Question: A study by researchers at North Carolina

> Refer to Exercise 14.14. Despite failing to show that differences in the three types of fertilizer exist, the scientist continued to believe that there were differences, and that the differences were masked by the variation between the plots of land. Acc

> In recent years, lack of confidence in the Postal Service has led many companies to send all of their correspondence by private courier. A large company is in the process of selecting one of three possible couriers to act as its sole delivery method. To

> Econetics Research Corporation, a well-known Montreal-based consulting firm, wants to test how it can influence the proportion of questionnaires returned from surveys. In the belief that the inclusion of an inducement to respond may be important, the fir

> How well do diets work? In a preliminary study, 20 people who were more than 50 pounds overweight were recruited to compare four diets. The people were matched by age. The oldest four became block 1, the next oldest four became block 2, and so on. The nu

> As an experiment to understand measurement error, a statistics professor asks four students to measure the height of the professor, a male student, and a female student. The differences (in centimeters) between the correct dimension and the ones produced

> a. Calculate SS(Total), SST, SSB, and SSE, assuming that the accompanying data were generated from a randomized block experiment. b. Calculate SS(Total), SST, and SSE, assuming that the data below were generated from a oneway (independent samples) experi

> a. Assuming that the data shown here were generated from a randomized block experiment calculate SS(Total), SST, SSB, and SSE. b. Assuming that the data below were generated from a one-way (independent samples) experiment calculate SS(Total), SST, and SS

> A randomized block experiment produced the following statistics. k = 3 b = 8 SST = 1,500 SS(Total) = 3,500 a. Test at the 5% significance level to determine whether the treatment means differ given that SSB = 500. b. Repeat Part a with SSB = 1,000. c.

> Suppose the following statistics were calculated from data gathered from a randomized block experiment with k = 4 and b = 10: SS(Total) = 1,210 SST = 275 SSB = 625 a. Can we conclude from these statistics that the treatment means differ? (Use  = .01

> A randomized block experiment produced the following statistics: k = 5 b = 12 SST = 1,500 SSB = 1,000 SS(Total) = 3,500 a. Test to determine whether the treatment means differ. (Use  = .01.) b. Test to determine whether the block means differ. (Use 

> The following statistics were generated from a randomized block experiment with k = 3 and b = 7: SST = 100 SSB = 50 SSE = 25 a. Test to determine whether the treatment means differ. (Use  = .05.) b. Test to determine whether the block means differ. (U

> Are the data in Exercise 13.18 observational or experimental? Explain. If the data are observational, describe a method of producing experimental data.

> Refer to Exercise 13.17. If the data are observational, describe another conclusion other than the one that infers that Tastee is better for babies. Data from Exercise 13.17: The president of Tastee Inc., a baby-food producer, claims that her company’s

> One of the issues that came up in a recent national election (and is likely to arise in many future elections) is how to deal with a sluggish economy. Specifically, should governments cut spending, raise taxes, inflate the economy (by printing more money

> Random sampling from two normal populations produced the following results: x1 = 412 s1 = 128 n1 = 150 x2 = 405 s2 = 54 n2 = 150 a. Can we infer at the 5% significance level that 1 is greater than 2? b. Repeat part (a) decreasing the standard deviatio

> A management scientist believes that one way of judging whether a computer came equipped with enough memory is to determine the age of the computer. In a preliminary study, random samples of computer users were asked to identify the brand of computer and

> Random sampling from two normal populations produced the following results: x1 = 63 s1 = 18 n1 = 50 x2 = 60 s2 = 7 n2 = 45 a. Estimate with 90% confidence the difference between the two population means. b. Repeat part (a) changing the sample standard

> Spam is the price we pay for being able to easily communicate by e-mail. Does spam affect everyone equally? In a preliminary study, university professors, administrators, and students were randomly sampled. Each person was asked to count the number of sp

> Many college and university students obtain summer jobs. A statistics professor wanted to determine whether students in different degree programs earn different amounts. A random sample of 5 students in the B.A., B.Sc., and B.B.A. programs were asked to

