Chapter 5

  • 5.1 It is rare to have access to an entire population. That is why we study samples and use inferential statistics to estimate what is happening in the population.
  • 5.3 Generalizability refers to the ability of researchers to apply findings from one sample or in one context to other samples or contexts.
  • 5.5 Random sampling means that every member of a population has an equal chance of being selected to participate in a study. Random assignment means that each selected participant has an equal chance of being in any of the experimental conditions.
  • 5.7 Random assignment is a process in which every participant (regardless of how he or she was selected) has an equal chance of being in any of the experimental conditions. This avoids bias across experimental conditions.
  • 5.9 An illusory correlation is a belief that two events are associated when in fact they are not.
  • 5.11 Students’ answers will vary. Personal probability is a person’s belief about the probability of an event occurring; for example, someone’s belief about the likelihood that she or he will complete a particular task.
  • 5.13 In reference to probability, the term trial refers to each occasion that a given procedure is carried out. For example, each time we flip a coin, it is a trial. Outcome refers to the result of a trial. For coin-flip trials, the outcome is either heads or tails. Success refers to the outcome for which we’re trying to determine the probability. If we are testing for the probability of heads, then success is heads.
  • 5.15 The independent variable is the variable the researcher manipulates. Independent trials or events are those that do not affect each other; the flip of a coin is independent of another flip of a coin because the two events do not affect each other.
  • 5.17 A null hypothesis is a statement that postulates that there is no mean difference between populations or that the mean difference is in a direction opposite of that anticipated by the researcher. A research hypothesis, also called an alternative hypothesis, is a statement that postulates that there is a mean difference between populations or sometimes, more specifically, that there is a mean difference in a certain direction, positive or negative.
  • 5.19 We commit a Type I error when we reject the null hypothesis but the null hypothesis is true. We commit a Type II error when we fail to reject the null hypothesis but the null hypothesis is false.
  • 5.21 In each of the six groups of 10 passengers that go through the checkpoint, we would check the 9th, 9th, 10th, 1st, 10th, and 8th passengers, respectively.
  • 5.23 Only recording the numbers 1 to 5, the sequence appears as 5, 3, 5, 5, 2, 2, and 2. So, the first person is assigned to the fifth condition, the second person to the third condition, and so on.
  • 5.25 Illusory correlation is particularly dangerous because people might perceive there to be an association between two variables that does not in fact exist. Because we often make decisions based on associations, it is important that those associations be real and be based on objective evidence. For example, a parent might perceive an illusory correlation between body piercings and trustworthiness, believing that a person with a large number of body piercings is untrustworthy. This illusory correlation might lead the parent to unfairly eliminate anyone with a body piercing from consideration when choosing babysitters.
  • 5.27 The probability of winning is estimated as the number of people who have already won out of the total number of contestants, or 8/266 = 0.03.
  • 5.29
    • a. 0.627
    • b. 0.003
    • c. 0.042
  • 5.31
    • a. Expected relative-frequency probability
    • b. Personal probability
    • c. Personal probability
    • d. Expected relative-frequency probability
  • 5.33 Given that the population is high school students in Marseille and Lyon, it is possible that the researcher can compile a list of all members of the population, allowing her to use random selection. She could not, however, use random assignment because she could not assign the students to have lived in Marseille or Lyon.
  • 5.35
    • a. The independent variable is type of news information, with two levels: information about an improving job market and information about a declining job market.
    • b. The dependent variable is psychologists’ attitudes toward their careers.
    • c. The null hypothesis would be that, on average, the psychologists who received the positive article about the job market have the same attitude toward their career as those who read a negative article about the job market. The research hypothesis would be that a difference, on average, exists between the two groups.
  • 5.37 Although we all believe we can think randomly if we want to, we do not, in fact, generate numbers independently of the ones that came before. We tend to glance at the preceding numbers in order to make the next ones “random.” Yet once we do this, the numbers are not independent and therefore are not random. Moreover, even if we can keep ourselves from looking at the previous numbers, the numbers we generate are not likely to be random. For example, if we were born on the 6th of the month, then we may be more likely to choose 6’s than other digits. Humans just don’t think randomly.
  • 5.39
    • a. The typical study volunteer is likely someone who cares deeply about U.S. college football. Moreover, it is particularly the fans of the top ACC teams, who themselves are likely extremely biased, who are most likely to vote.
    • b. External validity refers to the ability to generalize beyond the current sample. In this case, it is likely that fans of the top ACC teams are voting and that the poll results do not reflect the opinions of U.S. college football fans at large.
    • c. There are several possible answers to this question. As one example, only eight options were provided. Even though one of these options was “other,” this limited the range of possible answers that respondents would be likely to provide. The sample is also biased in favor of those who know about and would spend time at the USA Today Web site in the first place.

