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Two amateur gardeners are interested in comparing the yields of two varieties of tomatoes. They each have small backyard gardens. Each gardener is going to plant three plants of each variety in his garden. The first gardener will select six small areas in his garden for planting, then choose three of these at random for the three plants of the first variety and then use the remaining three for the second variety. The second gardener will follow the same procedure with his own randomization in his garden. At the end of the growing season they will compare the yields of the two varieties. In this example the gardens are blocks Does giving an incentive really work on improving exam scores? For example, consider the following treatments to measure the use of incentives: What type of study would work best? An experiment One hundred volunteers who suffer from severe depression are available for a study. Fifty are selected at random and are given a new drug that is thought to be particularly effective in treating severe depression. The other 50 are given an existing drug for treating severe depression. A psychiatrist evaluates the symptoms of all volunteers after four weeks in order to determine if there has been substantial improvement in the severity of the depression. What is the explanatory variable or factor in this study? Which drug the volunteers receive A market research company wishes to find out whether the population of students at a university prefers brand A or brand B of instant coffee. A random sample of students is selected, and each one is asked to try first brand A and then brand B, or vice versa (with the order determined at random). They then indicate which brand they prefer. The response variable is which brand they prefer You want to test the effects of water aerobics on resting heart rate. You decide to test two different levels of exercise (water aerobics for 30 minutes twice a week and water aerobics for 60 minutes once per week.) You randomly find a group of 60 (30 men and 30 women) subjects for this study. The treatment in this experiment is exercise A statistics instructor wants to know which route will get her to school the fastest. Each day from October 2 to November 15, when she gets to the turn point she checks the odometer on her car. If it shows an even number she takes the freeway; if it shows an odd number, she takes the in-town route. She records the total time each day. What is the response variable in this study? the time to school A group of college students believes that herbal tea has remarkable restorative powers. To test its theory, the group makes weekly visits to a local nursing home, visiting with residents, talking with them, and serving them herbal tea. After several months, many of the residents are more cheerful and healthy. What is the explanatory variable in this experiment? Herbal tea In order to determine if smoking causes cancer, researchers surveyed a large sample of adults. For each adult they recorded whether the person had smoked regularly at any period in their life and whether the person had cancer. They then compared the proportion of cancer cases in those who had smoked regularly at some time in their lives with the proportion of cases in those who had never smoked regularly at any point in their lives. The researchers found a higher proportion of cancer cases among those who had smoked regularly than among those who had never smoked regularly. What type of study is this? An observational study In conducting a randomized comparative experiment, an experimenter will often include a group of subjects, known as a control group, to receive a fake treatment. What is (are) the reason(s) such a control group might be included in the experiment? To enable the experimenter to control the effects of outside variables, such as lurking variables, on the outcome of the experiment. In order to be able to select a simple random sample to carry out a survey, it is necessary to define carefully the population from which information is desired and to have a list of all the members of that population. The list, from which the sample is actually selected, called the sampling frame, may not be a complete listing of the members of the population. In this case the survey will be said to suffer from undercoverage bias David A. Miller owns a small advertising business. He has nine employees. The names of the employees are given below: Determine whether each of the following statements is true or false. If we used another list of random digits to select the sample, we would get a completely different sample than that obtained with the list actually used. FALSE If we used another list of random digits to select the sample, we would get the same result as obtained with the list actually used. FALSE If we used another list of random digits to select the sample, the result obtained with the list actually used would be just as likely to be selected as any other set of three names. TRUE A call-in poll conducted by USA Today concluded that Americans love Donald Trump. This conclusion was based on data collected from 7800 calls made by USA Today readers. What sampling technique is being used? Volunteer sampling The administration at a large state university is interested in getting the opinions of students on a proposed instructional fee for use of computer labs on campus. They select a simple random sample of 50 freshmen, 50 sophomores, 50 juniors, and 50 seniors. This is an example of stratified random sample A marketing research firm wishes to determine if the adult men in Laramie, Wyoming, would be interested in a new upscale men's clothing store. From a list of all residential addresses in Laramie, the firm selects a simple random sample of 100 and mails a brief questionnaire to each. What do we know about the chance that all 100 homes in a particular neighborhood in Laramie end up being the