Exercises

Clarifying the Concepts

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Question 5.1

1.1

Why do we study samples rather than populations?

Question 5.2

5.2

What is the difference between a random sample and a convenience sample?

Question 5.3

5.3

What is generalizability?

Question 5.4

5.4

What is a volunteer sample, and what is the main risk associated with it?

Question 5.5

5.5

What is the difference between random sampling and random assignment?

Question 5.6

5.6

What does it mean to replicate research, and how does replication impact our confidence?

Question 5.7

5.7

Ideally, an experiment would use random sampling so that the data would accurately reflect the larger population. For practical reasons, this is difficult to do. How does random assignment help make up for a lack of random selection?

Question 5.8

5.8

What is the confirmation bias?

Question 5.9

5.9

What is an illusory correlation?

Question 5.10

5.10

How does the confirmation bias lead to the perpetuation of an illusory correlation?

Question 5.11

5.11

In your own words, what is personal probability?

Question 5.12

5.12

In your own words, what is expected relative-frequency probability?

Question 5.13

5.13

Statisticians use terms like trial, outcome, and success in a particular way in reference to probability. What do each of these three terms mean in the context of flipping a coin?

Question 5.14

5.14

We distinguish between probabilities and proportions. How does each capture the likelihood of an outcome?

Question 5.15

5.15

How is the term independent used by statisticians?

Question 5.16

5.16

One step in hypothesis testing is to randomly assign some members of the sample to the control group and some to the experimental group. What is the difference between these two groups?

Question 5.17

5.17

What is the difference between a null hypothesis and a research hypothesis?

Question 5.18

5.18

What are the two decisions or conclusions we can make about our hypotheses, based on the data?

Question 5.19

5.19

What is the difference between a Type I error and a Type II error?

Calculating the Statistics

Question 5.20

5.20

Forty-three tractor-trailers are parked for the night in a rest stop along a major highway. You assign each truck a number from 1 to 43. Moving from left to right and using the second line in the random numbers table below, select four trucks to weigh as they leave the rest stop in the morning.

00190 27157 83208 79446 92987 61357
23798 55425 32454 34611 39605 39981
85306 57995 68222 39055 43890 36956
99719 36036 74274 53901 34643 06157

Question 5.21

5.21

Airport security makes random checks of passenger bags every day. If 1 in every 10 passengers is checked, use the random numbers table in Exercise 5.20 to determine the first 6 people to be checked. Work from top to bottom, starting in the fourth column (the fourth digit from the left in the top line), and allow the number 0 to represent the 10th person.

Question 5.22

5.22

Randomly assign eight people to three conditions of a study, numbered 1, 2, and 3. Use the random numbers table in Exercise 5.20, and read from right to left, starting in the top row. (Note: Assign people to conditions without concern for having an equal number of people in each condition.)

Question 5.23

5.23

You are running a study with five conditions, numbered 1 through 5. Assign the first seven participants who arrive at your lab to conditions, not worrying about equal assignment across conditions. Use the random numbers table in Exercise 5.20, and read from left to right, starting in the third row from the top.

Question 5.24

5.24

Explain why, given the general tendency people have of exhibiting the confirmation bias, it is important to collect objective data.

Question 5.25

5.25

Explain why, given the general tendency people have of perceiving illusory correlations, it is important to collect objective data.

Question 5.26

5.26

What is the probability of hitting a target if, in the long run, 71 out of every 489 attempts actually hit the target?

Question 5.27

5.27

On a game show, 8 people have won the grand prize and a total of 266 people have competed. Estimate the probability of winning the grand prize.

Question 5.28

5.28

Convert the following proportions to percentages:

  1. 0.0173

  2. 0.8

  3. 0.3719

Question 5.29

5.29

Convert the following percentages to proportions:

  1. 62.7%

  2. 0.3%

  3. 4.2%

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Question 5.30

5.30

Using the random numbers table in Exercise 5.20, estimate the probability of the number 6 appearing in a random sequence of numbers. Base your answer on the numbers that appear in the first two rows.

Question 5.31

5.31

Indicate whether each of the following statements refers to personal probability or to expected relative-frequency probability. Explain your answers.

  1. The chance of a die showing an even number is 50%.

  2. There is a 1 in 4 chance that I’ll be late for class tomorrow.

  3. The likelihood that I’ll break down and eat ice cream while studying is 80%.

  4. PlaneCrashInfo.com reported that the odds of being killed on a single flight on 1 of the top 25 safest airlines is 1 in 9.2 million.

