 steady smokers revealed that = $20.a. What is the
Suppose you want an 85 percent confidence level. What value would you use to multiply the standard error of the mean by?
A sample of 81 observations is taken from a normal population with a standard deviation of 5. The sample mean is 40. Determine the 95 percent confidence interval for the population mean
A sample of 49 observations is taken from a normal population with a standard deviation of 10. The sample mean is 55. Determine the 99 percent confidence interval for the population mean.
The Bun-and-Run is a franchise fast-food restaurant located in the Northeast specializing in half-pound hamburgers, fish sandwiches, and chicken sandwiches. Soft drinks and french fries are also available. The Planning Department of Bun-and-Run, Inc., reports that the distribution of daily sales
From many years in the automobile leasing business, Town Bank knows the mean distance driven on a four-year lease is 50,000 miles and the standard deviation is 5,000. Suppose, using the MINITAB statistical software system, we want to find what proportion of the 95 percent confidence intervals will
The American Management Association wishes to have information on the mean income of middle managers in the retail industry. A random sample of 256 managers reveals a sample mean of$45,420. The standard deviation of this population is $2,050. The association would like answers to the following
Define level of confidence.
Define a point estimate.
Refer to the CIA data, which report demographic and economic information on 46 countries. Select a random sample of 10 countries.For this sample calculate the mean GDP/capita. Repeat this sampling and calculation process five more times. Then find the mean and standard deviation of your six sample
Refer to the Real Estate data, which report information on the homes sold in the Denver, Colorado, area last year.a. Compute the mean and the standard deviation of the distribution of the selling prices for the homes. Assume this to be the population.Develop a histogram of the data. Would it seem
There are several websites that will report the 30 stocks that make up the Dow Jones Industrial Average (DJIA). One site is http://www.bloomberg.com/markets/stocks/movers_index_dow.ht.Compute the mean of the 30 stocks.a. Use a random number table, such as Appendix B.6, to select a random sample of
You need to find the “typical” or mean annual dividend per share for large banks. You decide to sample six banks listed on the New York Stock Exchange. These banks and their trading symbols follow.a. After numbering the banks from 01 to 24, which banks would be included in a sample if the
Nike’s annual report says that the average American buys 6.5 pairs of sports shoes per year. Suppose the population standard deviation is 2.1 and that a sample of 81 customers will be examined next year.a. What is the standard error of the mean in this experiment?b. What is the probability that
The Oil Price Information Center reports the mean price per gallon of regular gasoline is $3.26 with a population standard deviation of$0.18. Assume a random sample of 40 gasoline stations is selected and their mean cost for regular gasoline is computed.a. What is the standard error of the mean in
Over the past decade the mean number of members of the Information Systems Security Association who have experienced a denial-of-service attack each year is 510 with a standard deviation of 14.28 attacks. Suppose nothing in this environment changes.a. What is the likelihood this group will suffer
Human Resource Consulting (HRC) is surveying a sample of 60 firms in order to study health care costs for a client. One of the items being tracked is the annual deductible that employees must pay. The state Bureau of Labor reports the mean of this distribution is $502 with a standard deviation of
The following table lists the per capita personal income for each of the 50 states in 2005.a. You wish to select a sample of eight from this list. The selected random numbers are 45, 15, 81, 09, 39, 43, 90, 26, 06, 45, 01, and 42. Which states are included in the sample?b. You wish to use a
Suppose we roll a fair die two times.a. How many different samples are there?b. List each of the possible samples and compute the mean.c. On a chart similar to Chart 8–1, compare the distribution of sample means with the distribution of the population.d. Compute the mean and the standard
The mean SAT score for Division I student-athletes is 947 with a standard deviation of 205. If you select a random sample of 60 of these students, what is the probability the mean is below 900?
Crossett Trucking Company claims that the mean weight of its delivery trucks when they are fully loaded is 6,000 pounds and the standard deviation is 150 pounds. Assume that the population follows the normal distribution. Forty trucks are randomly selected and weighed. Within what limits will 95
A recent study by the Greater Los Angeles Taxi Drivers Association showed that the mean fare charged for service from Hermosa Beach to Los Angeles International Airport is $18.00 and the standard deviation is $3.50. We select a sample of 15 fares.a. What is the likelihood that the sample mean is
The mean age at which men in the United States marry for the first time follows the normal distribution with a mean of 24.8 years. The standard deviation of the distribution is 2.5 years. For a random sample of 60 men, what is the likelihood that the age at which they were married for the first
Information from the American Institute of Insurance indicates the mean amount of life insurance per household in the United States is$110,000. This distribution follows the normal distribution with a standard deviation of $40,000.a. If we select a random sample of 50 households, what is the
Recent studies indicate that the typical 50-year-old woman spends$350 per year for personal-care products. The distribution of the amounts spent follows a normal distribution with a standard deviation of $45 per year. We select a random sample of 40 women.The mean amount spent for those sampled is
CRA CDs, Inc., wants the mean lengths of the “cuts” on a CD to be 135 seconds (2 minutes and 15 seconds). This will allow the disk jockeys to have plenty of time for commercials within each 10-minute segment. Assume the distribution of the length of the cuts follows the normal distribution with
Mattel Corporation produces a remote-controlled car that requires three AA batteries. The mean life of these batteries in this product is 35.0 hours. The distribution of the battery lives closely follows the normal probability distribution with a standard deviation of 5.5 hours. As a part of its
The Appliance Center has six sales representatives at its North Jacksonville outlet. Listed below is the number of refrigerators sold by each last month.a. How many samples of size two are possible?b. Select all possible samples of size two and compute the mean number sold.c. Organize the sample
The Quality Control Department employs five technicians during the day shift. Listed below is the number of times each technician instructed the production foreman to shut down the manufacturing process last week.a. How many different samples of two technicians are possible from this population?b.
At the downtown office of First National Bank there are five tellers.Last week the tellers made the following number of errors each: 2, 3, 5, 3, and 5.a. How many different samples of 2 tellers are possible?b. List all possible samples of size 2 and compute the mean of each.c. Compute the mean of
Suppose your statistics instructor gave six examinations during the semester. You received the following grades (percent correct): 79, 64, 84, 82, 92, and 77. Instead of averaging the six scores, the instructor indicated he would randomly select two grades and compute the final percent correct
As a part of their customer-service program, United Airlines randomly selected 10 passengers from today’s 9 a.m. Chicago–Tampa flight. Each sampled passenger is to be interviewed in depth regarding airport facilities, service, and so on. To identify the sample, each passenger was given a number
There are 25 motels in Goshen, Indiana. The number of rooms in each motel follows:a. Using a table of random numbers (Appendix B.6), select a random sample of five motels from this population.b. Obtain a systematic sample by selecting a random starting point among the first five motels and then
Answer the following questions in one or two well-constructed sentences.a. What happens to the standard error of the mean if the sample size is increased?b. What happens to the distribution of the sample means if the sample size in increased?c. When using the distribution of sample means to
The manufacturer of eMachines, an economy-priced computer, recently completed the design for a new laptop model. eMachine’s top management would like some assistance in pricing the new laptop. Two market research firms were contacted and asked to prepare a pricing strategy. Marketing-Gets-Results
List the reasons for sampling. Give an example of each reason for sampling.

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