As all baseball fans know, first base is the only base that the base runner may overrun. At both second and third base, the runner may be tagged out if he runs past the base. Consequently, on close plays at second and third base, the runner will slide, enabling him to stop at the base. In recent years, however, several players have chosen to slide headfirst when approaching first base, claiming that this is faster than simply running over the base. In an experiment to test this claim, 25 players on one National League team were recruited. Each player ran to first base with and without sliding, and the times to reach the base were recorded. Can we conclude that sliding is slower than not sliding?
> Refer to Exercise 21.9. a. Find the probability that the x chart does not detect a shift of 1.5 standard deviations on the first sample after the shift occurs. b. Compute the probability that the x chart will not detect the shift for the first eight samp
> What is meant by chance variation?
> The general manager of an engineering firm wants to know whether a draftsman’s experience influences the quality of his work. She selects 24 draftsmen at random and records their years of work experience and their quality rating (as ass
> The weekly returns of two stocks for a 13-week period were recorded and are listed here. Assuming that the returns are not normally distributed, can we infer at the 5% significance level that the stock returns are correlated? Stock 1 -7 -4 -7 -3 2 -1
> Does the number of commercials shown during a half-hour television program affect how viewers rate the show? In a preliminary study eight people were asked to watch a pilot for a situation comedy and rate the show (1 = Terrible, 2 = Bad, 3 = OK, 4 = Good
> Millions of people suffer from migraine headaches. The costs in work days lost, medication, and treatment are measured in the billions of dollars. A study reported in the Journal of the American Medical Association (2005, 203: 2118–2125) described an exp
> A statistics student asked seven first-year economics students to report their grades in the required mathematics and economics courses. The results (where 1 = F, 2 = D, 3 = C, 4 = B, 5 = A) are as follows: Calculate the Spearman rank correlation coeffi
> Is there sufficient evidence at the 5% significance level to infer that there is a positive relationship between two ordinal variables given that rs = .15 and n = 12?
> Test the following hypotheses: H: P,=0 H;: P,#0 n= 50 r,= .23 a= .05
> In recent years, insurance companies offeringmedical coverage have given discounts to companies that are committed to improving the health of their employees. To help determine whether this policy is reasonable, the general manager of onelarge insurance
> In anticipation of buying a new scanner, a student turned to a website that reported the results of surveys of users of the different scanners. A sample of 133 responses was listed showing the ease of use of five different brands. The survey responses we
> Do university students become more supportive of their varsity teams as they progress through their 4-year stint? To help answer this question, a sample of students was drawn. Each was asked their class standing (freshman, sophomore, junior, or senior) a
> It is common practice in the advertising business to create several different advertisements and then ask a random sample of potential customers to rate the ads on several different dimensions. Suppose that an advertising firm developed four different ad
> During the last presidential campaign, the Gallup organization surveyed a random sample of 30 registered Democrats in January, another 30 in February, and yet another 30 in March. All 90 Democrats were asked to “rate the chances of the Democrats winning
> A consumer testing service compared the effectiveness of four different brands of drain cleaner. The experiment consisted of using each product on 50 different clogged sinks and measuring the amount of time that elapsed until each drain became unclogged.