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  • 5.41
    • a. These numbers are likely not representative. This is a volunteer sample.
    • b. Those most likely to volunteer are those who have stumbled across, or searched for, this Web site: a site that advocates for self-government. Those who respond are more likely to tend toward supporting self-government than are those who do not respond (or even find this Web site).
    • c. This description of libertarians suggests they would advocate for self-government—as that is part of the name of the group that hosts this quiz—a likely explanation for the predominance of libertarians who responded to this survey. The repeated use of the word “Libertarian” (in the heading and in the icon) likely helps preselect who would come to this Web site in the first place.
    • d. It doesn’t matter how large a sample is if it’s not representative. With respect to external validity, it would be far preferable to have a smaller but representative sample than a very large but unrepresentative sample.
  • 5.43 Your friend’s bias is an illusory correlation—he perceives a relation between gender and driving performance, when in fact there is none.
  • 5.45 If a depressed person has negative thoughts about himself or herself and about the world, confirmation bias may make it difficult to change those thoughts because confirmation bias would lead this person to pay more attention to and better remember negative events than positive events. For example, he or she might remember the one friend who slighted him or her at a party but not the many friends who were excited to see him or her.
  • 5.47
    • a. Probability refers to the proportion of aces that we expect to see in the long run. In the long run, given 4 aces out of 52 cards, we would expect the proportion of aces to be 4/52 = 0.077, rounded to 0.08.
    • b. Proportion refers to the observed fraction of cards that are aces—the number of successes divided by the number of trials. In this case, the proportion of aces is 5/15 = 0.333, rounded to 0.33.
    • c. Percentage refers to the proportion multiplied by 100: 0.333(100) = 33.30. Thus, 33.30% of the cards drawn were aces.
    • d. Although 0.33 is far from 0.08, we would expect a great deal of fluctuation in the short run. These data are not sufficient to determine whether the deck is stacked.
  • 5.49 These polls could be considered independent trials if they were conducted for each state individually, and if the state currently being polled did not have any information about the polling results from other states. However, these are not truly independent trials, as state-by-state polls are often presented in the media as they take place, thus potentially influencing voters in states that have not yet been polled.
  • 5.51
    • a. The null hypothesis is that the average tendency to develop false memories is either unchanged or is lowered by the repetition of false information. The research hypothesis is that false memories are higher, on average, when false information is repeated than when it is not.
    • b. The null hypothesis is that the average outcome is the same or worse whether or not structured assessments are used. The research hypothesis is that the average outcome is better when structured assessments are used than when they are not used.
    • c. The null hypothesis is that average employee morale is the same whether employees work in enclosed offices or in cubicles. The research hypothesis is that average employee morale is different when employees work in enclosed offices versus in cubicles.
    • d. The null hypothesis is that ability to speak one’s native language is the same, on average, whether or not a second language is taught from birth. The research hypothesis is that the ability to speak one’s native language is different, on average, when a second language is taught from birth than when no second language is taught.
  • 5.53
    • a. If this conclusion is incorrect, the researcher has made a Type I error. The researcher rejected the null hypothesis when the null hypothesis is really true. (Of course, he or she never knows whether there has been an error! She or he just has to acknowledge the possibility.)
    • b. If this conclusion is incorrect, the researcher has made a Type I error. She has rejected the null hypothesis when the null hypothesis is really true.
    • c. If this conclusion is incorrect, the researcher has made a Type II error. He has failed to reject the null hypothesis when the null hypothesis is not true.
    • d. If this conclusion is incorrect, the researcher has made a Type II error. She has failed to reject the null hypothesis when the null hypothesis is not true.
  • 5.55
    • a. Confirmation bias has guided his logic in that he looked for specific events that occurred during the day to fit the horoscope but ignored the events that did not fit the prediction.
    • b. If this conclusion is incorrect, they have made a Type I error. Dean and Kelly would have failed to reject the null hypothesis when the null hypothesis is not true.
    • c. If an event occurs regularly or a research finding is replicated many times and by other researchers and in a range of contexts, then it is likely the event or finding is not occurring in error or by chance alone.
  • 5.57
    • a. The population in which you would be interested is all people who already had read Harry Potter and the Half- Blood Prince.
    • b. The sample would be just bel 78. It is dangerous to rely on just one review, bel 78’s testimonial. She clearly felt strongly about the book if she spent the time to post her review. She is not likely to be representative of the typical reader of this book.
    • c. This is a large sample, but it is not likely representative of those who had read this book. Not only does this sample consist solely of Amazon users, but it consists of readers who chose to post a review. It is likely that those who took the time to write and post a review were those who felt more strongly about the book than did the typical reader.
    • d. In this case, the population of interest would be all Amazon users who had read this book. We would need Amazon to generate a list of everyone who bought the book (something that they would not do because of ethical considerations), and we would have to randomly select a sample from this population. We would then have to identify the people who actually read the book (who may not be the buyers) and elicit the ratings from the randomly selected sample.

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    • e. We could explain that testimonials are typically written by those who feel most strongly about a book. The sample of reviewers, therefore, is unlikely to be representative of the population of readers.
  • 5.59
    • a. The population of interest is male students with alcohol problems. The sample is the 64 students who were ordered to meet with a school counselor.
    • b. Random selection was not used. The sample was comprised of 64 male students who had been ordered to meet with a school counselor; they were not chosen out of all male students with alcohol problems.
    • c. Random assignment was used. Each participant had an equal chance of being assigned to either of the two conditions.
    • d. The independent variable is type of counseling. It has two levels: BMI and AE. The dependent variable is number of alcohol-related problems at follow-up.
    • e. The null hypothesis is that the mean number of alcohol- related problems at follow-up is the same, regardless of type of counseling (BMI or AE). The research hypothesis is that students who undergo a BMI have different mean numbers of alcohol-related problems at follow-up than do students who participate in AE.
    • f. The researchers rejected the null hypothesis.
    • g. If the researchers were incorrect in their decision, then they made a Type I error, rejecting the null hypothesis when the null hypothesis is true. The consequences of this type of error are that a new treatment that is no better, on average, than the standard treatment would be implemented. This might lead to unnecessary costs to train counselors to implement the new treatment.