sample of residential addresses that is selected? t is the same as for any other set of 100 residential addresses An opinion poll is to be given to a sample of 90 members of a local gym. The members are first divided into men and women, and then a simple random sample of 45 men and a separate simple random sample of 45 women are taken. What is this is an example of? A stratified random sample A study was conducted with the object of determining the effect on blood pressure and cholesterol levels in women over the age of 60 of two different strength-training programs, one involving the use of a balance ball and the other using stationary exercise equipment. Eighty women over the age of 60 were identified and randomly divided into two equal-sized experimental groups. Each member of the two groups was trained and allowed to follow the prescribed routine for eight weeks. The subjects were aware of the purpose of the study but not that there were two different treatment groups involved. The cholesterol levels and blood pressure for subjects were measured at the start and at the end of the eight weeks. The experimenter and the medical technician were not told to which group any of the subjects were assigned. This is an example of an attempt to conduct a double-blind randomized experiment. Does giving an incentive really work on improving exam scores? For example, consider the following treatments to measure the use of incentives: If a block design were used, what would be an appropriate blocking variable for this study? None of the above Do people prefer tap or bottle water? For this study, pour two water samples into two cups that are the same but marked on the bottom. Each subject then tastes both water samples and rates the taste on a 5 point scale (1 = poor to 5 = excellent.) What type of design is this? Matched-pairs design Sickle-cell disease is a painful disorder of the red blood cells that in the United States affects mostly African-Americans. To investigate whether the drug hydroxyurea can reduce the pain associated with sickle-cell disease, a study by the National Institutes of Health gave the drug to 150 sickle-cell sufferers and a placebo to another 150. The researchers then counted the number of episodes of pain reported by each subject. What is the response variable in this study? The number of episodes of pain The head of the quality control department at a publishing company is studying the effect of type of glue and type of binding on the strength of the bookbinding. The company has three possible glues to choose from and the book can either be bound as a paperback or a hardback. What is/are the factor(s) in this study? Type of glue and type of binding To investigate whether or not sending text messages while driving impacts driving ability, we have 100 participants (50 men and 50 women) drive an obstacle course under one of the following conditions: 1) No texting while driving, 2) Sending five text messages while driving, or 3) Sending 10 text messages while driving. We measure the accuracy the subjects drove the obstacle course from a scale of 1 to 10 (1= poor and 10= excellent). Why is a control necessary in this experiment? To help control for the lurking variables You want to test the effects of water aerobics on resting heart rate. You decide to test two different levels of exercise (water aerobics for 30 minutes twice a week and water aerobics for 60 minutes once per week.) You randomly find a group of 60 (30 men and 30 women) subjects for this study. Which of the following was used in this experiment? None of the above Seventy-five college students are taking part in a study initiated by a large computer manufacturer. The company is designing a new type of laptop computer and has created prototypes of it with two different keyboard designs. They are also including the current design of the laptop in the experiment. Each of the students was randomly assigned to one of the three types of computers. The students are asked to spend 15 minutes on one of the computers performing several tasks (typing words, numbers, making corrections, etc.). The ease of use of the keyboard was then rated on a five-point scale by having the students fill out a short questionnaire. Which of the following basic principles of statistical design was not used in this experiment? Blinding Ann Landers once asked her female readers whether they would be content with affectionate treatment from men, with no sex ever. Over 90,000 women wrote in, with 72% answering "Yes." Why shouldn't we believe the results of this "poll?" It was voluntary response. In order to select a sample of undergraduate students in the United States, a simple random sample of four states is selected. From each of these states, a simple random sample of two colleges or universities is then selected. Finally, from each of these eight colleges or universities, a simple random sample of 20 undergraduates is selected. The final sample consists of 160 undergraduates. What sampling technique is being used? Multistage sampling There are four people in a family-a father, a mother and two children-and they have won two tickets to go to Disneyland for a week. They decide to select a sample of two people for the trip as follows: The mother and father flip a coin to see which of the two of them will go, and they then flip a coin to see which of the two children will go. This is a probability sample from the family since each member of the family has a known chance of being selected to go on the trip Twelve people, who suffer from chronic fatigue syndrome, volunteer to take part in an experiment to see if shark fin extract will increase one's energy level. Eight of the volunteers are men and four are women. Half of the volunteers are to be given shark fin extract twice a day and the other half a placebo twice a day. We wish to make sure that four men and two women are assigned to each of the treatments, so we decide to use a block