> Are Canadian public servants gaming the system by taking more sick days than do private sector workers? To answer the question Statistics Canada took a random sample of white-collar public servants and a random sample of white collar private sector worke

> Which Canadians give the most to charity? A Statistics Canada study took random samples of men and women and recorded the amount donated to charity in the previous year. Is there sufficient evidence to infer that there are differences between the two sex

> Refer to Exercise 13.49. The NCPA conducted another study, this one on alcohol. They randomly sample low-income and middle-income alcohol drinkers and determined how much each spends annually on alcoholic drinks. Can we infer that low-income alcoholic dr

> A consumer organization was concerned about the differences between the advertised sizes of containers and the actual amount of product. In a preliminary study, six packages of three different brands of margarine that are supposed to contain 500 ml were

> Is there a tax on the poor? The tax on income is progressive in that higher income individuals pay at a high rate than lower-income people. For example, the top 0.1 percent of taxpayers earn 9.1 percent of the income, but pay 17.4 percent of all federal

> The operations manager of a company that manufactures shirts wants to determine whether there are differences in the quality of workmanship among the three daily shifts. She randomly selects 600 recently made shirts and carefully inspects them. Each shir

> How does exercise affect memory in older adults with mild cognitive impairment? A study published in the Journal of Aging Research asked a random sample of women aged 70–80 with subjective memory complaints to exercise twice a week for six months. At the

> Researchers at the University of California, San Diego conducted an experiment that studied the sleep of 164 American adults. The researchers used a device called a polysomnography machine to document slow-wave sleep, which is thought to be the most rest

> Refer to Exercise 12.51. The researchers also recorded the number of missing teeth of a random sample of Britons. Can we infer that, in fact, Americans have more missing teeth? Data from Exercise 12.51: It is a long-running joke that Britons have bad an

> Does drinking hot chocolate boost the memory in older people? A random sample of people around the age of 73 was recruited. All had some form of cognitive deterioration. Half the participants drank two cups of hot chocolate a day for 30 days. Each was te

> Michigan State’s Collegiate Employment Research Institute collected data from mid-August to mid-September, tapping the employment offices at 200 schools, which gathered starting salary data from 3,300 employers. The starting salaries for a random sample

> In a Reason-Rupe poll, a random sample of people were asked, “Just a rough guess, what percent profit on each dollar of sales do you think the average company makes after taxes?” The results from 5 years ago and this year were recorded. Can we infer that

> Is it true that an apple a day keeps the doctor away? A study designed and conducted by the National Health and Nutrition Examination Study (results published in the Journal of the American Medical Association) considered 8,399 American adults of whom 75

> A researcher recruited 40 adults at a PTA meeting and asked them to view a video. To thank them for their participation, 20 adults were given a one-pound bag of M&Ms and the other half a half pound. All were told that they can snack on the M&Ms while the

> A group of MBA students was invited to watch a Super Bowl game at a local sports bar. They were promised free chicken wings and free soda drinks. The students loaded up on the wings and when they were eaten could refill their plates. Waitresses were pa

> How does an MBA major affect the number of job offers received? An MBA student randomly sampled four recent graduates, one each in finance, marketing, and management, and asked them to report the number of job offers. Can we conclude at the 5% significan

> The trustee of a company’s pension plan has solicited the opinions of a sample of the company’s employees about a proposed revision of the plan. A breakdown of the responses is shown in the accompanying table. Is there

> Consider a multinomial experiment involving n = 150 trials and k = 4 cells. The observed frequencies resulting from the experiment are shown in the accompanying table, and the null hypothesis to be tested is as follows: H0: p1 = .3, p2 = .3, p3 = .2, p4

> Diners at a restaurant were informed on entering that they would be receiving a free glass of wine, which they were told was Cabernet Sauvignon. However, it was not. It was a cheap wine sold for $2 a bottle, popularly known as Two Buck Chuck. Half of the