Applying the Concepts

Question 5.32

5.32

Coincidence and the lottery: “Woman wins millions from Texas lottery for 4th time” read the headline about Joan Ginther’s amazing luck (Baird, 2010). Two of the tickets were from the same store, whose owner, Bob Solis, said, “This is a very lucky store.” Citing concepts from the chapter, what would you tell Ginther and Solis about the roles that probability and coincidence played in their fortunate circumstances?

Question 5.33

5.33

Random numbers and PINs: How random is your personal identification number or PIN? Your PIN is one of the most important safeguards for the accounts that hold your money and valuable information about you. The BBC reported that, when choosing a four-digit PIN, “people drift towards a small subset of the 10,000 available. In some cases, up to 80% of choices come from just 100 different numbers” (Ward, 2013). Based on what you know about our ability to think randomly, explain this finding.

Question 5.34

5.34

Random selection and a school psychologist career survey: The Canadian government reported that there are 7550 psychologists working in Canada (2013). A researcher wants to randomly select 100 of the Canadian psychologists for a survey study regarding aspects of their jobs. Use this excerpt from a random numbers table to answer the following questions:

04493 52494 75246 33824 45862 51025
00549 97654 64051 88159 96119 63896
35963 15307 26898 09354 33351 35462
59808 08391 45427 26842 83609 49700
  1. What is the population targeted by this study? How large is it?

  2. What is the sample desired by this researcher? How large is it?

  3. Describe how the researcher would select the sample. Be sure to explain how the members of the population would be numbered and which sets of digits the researcher should ignore when using the random numbers table.

  4. Beginning at the left-hand side of the top line and continuing with each succeeding line, list the first 10 participants that this researcher would select for the study.

Question 5.35

5.35

Hypotheses and the school psychologist career survey: Continuing with the study described in Exercise 5.34, once the researcher had randomly selected the sample of 100 Canadian psychologists, she decided to randomly assign 50 of them to receive, as part of their survey materials, a (fictional) newspaper article about the improving job market. She assigned the other 50 to receive a (fictional) newspaper article about the declining job market. The participants then responded to questions about their attitudes toward their careers.

  1. What is the independent variable in this experiment, and what are its levels?

  2. What is the dependent variable in this experiment?

  3. Write a null hypothesis and a research hypothesis for this study.

Question 5.36

5.36

Random assignment and the school psychologist career survey: Refer to Exercises 5.34 and 5.35 when responding to the following questions:

  1. Describe how the researcher would randomly assign the participants to the levels of the independent variable. Be sure to explain how the levels of the independent variable would be numbered and which sets of digits the researcher should ignore when using the random numbers table.

  2. Beginning at the left-hand side of the bottom line of the random numbers table in Exercise 5.34 and continuing with the left-hand side of the line above it, list the levels of the independent variable to which the first 10 participants would be assigned. Use 0 and 1 to represent the two conditions.

  3. Why do these numbers not appear to be random? Discuss the difference between short-run and long-run proportions.

Question 5.37

5.37

Random selection and a survey of psychology majors: Imagine that you have been hired by the psychology department at your school to administer a survey to psychology majors about their experiences in the department. You have been asked to randomly select 60 of these majors from the overall pool of 300. You are working on this project in your dorm room using a random numbers table because the server is down and you cannot use an online random numbers generator. Your roommate offers to write down a list of 60 random numbers between 001 and 300 for you so you can be done quickly. In three to four sentences, explain to your roommate why she is not likely to create a list of random numbers.

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Question 5.38

5.38

Random selection and random assignment: For each of the following studies, state (1) whether random selection was likely to have been used, and explain whether it would have been possible to use it. Also, describe the population to which the researcher wanted to and could generalize, and state (2) whether random assignment was likely to have been used, and whether it would have been possible to use it.

  1. A developmental psychologist wondered whether children born preterm (prematurely) had different social skills at age 5 than children born at full term.

  2. A counseling center director wanted to compare the length of therapy in weeks for students who came in for treatment for depression versus students who came in for treatment for anxiety. She wanted to report these data to the university administrators to help develop the next year’s budget.

  3. An industrial-organizational psychologist wondered whether a new laptop design would affect people’s response time when using the computer. He wanted to compare response times when using the new laptop with response times when using two standard versions of laptops, a Mac and a PC.