> A survey of statistics professors asked them to rate the importance of teaching nonparametric techniques. The possible responses are Very important Quite important Somewhat important Not too important Not important at all The professors were classified a
> An economist working for a state university wanted to acquire information about salaries in publicly funded and private colleges and universities. She conducted a survey of 623 public-university faculty members and 592 private-university faculty members
> The management of fast-food restaurants is extremely interested in knowing how their customers rate the quality of food and service and the cleanliness of the restaurants. Customers are given the opportunity to fill out customer comment cards. Suppose th
> A well-known soft-drink manufacturer has used the same secret recipe for its product since its introduction over 100 years ago. In response to a decreasing market share, however, the president of the company is contemplating changing the recipe. He has d
> Many North Americans suffer from high levels of cholesterol, which can lead to heart attacks. For those with very high levels (over 280), doctors prescribe drugs to reduce cholesterol levels. A pharmaceutical company has recently developed three such dru
> Because there are no national or regional standards, it is difficult for university admission committees to compare graduates of different high schools. University administrators have noted that an 80% average at a high school with low standards may be e
> The manager of a personnel company is in the process of examining her company’s advertising programs. Currently, the company advertises in each of the three local newspapers for a wide variety of positions, including computer programmer
> In recent years, lack of confidence in the U.S. 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
> The manager of a chain of electronicproducts retailers is trying to decide on a location for its newest store. After a thorough analysis, the choice has been narrowed to three possibilities. An important factor in the decision is the number of people pas
> Ten judges were asked to test the quality of fourdifferent brands of orange juice. The judges assigned scores using a 5-point scale where 1 = Bad, 2 = Poor, 3 = Average, 4 = Good, and 5 = Excellent. The results are shown here. Can we conclude at the 5% s
> Applicants to MBA programs must take the Graduate Management Admission Test (GMAT). There are several companies that offer assistance in preparing for the test. To determine whether they work, and if so, which one is best, an experiment was conducted. Se
> In an effort to determine whether differences exist between three methods of teaching statistics, a professor of business taught his course differently in each of three large sections. In the first section, he taught by lecturing; in the second, he taugh
> Physicians have been recommending more exercise for their patients, particularly those who are overweight. One benefit of regular exercise appears to be a reduction in cholesterol, a substance associated with heart disease. To study the relationship more
> Conduct tests of hypotheses at the 5% significance level. a. Refer to Example 19.2. Suppose that the responses were coded as follows: 100 = The drug was extremely effective. 60 = The drug was quite effective. 40 = The drug was somewhat effective. 35 = Th
> a. Refer to Example 19.6. Suppose that the responses were recoded so that the numbers equaled the midpoint of the range of percentiles. That is: 97.5 = The candidate is in the top 5% of applicants 92.5 = The candidate is in the top 10% of applicants, but
> a. A random sample of 30 people was asked to rate each of four different premium brands of coffee. The ratings are: Excellent Good Fair Poor The responses were assigned numbers 1 through 4, respectively. Can we infer that differences exist between the ra
> The following data were generated from a blocked experiment. Conduct a Friedman test to determine whether at least two population locations differ. (Use  = .05.) Treatment Block 1 3 1 73 6.9 8.4 2 8.2 7.0 7.3 3 5.7 6.0 8.1 4 6.1 6.
> Apply the Friedman test to the accompanying table of data to determine whether we can conclude that at least two population locations differ. (Use  = .10.) Treatment Block 1 2 3 4 1 10 12 15 9 8 10 11 6 3 13 14 16 11 4 9 9. 12 13 5
> a. Four random samples of 50 people each were asked to rate four different computer printers in terms of their ease of use. The responses are: Very easy to use Easy to use Difficult to use Very difficult to use The responses were coded using a 4-3-2-1 sy
> Using the Kruskal–Wallis test, determine whether there is enough evidence provided by the accompanying data to enable us to infer that at least two population locations differ. (Use  = .05.) Sample 1: 25 15 20 22
> Use the Kruskal–Wallis test on the following data to determine whether the population locations differ. (Use  = .05.) Sample 1: Sample 2: 27 33 18 29 41 52 75 37 12 17 22 30 Sample 3: 19 12 33 41 28 18
> Apply the Kruskal–Wallis test and the following statistics to determine whether there is enough statistical evidence at the 10% significance level to infer that the population locations differ. T1 = 3,741 n1 = 47 T2 = 1,610 n2 = 29 T3 = 4,945 n3 = 67
> From the following statistics, use the Kruskal–Wallis test (with = .01) to determine whether the population locations differ. T1 = 1,207 n1 = 25 T2 = 1,088 n2 = 25 T3 = 1,310 n3 = 25 T4 = 1,445 n4 = 25
> How does mental outlook affect a person’s health? The answer to this question may allow physicians to care more effectively for their patients. In an experiment to examine the relationship between attitude and physical health, Dr. Daniel Mark, a heart sp
> Conduct the Kruskal–Wallis test on the following statistics. Use a 5% significance level. T, = 984 n, = 23 T2 = 1,502 n2 = 36 T3 = 1,430 n3 = 29