> Students were invited to watch a newly released movie shortly after lunch. Half the students were given a medium-sized bucket of popcorn and the other half a large-sized bucket. The popcorn was not fresh. In fact, it was five days old and very stale. Bot

> Studies have shown that tired children have trouble learning because neurons become incapable of forming new synaptic connections that are necessary to encode memory. The problem is that the school day starts too early. Awakened at dawn, teenage brains a

> Traditionally, wine has been sold in glass bottles with cork stoppers. The stoppers are supposed to keep air out of the bottle because oxygen is the enemy of wine, particularly red wine. Recent research appears to indicate that metal screw caps are more

> Credit scorecards were designed to be used to help financial institutions make decisions about loan applications. However, some insurance companies have suggested that credit scores could also be used to determine insurance premiums, particularly car ins

> It is generally believed that salespeople who are paid on a commission basis outperform salespeople who are paid a fixed salary. Some management consultants argue, however, that in certain industries the fixed-salary salesperson may sell more because the

> Tire manufacturers are constantly researching ways to produce tires that last longer. New innovations are tested by professional drivers on racetracks. However, any promising inventions are also test-driven by ordinary drivers. The latter tests are close

> It is often useful for companies to know who their customers are and how they became customers. In a study of credit card use, random samples were drawn of cardholders who applied for the credit card and credit cardholders who were contacted by telemarke

> Lack of sleep is a serious medical problem. It has been linked to heart attacks and automobile collisions. A Statistics Canada study asked a random sample of Canadian adults to report the amount of sleep they normally get. Can we conclude from the data t

> Between Wendy’s and McDonald’s, which fast-food drive-through window is faster? To answer the question, a random sample of service times for each restaurant was measured. Can we infer from these data that there are differences in service times between th

> Conduct a test to determine whether the two classifications R and C are independent, using the data in the accompanying cross-classification table. (Use  = .10.) C3 R, R2 40 32 48 30 48 52

> The following statistics were calculated: a. Complete the ANOVA table. b. Repeat part (a) changing the sample means to 130, 135, 133, and 140. c. Describe the effect on the F-statistic of increasing the sample means by 100. Treatment Statistic 1 2 3

> Most consumers who require someone to perform various professional services undertake research before making their selection. A random sample of people who recently selected a financial planner and a random sample of individuals who chose a stockbroker w

> Refer to Exercise 13.26. To determine whether the type of phone usage affects reaction times, another study was launched. A group of drivers was asked to participate in a discussion. Half the group engaged in simple chitchat, and the other half participa

> Recent studies seem to indicate that using a cell phone while driving is dangerous. One reason for this is that a driver’s reaction time may slow while he or she is talking on the phone. Researchers at Miami (Ohio) University measured the reaction times

> After determining in Exercise 13.229 that teenagers watch more movies than do 20–30-year-olds, teenagers were further segmented into three age groups: 12 to 14, 15 to 16, and 17 to 19. Random samples were drawn from each segment, and the number of movies

> You are given the following statistics: a. Complete the ANOVA table. b. Repeat part (a) changing the variances to 25 each. c. Describe the effect on the F-statistic of increasing the sample variances. Treatment Statistic 1 2 n 4 4 4 20 22 25 10 10 1

> A manufacturer of novelty items is undecided about the price to charge for a new product. The marketing manager knows that it should sell for about $10 but is unsure of whether sales will vary significantly if it is priced at either $9 or $11. To conduct

> There is a bewildering number of breakfast cereals on the market. Each company produces several different products in the belief that there are distinct markets. For example, there is a market composed primarily of children, another for diet-conscious ad

> In 1994, the chief executive officers of the major tobacco companies testified before a U.S. Senate subcommittee. One of the accusations made was that tobacco firms added nicotine to their cigarettes, which made them even more addictive to smokers. Compa

> Review the results of Exercises 15.26–15.28. What is the effect of decreasing the sample size?