Question 5.39

5.39

Volunteer samples and a college football poll: A volunteer sample is a kind of convenience sample in which participants select themselves to participate. One recent year, USA Today published an online poll on its Web site asking this question about U.S. college football: “Who is your pick to win the ACC conference this year?” Eight options—seven universities, including top vote-getters Virginia Tech and Miami, as well as “Other”—were provided.

  1. Describe the typical person who might volunteer to be in this sample. Why might this sample be biased, even with respect to the population of U.S. college football fans?

  2. What is external validity? Why might external validity be limited in this sample?

  3. What other problem can you identify with this poll?

Question 5.40

5.40

Samples and Cosmo quizzes: Cosmopolitan magazine (Cosmo, as it’s known popularly) publishes many of its well-known quizzes on its Web site. One quiz, aimed at heterosexual women, is titled “Are You Way Too Obsessed with Your Ex?” A question about “your rebound guy” offers these three choices: “Any random guy who will take your mind off the split,” “A doppelgänger of your ex,” and “The polar opposite of the last guy you dated.” Consider whether you want to use the quiz data to determine how obsessed women are with their exes.

  1. Describe the typical person who might respond to this quiz. How might data from such a sample be biased, even with respect to the overall Cosmo readership?

  2. What is the danger of relying on volunteer samples in general?

  3. What other problems do you see with this quiz? Comment on the types of questions and responses.

Question 5.41

5.41

Samples and political leanings: On its Web site, Advocates for Self-Government offers the “World’s Smallest Internet Political Quiz,” focusing on the U.S. political spectrum. Using just 10 questions, the quiz identifies a person’s political leanings. As of 2012, almost 20 million people had taken the quiz. In 2007, the Web site reported the following breakdown into the five possible categories: centrist, 33.49%; conservative, 8.88%; libertarian, 32.64%; liberal, 17.09%; and statist (big government), 7.89%.

  1. Do you think these numbers are representative of the U.S. population? Why or why not?

  2. Describe the people most likely to volunteer for this sample. Why might this group be biased in comparison to the overall U.S. population?

  3. The Web site says, “Libertarians support maximum liberty in both personal and economic matters.” Libertarians are not the predominant political group in the United States. Why, then, might libertarians form one of the largest categories of quiz respondents?

  4. This is a huge sample—close to 20 million people. Why is it not enough to have a large sample to conduct a study with high external validity? What would we need to change about this sample to increase external validity?

Question 5.42

5.42

Random selection or random assignment: For each of the following hypothetical scenarios, state whether selection or assignment is being described. Is the method of selection or assignment random? Explain your answer.

  1. A study of the services offered by counseling centers at Canadian universities studied 20 universities; every Canadian university had an equal chance of being in this study.

  2. In a study of phobias, 30 rhesus monkeys were either exposed to fearful stimuli or not exposed to fearful stimuli. Every monkey had an equal chance of being placed in either of the exposure conditions.

  3. In a study of cell phone usage, participants were recruited by including along with their cell phone bill an invitation to participate in the study.

  4. In a study of visual perception, 120 Introduction to Psychology students were recruited to participate.

Question 5.43

5.43

Bias about driver gender: Assume that one of your male friends is complaining about female drivers, and says that men are much better drivers than women. If objective studies of the driving performance of men and women revealed no mean difference between the two groups, what kind of bias has your friend shown?

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Question 5.44

5.44

Confirmation bias, illusory correlation, and driver gender: Referring to your friend from Exercise 5.43, assume he backs up his claim by recounting two events over the past week in which female drivers have erred (e.g., cut him off in traffic, not used a turn signal). Explain how the confirmation bias is at work in your friend’s statements and how this confirmation bias may be perpetuating an illusory correlation.

Question 5.45

5.45

Confirmation bias and negative thought ­patterns: Explain how the general tendency of a confirmation bias might make it difficult to change negative thought patterns that accompany Major Depressive Disorder.

Question 5.46

5.46

Probability and coin flips: Short-run proportions are often quite different from long-run probabilities.

  1. In your own words, explain why we would expect proportions to fluctuate in the short run, but why long-run probabilities are more predictable.

  2. What is the expected long-run probability of heads if a person flips a coin many, many times? Why?

  3. Flip a coin 10 times in a row. What proportion is heads? Do this 5 times. Note: You will learn more by actually doing it, so don’t just write down numbers!