> Conduct tests of hypotheses at the 5% significance level. a. To determine whether the satisfaction rating of an airline differs between business class and economy class, a survey was performed. Random samples of both groups were asked to rate their satis
> Some movie studios believe that by adding sexually explicit scenes to the home video version of a movie, they can increase the movie’s appeal and profitability. A studio executive decided to test this belief. She organized a study that involved 40 movies
> Admissions officers at universities and colleges face the problem of comparing grades achieved at different high schools. As a step toward developing a more informed interpretation of such grades, an admissions officer at a large state university conduct
> In a study to determine whether gender affects salary offers for graduating MBA students, 45 pairs of students were selected. Each pair consisted of a male and a female student who had almost identical grade-point averages, courses taken, ages, and previ
> Do children feel less pain than adults? That question was addressed by nursing professors at the University of Alberta and the University of Saskatchewan. Suppose that in a preliminary study, 50 8-year-old children and their mothers were subjected to mod
> Does the brand name of an ice cream affect consumers’ perceptions of it? The marketing manager of a major dairy pondered this question. She decided to ask 60 randomly selected people to taste the same flavor of ice cream in two different dishes. The dish
> A large sporting-goods store located in Florida is planning a renovation that will result in an increase in the floor space for one department. The manager of the store has narrowed her choice about which department’s floor space to increase to two possi
> A locksmith is in the process of selecting a new key-cutting machine. If there is a difference in key-cutting speed between the two machines under consideration, he will purchase the faster one. If there is no difference, he will purchase the cheaper mac
> At the height of the energy shortage during the 1970s, governments were actively seeking ways to persuade consumers to reduce their energy consumption. Among other efforts undertaken, several advertising campaigns were launched. To provide input on how t
> Conduct tests of hypotheses at the 5% significance level. a. In a taste test of a new beer, 25 people rated the new beer and another 25 rated the leading brand on the market. The possible ratings were Poor, Fair, Good, Very Good, and Excellent. The respo
> Suppose that the housework study referred to in Exercise 19.10 was repeated with some changes. In the revised experiment, 60 women were asked last year and again this year how many hours of housework they perform weekly. Can we conclude at the 1% signifi
> Research scientists at a pharmaceutical company have recently developed a new nonprescription sleeping pill. They decide to test its effectiveness by measuring the time it takes for people to fall asleep after taking the pill. Preliminary analysis indica
> a. Data from a matched pairs experiment were recorded. Use the sign test to determine whether the population locations differ. b. Repeat Part (a) using the Wilcoxon signed rank sum test. c. Why do the results of Parts (a) and (b) differ?
> a. Data from a matched pairs experiment were recorded. Use the sign test to determine whether the population locations differ. b. Repeat Part (a) using the Wilcoxon signed rank sum test. c. Why do the answers to Parts (a) and (b) differ?
> a. A random sample of 50 people was asked to rate two brands of ice cream using the following responses: Delicious OK Not bad Terrible The responses were converted to codes 4, 3, 2, and 1, respectively. Can we infer that Brand A is preferred? b. The resp
> a. In a taste test of a new beer 100 people rated the new beer and the leading brand on the market. The possible ratings were Poor, Fair, Good, Very good, and Excellent. The responses for the new beer and the leading beer were recorded using a 1-2-3-4-5
> Perform the Wilcoxon signed rank sum test to determine whether the location of population 1 differs from the location of population 2 given the data shown here. (Use  = .05.) 1 2 3 4 5 6 7 8 9 10 11 12 Sample 1 18.2 14.1 245 11.9 9
> Perform the Wilcoxon signed rank sum test for the following matched pairs to determine whether the two population locations differ. (Use  = .10.) Pair 1 3 4 5 6. Sample 1 Sample 2 9 12 13 8 7 10 10 11 9 3 9
> A matched pairs experiment produced the following statistics. Conduct a Wilcoxon signed rank sum test to determine whether the location of population 1 is to the right of the location of population 2. (Use = .01.) T+ = 3,457 T− = 2,429 n = 108
> Betting on the results of National Football League games is a popular North American activity. In some states and provinces, it is legal to do so provided that wagers are made through a government-authorized betting organization. In the province of Ontar
> Use the Wilcoxon Rank Sum Test on the following data to determine whether the two population locations differ. (Use a 10% significance level.) Sample 1: 15 7 22 20 32 18 26 17 23 30 Sample 2: 8 27 17 25 20 16 21 17 10 18
> Given the following statistics from a matched pairs experiment, perform the Wilcoxon signed rank sum test to determine whether we can infer at the 5% significance level that the two population locations differ. T+ = 660 T− = 880 n = 55
> Use the sign test on the following data to determine whether the location of population 1 is to the right of the location of population 2. (Use  = .05.) Pair: 12 3 4 5 6 789 10 11 12 13 14 15 16 Sample 1 5 3 4 2 3 4 3 5 4 3 4 5 4 5
> A matched pairs experiment yielded the following results: Positive differences: 18 Zero differences: 0 Negative differences: 12 Can we infer at the 5% significance level that the location of population 1 is to the right of the location of population 2?