> Does the level of success of publicly traded companies affect the way their board members are paid? Publicly traded companies were divided into four quarters using the rate of return in their stocks to differentiate among the companies. The annual paymen

> A study performed by a Columbia University professor (described in Report on Business, August 1991) counted the number of times per minute professors from three different departments said “uh” or “ah” during lectures to fill gaps between words. The data

> In the introduction to this chapter, we mentioned that the first use of the analysis of variance was in the 1920s. It was employed to determine whether different amounts of fertilizer yielded different amounts of crop. Suppose that a scientist at an agri

> In early 2001, the economy was slowing down and companies were laying off workers. A Gallup poll asked a random sample of workers how long it would be before they had significant financial hardships if they lost their jobs and couldn’t find new ones. The

> A manufacturer of outdoor brass lamps and mailboxes has received numerous complaints about premature corrosion. The manufacturer has identified the cause of the problem as the low-quality lacquer used to coat the brass. He decides to replace his current

> A paint manufacturer is attempting to improve the process that fills the 1-gallon containers. The foreperson has suggested that the nozzle can be made from several different alloys. Furthermore, the way that the process “knows” when to stop the flow of p

> The headrests on a car’s front seats are designed to protect the driver and front-seat passenger from whiplash when the car is hit from behind. The frame of the headrest is made from metal rods. A machine is used to bend the rod into a U-shape exactly 44

> Are proficiency test scores affected by the education of the child’s parents? (Proficiency tests are administered to a sample of students in private and public schools. Test scores can range from 0 to 500.) To answer this question, a random sample of 9-y

> Most college instructors prefer to have their students participate actively in class. Ideally, students will ask their professor questions and answer their professor’s questions, making the classroom experience more interesting and usef

> Headaches are one of the most common, but least understood, ailments. Most people get headaches several times per month; overthe- counter medication is usually sufficient to eliminate their pain. However, for a significant proportion of people, headaches

> Repeat Exercise 15.26 using the following table: M, M2 7 17 14 9

> Detergent manufacturers frequently make claims about the effectiveness of their products. A consumer-protection service decided to test the five best selling brands of detergent, where each manufacturer claims that its product produces the “whitest white

> Refer to Exercise 14.10. Suppose that the experiment is redone in the following way. Thirty taxpayers fill out each of the four forms. However, 10 taxpayers in each group are in the lowest income bracket, 10 are in the next income bracket, and the remain

> Refer to Example 14.4. We’ve altered the data by subtracting 4 from the numbers of treatment 8. What do these data tell you? Data from Exercise 14.4: How does an MBA major affect the number of job offers received? An MBA student randomly sampled four re

> Refer to Example 14.4. We’ve revised the data by adding 2 to each of the numbers of the men. What do these data tell you? Data from Exercise 14.4: How does an MBA major affect the number of job offers received? An MBA student randomly sampled four recen

> The data shown here were taken from a 2 × 3 factorial experiment with 4 replicates: a. Test at the 5% significance level to determine whether factors A and B interact. b. Test at the 5% significance level to determine whether differences ex

> The following data were generated from a 2 × 2 factorial experiment with 3 replicates: a. Test at the 5% significance level to determine whether factors A and B interact. b. Test at the 5% significance level to determine whether differences

> A statistics practitioner conducted a two-factor analysis of variance experiment with a = 4, b = 3, and r = 8. The sums of squares are listed here: SS(Total) = 9420 SS(A) = 203 SS(B) = 859 SS(AB) = 513 a. Test at the 5% significance level to determine wh

> A two-factor analysis of variance experiment was performed with a = 3, b = 4, and r = 20. The following sums of squares were computed: SS(Total) = 42,450 SS(A) = 1,560 SS(B) = 2,880 SS(AB) = 7,605 Conduct whatever test you deem necessary at the 1% sig

> The friendly folks at the Internal Revenue Service (IRS) in the United States and Canada Revenue Agency (CRA) are always looking for ways to improve the wording and format of its tax return forms. Three new forms have been developed recently. To determin

> A statistics practitioner calculated the following statistics: a. Complete the ANOVA table. b. Repeat part (a) changing the sample sizes to 10 each. c. Describe what happens to the F-statistic when the sample sizes increase. Treatment Statistic 1 5