    Proportion for the first 10 flips:

    Proportion for the second 10 flips:

    Proportion for the third 10 flips:

    Proportion for the fourth 10 flips:

    Proportion for the fifth 10 flips:

  4. Do the proportions in part (c) match the expected long-run probability in part (b)? Why or why not?

  5. Imagine that a friend flipped a coin 10 times, got 9 out of 10 heads, and complained that the coin was biased. How would you explain to your friend the difference between short-term and long-term probability?

Question 5.47

5.47

Probability, proportion, percentage, and Where’s Waldo?: Salon.com reporter Ben Blatt analyzed the location of Waldo in the game in which you must find Waldo, a cartoon man who always wears a red-and-white-striped sweater and hat, in a highly detailed illustration (2013). Blatt reported that “53 percent of the time Waldo is hiding within one of two 1.5-inch tall bands, one starting three inches from the bottom of the page and another one starting seven inches from the bottom, stretching across the spread.” One of Blatt’s colleagues used this trick to find Waldo more quickly than another colleague who did not have this information across 11 illustrations.

  1. What does the term probability refer to? What is the probability of finding Waldo in one of the two 1.5 inch bands that Blatt identified?

  2. What does the term proportion refer to? What is the proportion of Waldos in one of these two 1.5 inch bands?

  3. What does the term percentage refer to? What is the percentage of Waldos in one of these two bands?

  4. Based on these data, do you have enough information to determine whether the Where’s Waldo? game is fixed? Why or why not? (Note: Blatt reported that the “probability of any two 1.5-inch bands containing at least 50 percent of all Waldo’s is remarkably slim, less than 0.3 percent.”)

Question 5.48

5.48

Independent trials and Eurovision Song Contest bias: As reported in the Telegraph (Highfield, 2005), Oxford University researchers investigated allegations of voting bias in the annual Eurovision Song Contest, which pits pop music acts from across Europe, one per country, against each other. The research team found that neighboring countries tended to vote as a block—Norway with Sweden, Belarus with Russia, and Greece with Cyprus, for example. Explain why one could not consider the votes to be independent of each other in this case.

Question 5.49

5.49

Independent trials and the U.S. presidential ­election: Nate Silver is a statistician and journalist well known for his accurate prediction tools. In an article leading up to the 2012 U.S. presidential election in which Barack Obama bested Mitt Romney, Silver (2012) explained his prediction methods as “principally, an Electoral College simulation, [which] therefore relies more heavily on state-by-state polls.” Consider Silver’s consolidation of data from polls across the 50 states. In what way are these polls likely to be independent trials? Why could someone argue that they are not truly independent trials?

Question 5.50

5.50

Independent or dependent trials and ­probability: Gamblers often falsely predict the outcome of a future trial based on the outcome of previous trials. When trials are independent, the outcome of a future trial cannot be predicted based on the outcomes of previous trials. For each of the following examples, (1) state whether the trials are independent or dependent and (2) explain why. In addition, (3) state whether it is possible that the quote is accurate or whether it is definitely fallacious, explaining how the independence or dependence of trials influences accuracy.

  1. You are playing Monopoly and have rolled a pair of sixes in 4 out of your last 10 rolls of the dice. You say, “Cool. I’m on a roll and will get sixes again.”

  2. You are an Ohio State University football fan and are sad because the team has lost two games in a row. You say, “That is really unusual; the Buckeyes are doomed this season. That’s what happens with lots of early-season injuries.”

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  3. You have a 20-year-old car that has trouble starting from time to time. It has started every day this week, and now it’s Friday. You say, “I’m doomed. It’s been reliable all week, and even though I did get a tune-up last week, today is bound to be the day it fails me.”

  4. It’s the first week of your corporate internship and you have to wear nylon stockings to the office if you’re wearing a skirt. On the first and second days, you get a run in your stockings almost immediately, an indication of a defect. The third day, you put on yet another new pair of stockings and say, “OK, this pair has to be good. There’s no way I’d have three bad pairs in a row. They’re even from different stores!”

Question 5.51

5.51

Null hypotheses and research hypotheses: For each of the following studies, cite the likely null hypothesis and the likely research hypothesis.

  1. A forensic cognitive psychologist wondered whether repetition of false information (versus no repetition) would increase the tendency to develop false memories, on average.

  2. A clinical psychologist studied whether ongoing structured assessments of the therapy process ­(versus no assessment) would lead to better outcomes, on average, among outpatient therapy clients with depression.

  3. A corporation recruited an industrial-organizational psychologist to explore the effects of cubicles (versus enclosed offices) on employee morale.

  4. A team of developmental cognitive psychologists studied whether teaching a second language to children from birth affects children’s ability to speak their native language.