> Suppose that in a matched pairs experiment we find 28 positive differences, 7 zero differences, and 41 negative differences. Can we infer at the 10% significance level that the location of population 1 is to the left of the location of population 2?
> In a matched pairs experiment, if we find 30 negative, 5 zero, and 15 positive differences, perform the sign test to determine whether the two population locations differ. (Use a 5% significance level.)
> Use the Wilcoxon Rank Sum Test on the following data to determine whether the location of population 1 is to the left of the location of population 2. (Use  = .05.) Sample 1: 75 60 73 66 81 Sample 2: 90 72 103 82 78
> These problems can be solved manually or by creating an Excel spreadsheet. a. From the following statistics, test (with = .05) to determine whether the location of population 1 is to the right of the location of population 2. t1 = 1,205 n1 = 30 t2 = 1
> Burger King Restaurants regularly survey customers to determine how well they are doing. Suppose that a survey asked customers to rate (among other things) the speed of service. The responses are 1 = Poor 2 = Good 3 = Very good 4 = Excellent The response
> Do the ways that women dress influence the ways that other women judge them? This question was addressed by a researcher at Ohio State University (Working Mother, April 1992). The experiment consisted of asking women to rate how professional two women lo
> There are enormous differences between health-care systems in the United States and Canada. In a study to examine one dimension of these differences, 300 heart attack victims in each country were randomly selected. (Results of the study conducted by Dr.
> Can you become addicted to exercise? In a study conducted at the University of Wisconsin at Madison, a random sample of dedicated exercisers who usually work out every day was drawn. Each completed a questionnaire that gauged their mood on a 5-point scal
> How does alcohol affect judgment? To provide some insight, an experiment was conducted. A random sample of customers of an Ohio club was selected. Each respondent was asked to assess the attractiveness of members of the opposite sex who were in the club
> According to a CNN news report 9% of full-time workers telecommute. This means that they do not work in their employers’ offices but instead perform their work at home using a computer and modem. To ascertain whether such workers are more satisfied than
> It is an unfortunate fact of life that the characteristics that one is born with play a critical role in later life. For example, race is a critical factor in almost all aspects of North American life. Height and weight also determine how friends, teache
> How does gender affect teaching evaluations? Several researchers addressed this question during the past decade. In one study several female and male professors in the same department with similar backgrounds were selected. A random sample of 100 female
> Scientists have been studying the effects of lead in children’s blood, bones, and tissue for a number of years. It is known that lead reduces intelligence and can cause a variety of other problems. A study directed by Dr. Herman Needleman, a psychiatrist
> The town of Stratford, Ontario, is very much dependent on the Shakespearean Festival it holds every summer for its financial well-being. Thousands of people visit Stratford to attend one or more Shakespearean plays and spend money in hotels, restaurants,
> To examine the effect that a tough midterm test has on student evaluations of professors, a statistics professor had her class evaluate her teaching effectiveness before the midterm test. The questionnaire asked for opinions on a number of dimensions, bu
> The increasing number of traveling businesswomen represents a large potential clientele for the hotel industry. Many hotel chains have made changes designed to attract more women. To help direct these changes, a hotel chain commissioned a study to determ
> It is common practice in many MBA programs to require applicants to arrange for a letter of reference. Some universities have their own forms in which referees assess the applicant using the following categories: 5: The candidate is in the top 5% of appl
> Several years ago we heard about the “Mommy Track,” the phenomenon of women being underpaid in the corporate world because of what is seen as their divided loyalties between home and office. There may also be a “Daddy Differential,” which refers to the s