design with the men forming one block and the women the other. Suppose one of the researchers is responsible for measuring if a subject displays an increase in energy level. What design principle should be added to this experiment? Conduct the study as a double-blind experiment. A television station is interested in predicting whether or not voters in its listening area are in favor of federal funding for abortions. It asks its viewers to phone in and indicate whether they are in favor of or opposed to this. Of the 2241 viewers who phoned in, 1574 (70.24%) were opposed to federal funding for abortions. What type of sampling method was used to collect the data? Voluntary response Suppose you want to determine if there are differences in the average prices among items at three local supermarket chains. What type of study would work best? An observational study To investigate whether or not sending text messages while driving impacts driving ability, we have 100 participants (50 men and 50 women) drive an obstacle course under one of the following conditions: 1) No texting while driving, 2) Sending five text messages while driving, or 3) Sending 10 text messages while driving. We measure the accuracy the subjects drove the obstacle course from a scale of 1 to 10 (1= poor and 10= excellent). What is the treatment in this study? Number of text messages sent while driving A baseball enthusiast believes pitchers who strike out a lot of batters also walk a lot of batters. He reached this conclusion by going to the library and examining the records of all major league pitchers between 1990 and 1995. What type of study is his decision based on? An observational study based on available data The head of the quality control department at a publishing company is studying the effect of type of glue and type of binding on the strength of the bookbinding. The company has three possible glues to choose from and the book can either be bound as a paperback or a hardback. What should the company do if repetition is to be part of this study? The company should use multiple books of the same binding type for each of the three types of glue You want to test the effects of water aerobics on resting heart rate. You decide to test two different levels of exercise (water aerobics for 30 minutes twice a week and water aerobics for 60 minutes once per week.) You randomly find a group of 60 (30 men and 30 women) subjects for this study. What is an appropriate blocking variable for this study? Gender A study was conducted to determine the effect of weather on varieties of corn grown for grazing by cattle in Alberta, Canada. To conduct the study, five varieties of corn were considered (one grazing, one short-stature, and three conventional) with harvesting of crops conducted on four occasions (two dates in September, one in December, and one in January). The experimental treatments were assigned at random to plots of land at each of two different locations in Alberta in order to control for natural variations in location. The crude protein concentration of the harvested corn was determined. The two Alberta locations used in the study were Lacombe and Brooks. In this study Location is considered to be what kind of variable? A blocking variable A study sponsored by American Express Co. and the French government tourist office found that old American stereotypes about French unfriendliness weren't true. The respondents were more than 1,000 Americans who have visited France more than once for pleasure over the past two years. The results of this study are probably biased, overstating the extent to which the old stereotypes weren't true A large university wishes to determine the percentage of its students that have committed some form of academic dishonesty, such as cheating on an examination or plagiarism on assignments during their academic career. To determine the desired percentage, a random sample of their current students is selected. Each selected student is then interviewed by a staff member and asked if they had cheated. The results of this survey likely will be unreliable because All of the above are reasons for concern The head of the quality control department at a publishing company is studying the effect of type of glue and type of binding on the strength of the bookbinding. The company has three possible glues to choose from and the book can either be bound as a paperback or a hardback. Many stacks of books are ready to be bound—some in paperback form, some in hardback form. As part of this study, 45 books are to be randomly selected from each type of binding, and then randomly assigned to one of the three types of glue. What type of sampling method is being used to select the books? Stratified sample Suppose several of the units selected into a random sample cannot be found or contacted during the conducting of a survey. What can we say about this situation? This will likely produce nonresponse bias in the sample results. A survey interviews 1000 Americans by telephone and asks "What do you think is the biggest problem facing education today?" The population of interest for this poll is most likely American adults A call-in poll conducted by USA Today concluded that Americans love Donald Trump. This conclusion was based on data collected from 7800 calls made by USA Today readers. USA Today later reported that 5640 of the 7800 calls for the poll came from the offices owned by one man, Cincinnati financier Carl Lindner, who is a friend of Donald Trump. What can we conclude about the results of this poll? They are biased overstating the popularity of Donald Trump The head of the quality control department at a publishing company is studying the effect of type of glue and type of binding on the strength of the bookbinding. The company has three possible glues to choose from and the book can either be bound as a paperback or a hardback. How many treatments is the company considering? 6 CONTINUED...