Question 5.52

5.52

Decision about null hypotheses: For each of the following fictional conclusions, state whether the researcher seems to have rejected or failed to reject the null hypothesis (contingent, of course, on inferential statistics having backed up the statement). Explain the rationale for your decision.

  1. When false information is repeated several times, people seem to be more likely, on average, to develop false memories than when the information is not repeated.

  2. Therapy clients with Major Depressive Disorder who have ongoing structured assessments of therapy seem to have lower post-therapy depression levels, on average, than do clients who do not have ongoing structured assessments.

  3. Employee morale does not seem to be different, on average, whether employees work in cubicles or in enclosed offices.

  4. A child’s native language does not seem to be different in strength, on average, whether the child is raised to be bilingual or not.

Question 5.53

5.53

Type I versus Type II errors: Examine the statements from Exercise 5.52, repeated here. For each, if this conclusion were incorrect, what type of error would the researcher have made? Explain your answer.

  1. When false information is repeated several times, people seem to be more likely, on average, to develop false memories than when the information is not repeated.

  2. Therapy clients with Major Depressive Disorder who have ongoing structured assessments of therapy seem to have lower post-therapy depression levels, on average, than do clients who do not have ongoing structured assessments.

  3. Employee morale does not seem to be different, on average, whether employees work in cubicles or enclosed offices.

  4. A child’s native language does not seem to be different in strength, on average, whether the child is raised to be bilingual or not.

Question 5.54

5.54

Rejecting versus failing to reject an invitation: Imagine you have found a new study partner in your statistics class. One day, your study partner asks you to go on a date. This invitation takes you completely by surprise, and you have no idea what to say. You are not attracted to the person in a romantic way, but at the same time you do not want to hurt his or her feelings.

  1. Create two possible responses to the person, one in which you fail to reject the invitation and another in which you reject the invitation.

  2. How is your failure to reject the invitation different from rejecting or accepting the invitation?

Question 5.55

5.55

Confirmation bias, errors, replication, and horoscopes: A horoscope on Astrology.com stated: “A big improvement is in the works, one that you may know nothing about, and today is the day for the big unveiling.” A job-seeking recent college graduate might spot some new listings for interesting positions and decide the horoscope was right. If you look for an association, you’re likely to find it. Yet, over and over again, careful researchers have failed to find evidence to support the accuracy of astrology (e.g., Dean & Kelly, 2003).

  1. Explain to the college graduate how confirmation bias guides his logic in deciding the horoscope was right.

  2. If Dean and Kelly and other researchers were wrong, what kind of error would they have made?

  3. Explain why replication (that is, “over and over again”) means that this finding is not likely to be an error.

Question 5.56

5.56

Probability and sumo wrestling: In their book Freakonomics, Levitt and Dubner (2005) describe a study conducted by Duggan and Levitt (2002) that broached the question: Do sumo wrestlers cheat? Sumo wrestlers garner enormous respect in Japan, where sumo wrestling is considered the national sport. The researchers examined the results of 32,000 wrestling matches over an 11-year time span. If a wrestler finishes a tournament with a losing record (7 or fewer wins out of 15 matches), his ranking goes down, as do the money and prestige that come with winning. The researchers wondered whether, going into the last match of the tournament, wrestlers with 7-7 records (needing only 1 more win to rise in the rankings) would have a better-than-expected win record against wrestlers with 8-6 records (those who already are guaranteed to rise in the rankings). Such a phenomenon might indicate cheating. One 7-7 wrestler (wrestler A), based on past matches against a given 8-6 opponent (wrestler B), was calculated to have won 48.7% of the time.

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  1. If there is no cheating, what is the probability that wrestler A will beat wrestler B in any situation, including the one in which A is 7-7 and B is 8-6?

  2. If matches tend to be rigged so that 8-6 wrestlers frequently throw matches to help other wrestlers maintain their rankings (and to get payback from 7-7 wrestlers in future matches), what would you expect to happen to the winning percentage when these two wrestlers meet under these exact ­conditions—that is, the first is 7-7 in the tournament and the second is 8-6?

  3. State the null hypothesis and research hypothesis for the study examining whether sumo wrestlers cheat.

  4. In this particular real-life example, wrestler A was found to have beaten wrestler B 79.6% of the time when A had a 7-7 record and B had an 8-6 record. If inferential statistics determined that it was very unlikely that this would happen by chance, what would your decision be? Use the language of hypothesis testing.