> Repeat Exercise 15.26 using the following table: M, M2 14 34 28 18

> The cost of health care is rising faster than most other items. To learn more about the problem a survey was undertaken to determine whether differences in health care expenditures exist between men and women. The survey randomly sampled men and women ag

> Because of the high cost of energy, homeowners in northern climates need to find ways to cut their heating costs. A building contractor wanted to investigate the effect on heating costs of increasing the insulation. As an experiment, he located a large s

> To determine the effect of advertising in the Yellow Pages, Bell Telephone took a sample of 40 retail stores that did not advertise in the Yellow Pages last year but did so this year. The annual sales (in thousands of dollars) for each store in both year

> Do waiters or waitresses earn larger tips? To answer this question, a restaurant consultant undertook a preliminary study. The study involved measuring the percentage of the total bill left as a tip for one randomly selected waiter and one randomly selec

> One measure of the state of the economy is the amount of money homeowners pay on their mortgage each month. To determine the extent of change between this year and 5 years ago, a random sample of 150 homeowners was drawn. The monthly mortgage payments fo

> The president of a large company is in the process of deciding whether to adopt a lunchtime exercise program. The purpose of such programs is to improve the health of workers and, in so doing, reduce medical expenses. To get more information, he institut

> In an effort to determine whether a new type of fertilizer is more effective than the type currently in use, researchers took 12 two-acre plots of land scattered throughout the county. Each plot was divided into two equal-size subplots, one of which was

> In a preliminary study to determine whether the installation of a camera designed to catch cars that go through red lights affects the number of violators, the number of red-light runners was recorded for each day of the week before and after the camera

> The operations manager of a manufacturer of television remote controls wants to determine which batteries last the longest in his product. He took a random sample of his remote controls and tested two brands of batteries. Here are the number of minutes o

> How effective are antilock brakes, which pump very rapidly rather than lock and thus avoid skids? As a test, a car buyer organized an experiment. He hit the brakes and, using a stopwatch, recorded the number of seconds it took to stop an ABS-equipped car

> Conduct a test to determine whether the two classifications L and M are independent, using the data in the accompanying cross-classification table. (Use  = .05.) M, M2 28 68 56 36

> Many people use scanners to read documents and store them in a Word (or some other software) file. To help determine which brand of scanner to buy, a student conducts an experiment wherein eight documents are scanned by each of the two scanners in which

> Suppose that you are analyzing one of the hundreds of statistical studies linking smoking with lung cancer. The study analyzed thousands of randomly selected people, some of whom had lung cancer. The statistics indicate that those who have lung cancer sm

> You wish to determine whether MBA graduates who majored in finance attract higher starting salaries than MBA graduates who majored in marketing. a. Describe a data-gathering process that produces observational data. b. Describe a data-gathering process t

> Put yourself in place of the director of research and development for a pharmaceutical company. When a new drug is developed it undergoes a number of tests. One of the tests is designed to determine whether the drug is safe and effective. Your company ha

> Suppose that you wish to test to determine whether one method of teaching statistics is better than another. a. Describe a data-gathering process that produces observational data. b. Describe a data-gathering process that produces experimental data.

> Refer to Exercise 13.24. a. Are the data observational or experimental? b. If the data are observational, describe a method of answering the question with experimental data? c. If the data are observational, produce another explanation for the statistica

> The owner of a small book-publishing company is concerned about the declining number of people who read books. To learn more about the problem she takes a random sample of customers in a retail book store and asked each how many books they read in the la

> A human resources manager for a car company wanted to know whether production-line workers have more days absent than office workers. He took a random sample of eight workers from each category and recorded the number of days absent the previous year. Ca

> For each of the following, determine the number of degrees of freedom assuming equal population variances and unequal population variances. a. n1 = 15, n2 = 15, s21 = 25, s22 = 15 b. n1 = 10, n2 = 16, s21 = 100, s22 = 15 c. n1 = 50, n2 = 50, s21 = 8, s22