> The president of Tastee Inc., a babyfood producer, claims that her company’s product is superior to that of her leading competitor because babies gain weight faster with her product. As an experiment, 40 healthy newborn infants are randomly selected. For
> In a Gallup poll this year, 200 people were asked, “Do you feel that the newspaper you read most does a good job of presenting the news?” The same question was asked of another 200 people 10 years ago. The possible responses were as follows: 3 = Good job
> Researchers at the U.S. National Institute of Aging in Bethesda, Maryland, have been studying hearing loss. They have hypothesized that as men age they will lose their hearing faster than comparably aged women because many more men than women have worked
> An advertising firm wants to determine the relative effectiveness of two recently produced commercials for a car dealership. An important attribute of such commercials is their believability. To judge this aspect of the commercials, 60 people were random
> Samuel’s is a chain of family restaurants. Like many other service companies, Samuel’s surveys its customers on a regular basis to monitor their opinions. Two questions (among others) asked in the survey are as follows: a. While you were at Samuel’s, did
> In recent years, consumers have become more safety conscious, particularly about children’s products. A manufacturer of children’s pajamas is looking for material that is as nonflammable as possible. In an experiment to compare a new fabric with the kind
> The printing department of a publishing company wants to determine whether there are differences in durability between three types of book bindings. Twenty-five books with each type of binding were selected and placed in machines that continually opened
> Suppose that a precise measuring device for new hair growth has been developed and is used in the experiment described in Exercise 19.122. The percentages of new hair growth for the 30 pairs of men involved in the experiment were recorded. Do these data
> Large potential profits for pharmaceutical companies exist in the area of hair growth drugs. The head chemist for a large pharmaceutical company is conducting experiments to determine which of two new drugs is more effective in growing hair among balding
> The editor of the student newspaper was in the process of making some major changes in the newspaper’s layout. He was also contemplating changing the typeface of the print used. To help make a decision, he set up an experiment in which 20 individuals wer
> A new antiflu vaccine designed to reduce the duration of symptoms has been developed. However, the effect of the drug varies from person to person. To examine the effect of age on the effectiveness of the drug, a sample of 140 flu sufferers was drawn. Ea
> The researchers at a large carpet manufacturer have been experimenting with a new dyeing process in hopes of reducing the streakiness that frequently occurs with the current process. As an experiment, 15 carpets are dyed using the new process, and anothe
> Certain drugs differ in their side effects depending on the gender of the patient. In a study to determine whether men or women suffer more serious side effects when taking a powerful penicillin substitute, 50 men and 50 women were given the drug. Each w
> In a study to determine which of two teaching methods is perceived to be better, two sections of an introductory marketing course were taught in different ways by the same professor. At the course’s completion, each student rated the course on a boring/s
> Are education and income related? To answer this question, a random sample of peoplewas selected and each was asked to indicate into which of the following categories of education they belonged: 1. Less than high school 2. High school graduate 3. Some co
> The American public’s support for the space program is important for the program’s continuation and for the financial health of the aerospace industry. In a poll conducted by the Gallup organization last year, a random sample of 100 Americans was asked,
> Gambling on sports is big business in the United States and Canada. A television executive wants to know whether the amount of money wagered on a professional football game affects the enjoyment of viewers. A random sample of 200 men who regularly watch
> explain that after they quit smoking food tastes better. To examine the relationship between smoking and taste, a researcher randomly sampled 280 smokers. Each was asked how many cigarettes they smoked on an average day. In addition, each person was aske