Question 5.57

5.57

Testimonials and Harry Potter: Amazon and other online bookstores offer readers the opportunity to write their own book reviews, and many potential readers scour these reviews to decide which books to buy. Harry Potter books attract a great deal of these reader reviews. One Amazon reviewer, “bel 78,” submitted her review of Harry Potter and the Half-Blood Prince from Argentina. Of the book, she said, “It’s simply outstandingly good,” and suggested that readers of her review “run to get your copy.” Do these reviews have an impact? In this case, more than 900 people had read bel 78’s review, and close to 700 indicated that the review was helpful to them.

  1. Imagine that you’re deciding whether to buy Harry Potter and the Half-Blood Prince, and you want to know what people who had already read the book thought before you invest the money and time. What is the population whose opinion you’re ­interested in?

  2. If you read only bel 78’s review, what is the sample from which you’re gathering your data? What are some of the problems in relying on just this one review?

  3. About 4700 readers had reviewed this book on Amazon by 2015. What if all reviewers agreed that this book was amazing? What is the problem with this sample?

  4. Given no practical or financial limitations, what would be the best way to gather a sample of Amazon users who had read this Harry Potter book?

  5. A friend plans to order a book online to take on spring break. She is reading online reviews of several books to make her decision. Explain to her in just a few sentences why her reliance on testimonials is not likely to provide her with objective information.

Putting It All Together

Question 5.58

5.58

Horoscopes and predictions: People remember when their horoscopes had an uncanny prediction—say, the prediction of a problem in love on the exact day of the breakup of a romantic relationship—and decide that horoscopes are accurate. Munro & Munro (2000) are among those who have challenged such a conclusion. They reported that 34% of students chose their own horoscope as the best match for them when the horoscopes were labeled with the signs of the zodiac, whereas only 13% chose their own horoscope when the predictions were labeled only with numbers and in a random order. Thirteen percent is not statistically significantly different from 8.3%, which is the percentage we’d expect by chance.

  1. What is the population of interest, and what is the sample in this study?

  2. Was random selection used? Explain your answer.

  3. Was random assignment used? Explain your answer.

  4. What is the independent variable and what are its levels? What is the dependent variable? What type of variables are these?

  5. What is the null hypothesis and what is the research hypothesis?

  6. What decision did the researchers make? (Respond using the language of inferential statistics.)

  7. If the researchers were incorrect in their decision, what kind of error did they make? Explain your answer. What are the consequences of this type of error, both in general and in this situation?

Question 5.59

5.59

Alcohol abuse interventions: Sixty-four male students were ordered, after they had violated university alcohol rules, to meet with a school counselor. Borsari and Carey (2005) randomly assigned these students to one of two conditions. Those in the first condition were assigned to undergo a newly developed brief motivational interview (BMI), an intervention in which educational material relates to the students’ own experiences; those in the second condition were assigned to attend a standard alcohol education session (AE) in which educational material is presented with no link to students’ experiences. Based on inferential statistics, the researchers concluded that those in the BMI group had fewer alcohol-related problems at follow-up, on average, than did those in the AE group.

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  1. What is the population of interest, and what is the sample in this study?

  2. Was random selection likely used? Explain your answer.

  3. Was random assignment likely used? Explain your answer.

  4. What is the independent variable and what are its levels? What is the dependent variable?

  5. What is the null hypothesis and what is the research hypothesis?

  6. What decision did the researchers make? (Respond using the language of inferential statistics.)

  7. If the researchers were incorrect in their decision, what kind of error did they make? Explain your answer. What are the consequences of this type of error, both in general and in this situation?

Question 5.60

5.60

Treatment for depression: Researchers conducted a study of 18 patients whose depression had not responded to treatment (Zarate, 2006). Half received one intravenous dose of ketamine, a hypothesized quick fix for depression; half received one intravenous dose of placebo. Far more of the patients who received ketamine improved, as measured by the Hamilton Depression Rating Scale, usually in less than 2 hours, than patients on placebo.

  1. What is the population of interest, and what is the sample in this study?

  2. Was random selection likely used? Explain your answer.

  3. Was random assignment likely used? Explain your answer.

  4. What is the independent variable and what are its levels? What is the dependent variable?

  5. What is the null hypothesis and what is the research hypothesis?

  6. What decision did the researchers make? (Respond using the language of inferential statistics.)

  7. If the researchers were incorrect in their decision, what kind of error did they make? Explain your answer. What are the consequences of this type of error, both in general and in this situation?