Question 5.1

Question 5.2

Question 5.3

Question 5.4

Question 5.5

Question 5.6

Question 5.7

Question 5.8

Question 5.9

Question 5.10

Question 5.11

Question 5.12

Question 5.13

Question 5.14

Question 5.15

Question 5.16

Question 5.17

Question 5.18

Question 5.19

Question 5.20

Question 5.21

Question 5.22

Question 5.23

Question 5.24

Question 5.25

Question 5.26

Question 5.27

Question 5.28

Convert the following proportions to percentages:

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2. yKw/e+JZeinpsNZTYQRFcsbJVI8=
3. 6ZGDotaPYiqNC46wwJBmwm7smZV7Z5aW

Question 5.29

Convert the following percentages to proportions:

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2. yLGicJc63eGSY1PhzeHSwl027Y0=
3. NjTabwcIf+8I1dWIJFl3jK2K5ys=

Question 5.30

123

Question 5.31

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

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2. 2ehNz6PFu+7sI0Iv4IrKnoVwvdiu7bJFahosRoN1jpkD5JBtyy5TjreMtXMubytLMq2Pw62YaQpyhhPNchUdgDYZvBsMRdN+dajs0uU5WMw=
3. S1yjx1lKxqRNOgo0JZrF9ts2/TYBiuWOao1nMbUafjQU0TsfXRXuwkZdkiQK6/XQkBKuAIRAa11iWiXj0lOLl/PTjX0ETmN29lnij56NWbGaufrgzgwiWOqK3nlDk54v
4. jd/k157qGW1Lc0lRmlgB9bGzFkU3W+KrI+F780tUdfdL2ExdmbgByN1QW+jycoByuxd4/yRoKfuH49FtmtD4u18xHIHKqp5XxTy30i/xff/S2mOHsrwF76Zp+OlYOVFCPfaCazynJMm9ChcKBJPQBa2wPZr55SAZzt//0t+iysW5xLsQk5jBPEgLhmUelhmgkCjcqkcenuZNVNd/8uvsguRgTZUBvJF6MGfRW/ePJ3RHkhaucb5i4AJETJUrs7jTahngqWBs9oxX/6p0SMyzXqIkXHM988OP

Question 5.32

Question 5.33

Question 5.34

Random selection and a school psychologist career survey: Approximately 21,000 school psychologists are members of the U.S.-based National Association of School Psychologists. Of these, about 5000 have doctoral degrees. A researcher wants to randomly select 100 of the doctoral-level school psychologists for a survey study regarding aspects of their jobs. Use this excerpt from a random numbers table to answer the following questions:

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2. BCX2ke9n2NUUb60nUD+HAmvkugldMlW2al3fngzJKD/vBrGlVgAoB34VzCBODg5QYDXtihul3Iw8X56C0cTmsaQnf4iEmwHaysFv2KGrquQ=
3. 0dSRkrTwbKQUpFvqY/GrlUJNFWSjbEGKkEBbGgy8oxa0hAaTSzSYwSIrZPUSeZxBRcUaytmy26rqR0if+SkQwz1DtXiMNO0WZ5DZzpEZK/0mM+5z6mAQlTZUzt/7AINhThvPUZK/oOdelvYWxpebkLIXpn1FoVU/9mAGe0XcG/kz0i0a88oDhPnCUr5LMdD63zlvQOjtnbek16skx5l/EmrFzOBjgthRvTGynp0U6UaozwKDScx+FvQTVuzFPOQQguI/zjpgVh6jqC6YuBsI172FbkpiqW8l9CqKIA5rYibbRJSCNk1Rog==
4. QEJvJ8c19Tu47IKJzA22tuing/vMQjDLPxjf/hrqUGxbRI10EMqnySLKW4+AyuWMqjNY5CHMFh1VM8gF1WnpkLx+sigamqk84y0Hn2ItiIH+26dkVPVKrar3ttr5TbBegnDtNNaz/0jhEOA0hWaMvaGUgvDoH9+WiP8zD4W4xIu1f6nNxz3QfBIvwBufimfYtPvzoOfNjEhIDMXUgiB7o1cuBBfYVru5sc4ys4TQjYOoUCThyf6FDf3ges2fSonoBv8Eazlj4Is9kYKxqoIIaCnnpvQFuD0VPdbw01jDIrJAA+Ao/QOlbg==

Question 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 school 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.

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2. 0XdCDqKZX7p9658a4tDbgadcKf/ZR+eD89gUOPtLvg3Ha4KbpHK/YgqHWN7u5GwFazRnp9VAarpHyU2hcHcja8NorJw=
3. 85xdjl5JNF0yWzsHcpwl0xeSPk7xOfK00SlKWgtBJvwVMUxQoNdFA+XqWs9otUsvz7OTq5ILUsLPeRs/FMhIiS0r2RxdEh9Ct/ooFw0MFLht3Ssb

Question 5.36

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

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2. 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
3. tgO4Z7xYJagTDAgYPFkQ6ehkXBM6Btin7DJPet7t4M5fYvfDRZLNbAf3DAR7VNr/ySVnsiq3JEfvLi+WDFgPUVtFPXAuU3lRipqiRzl2l+TP698bOoUsVt0bb4aK8LUvyhaXBjrXQbxBtVFYu1WYeoHPdljOAhsB46JGfKgtOcU7oO3VuW0NETJpmF8k9CrW/ciRXS21OtwR7eWDKip9UQubrAj9HI4iI4XPQ3E60qZupYsK2vX/Ig1bC+J2aQvRN2dU411dG5U8eTWrhgxZPjP/EX6xjHf/fgC+5GuxTvA=

Question 5.37

124

Question 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. Explain also to what population 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.

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2. JUP8xlVE8qEQyAzeD8ZjNcUIgF/esMdUTnkj1wOLyWf3u0eq3Fhpy+5VVirnG0cIXU/+w9zdJdlHw+Gjd0Si8bbSr8M7K7Pa74iGS+uMNOiDwrjVbobXu98Ad1vFD5Tx0+V7W1xGynoAxqxXh/353x/654cuXyq4eNoUTrvgMc3XJccfgMbEc+GbjvDi0viBOJZ8HIR9+ryinDAmv/1YLaHpxgioZ945
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4. AaOClZvqBcjFwUoGwsnp1zNZpy48iULkXbVPoBSqT3uGLtfe5CnA8NpsN4S7tslOhTAW1jgxRFTRjxwBkkbAOonGIuxfv53ceCAF8XCXdhb7V+7hgc7uU6rdq7oojCkvnRf1zJqLSa5xEzxmjTcujFsa8hxqXro4ZnebTZL7TGEiL6rSviR6+htVbf/Shfnyw2ziZ63XwVLjKib7ACnVlNkAuac7jHqLH942qYZA2zoDqsA9HPPt52tnmMraWfEhCTuPqE3s/UpT7WlDrPlbkvs6h0xVd2HUIPa4so2PNQViic9HpJdUwNTbhS/boioSx9cKAZH3O6E5GLbjKcss5+CgoGnxG3Fo15oB9fJmCbd7LiO2Lnk03v1ZXF2vMaHL/UOk2XuxGpy8DVdoco6MINYHoCGWucuLRs0OSk56qdADv5CLqDxo4buMzumvTEmQdHzHs9uwrGAOlu0z

Question 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. On August 19, 2005, 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.

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2. 0crN+QbO/RtlMCAi73gddb1ycLjyTBOBVv9IZI9Fq/zQAs+BkxhfyxR2sgcMy1F3yHexqaFisZ4xLUMkbunoW0cQBydRXjqYVye0LFzRIbUbLq5BlNqiAh1T60WM/gH7kgfYFw==
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Question 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.

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2. DMnkAZpfVV7jTMvyGTM2FcWPkFT+MxJHZrdL84bBsT1VgRpc+oXOFDmTVCniLXxzu9/9e9WN4kK1jq0u4fg3d/8rBF7vjzDNd/RudaKqnro=
3. E/wP7VUM97FBhVL8/TAGXGryvUu6xsvjZQR/iOhqlPCuZWSlG8bbYjkCb4It5zzLwaqhsWOsqpYCtt3RqZJHN/JCrWRbfN8r9wqwsSZtHhvUVQSpYlB3U4P17xhGqKtcBzcAWzhxoGEEWtnlRKZ4Eg==

Question 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%.

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Question 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.

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125

Question 5.43

Question 5.44

Question 5.45

Question 5.46

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

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Question 5.47

Probability, proportion, percentage, and a deck of cards: A deck of playing cards has four suits and 13 cards in each suit, for a total of 52 cards. Imagine you draw 1 card from the deck, record what the card is, and then put it back in the deck. Let’s say you repeat this process 15 times, and 5 of the 15 cards are aces. (A fair deck would only have 4 aces, 1 for each suit.) Keeping this example in mind, answer the following questions.

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Question 5.48

Question 5.49

Question 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.

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126

Question 5.51

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

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Question 5.52

Decision about the null hypothesis: 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.

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Question 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.

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Question 5.54

Rejecting versus failing to reject an invitation: Imagine you have found a new study partner in 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.

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Question 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).

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Question 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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Question 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.

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Question 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.

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Question 5.59

Alcohol abuse interventions: Borsari and Carey (2005) randomly assigned 64 male students who had been ordered, after a violation of university alcohol rules, to meet with a school counselor, to one of two conditions. Students were assigned to undergo either (1) a newly developed brief motivational interview (BMI), an intervention in which educational material relates to the students’ own experiences, or (2) 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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Question 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.

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