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Statistics For Psychology 1st Edition Aron - Solutions
3. A researcher tests five individuals who have seen paid political ads about a particular issue. These individuals take a multiple-choice test about the issue in which people in general (who know nothing about the issue) usually get 40 questions correct. The number correct for these five
24. ADVANCED TOPIC: An organizational psychologist predicts that assembly workers will have a somewhat higher level of job satisfaction if they are given a new kind of incentive program (that is, he predicts a medium effect size). On a standard job satisfaction scale, for assembly workers in this
23. ADVANCED TOPIC: A psychologist is planning a study on the effect of motivation on performance on an attention task. In this task, participants try to identify target letters in a stream of letters passing by at a rapid rate. The researcher knows from long experience that, under ordinary
22. You are planning a study that you compute as having quite low power. Name six things that you might do to increase power.
21. Tsang and colleagues (2009) conducted a review to examine the statistical power of studies that had compared patients’ experiences of serious adverse events (such as a life-threatening medical event) during randomized controlled trials of medical treatments. They identified six studies that
20. Caspi and colleagues (1997) analyzed results from a large-scale longitudinal study of a sample of children born around 1972 in Dunedin, New Zealand. As one part of their study, the researchers compared the 94 in their sample who were, at age 21, alcohol dependent (clearly alcoholic) versus the
19. In the Decision Errors, Effect Size, and Power in Research Articles section earlier in this chapter, you read about a review study conducted by Huey and Polo(2008) that examined psychological treatments for clinical problems among ethnic minority youth. As part of their review, the researchers
18. You read a study that just barely fails to be significant at the .05 level. That is, the result is not significant. You then look at the size of the sample. If the sample is very large (rather than very small), how should this affect your interpretation of (a) the probability that the null
17. Here is information about several possible versions of a planned experiment, each with a single sample. Figure effect size for each; then sketch the distributions involved, showing the areas for alpha, beta, and power. (Assume all populations have a normal distribution.) ADVANCED TOPIC: Figure
16. In a planned study, there is a known population with a normal distribution, = 17.5, and = 3.2. What is the predicted mean if the researcher predicts(a) a small positive effect size, (b) a medium negative effect size, (c) an effect size of d = .40, (d) an effect size of d = - .40, (e) an
15. In a planned study, there is a known population with a normal distribution, = 0, and = 10. What is the predicted effect size (d ) if the researchers predict that those given an experimental treatment have a mean of (a) -8, (b) -5,(c) -2, (d) 0, and (e) 10? For each part, also indicate
14. In a completed study, there is a known population with a normal distribution, = 122, and = 8. What is the estimated effect size if a sample given an experimental procedure has a mean of (a) 100, (b) 110, (c) 120, (d) 130, and(e) 140? For each part, also indicate whether the effect is
13. For each of the following studies, make a chart of the four possible correct and incorrect decisions, and explain what each would mean. (Each chart should be laid out like Table 1, but put into the boxes the possible results, using the names of the variables involved in the study.)(a) A study
8. Aron and colleagues (1997) placed strangers in pairs and asked them to talk together following a series of instructions designed to help them become close.At the end of 45 minutes, individuals privately answered some questions about how close they now felt to their partners. (The researchers
6. Here is information about several possible versions of a planned experiment.Figure effect size for each; sketch the distributions involved, showing the area for alpha, beta, and power. (Assume all populations have a normal distribution.)ADVANCED TOPIC: Figure the power for each version.
1. Define alpha and beta.
6. Here is information about several possible versions of a planned experiment.Figure effect size for each; sketch the distributions involved, showing the area for alpha, beta, and power. (Assume all populations have a normal distribution.)ADVANCED TOPIC: Figure the power for each version.
1. Define alpha and beta.
3. Explain the relationship between effect size and power.
2. Explain the idea of power as the probability of getting significant results if the research hypothesis is true. Be sure to mention that the standard minimum acceptable level of power for a research study is 80%. Explain the role played by power when you are interpreting the results of a study
1. Explain the idea of effect size as the degree of overlap between distributions, noting how this overlap is a function of mean difference and population standard deviation (and describing precisely how it is figured and why it is figured that way). If required by the question, discuss the effect
24. Cut up 90 small slips of paper, and write each number from 1 to 9 on 10 slips each. Put the slips in a large bowl and mix them up. (a) Take out a slip, write down the number on it, and put it back. Do this 20 times. Make a histogram, and figure the mean and the variance of the result. You
23. Maier and colleagues (2008) conducted a study to examine whether the perception of the color red can adversely affect intellectual performance. The researchers based their hypothesis on a theory that, in achievement situations, red is associated with the risk of failure, such as when teachers
22. Stankiewicz and colleagues (2006) examined how limitations in human perception and memory (and other factors) affect people’s ability to find their way in indoor spaces. In one of their experiments, eight students used a computer keyboard to move through a virtual indoor space of corridors
21. A government-sponsored telephone counseling service for adolescents tested whether the length of calls would be affected by a special telephone system that had a better sound quality. Over the past several years, the lengths of telephone calls (in minutes) were normally distributed with = 18
20. A psychologist is interested in the conditions that affect the number of dreams per month that people report in which they are alone. We will assume that based on extensive previous research, it is known that in the general population the number of such dreams per month follows a normal curve,
19. A researcher is interested in whether people are able to identify emotions correctly when they are extremely tired. It is known that, using a particular method of measurement, the accuracy ratings of people in the general population (who are not extremely tired) are normally distributed with a
18. For each of the following studies, the samples were given an experimental treatment and the researchers compared their results to the general population. For each, carry out a Z test using the five steps of hypothesis testing for a twotailed test at the .01 level, and make a drawing of the
17. For each of the following studies, the samples were given an experimental treatment and the researchers compared their results to the general population. (Assume all populations are normally distributed.) For each, carry out a Z test using the five steps of hypothesis testing for a two-tailed
16. ADVANCED TOPIC: Figure the 99% confidence interval (that is, the lower and upper confidence limits) for each part of problem 14. Assume that in each case the researcher’s sample has a mean of 50 and that the population of individuals is known to follow a normal curve.
15. ADVANCED TOPIC: Figure the 95% confidence interval (that is, the lower and upper confidence limits) for each part of problem 13. Assume that in each case the researcher’s sample has a mean of 80 and the population of individuals is known to follow a normal curve.
14. Figure the standard deviation of the distribution of means for a population with a standard deviation of 20 and sample sizes of (a) 10, (b) 11, (c) 100, and (d) 101.
13. Indicate the mean and the standard deviation of the distribution of means for each of the following situations.
12. Under what conditions is it reasonable to assume that a distribution of means will follow a normal curve?
11. ADVANCED TOPIC: Christakis and Fowler (2007) studied more than 12,000 people over a 32-year period to examine if people’s chances of becoming obese are related to whether they have friends and family who become obese. They reported that “A person’s chance of becoming obese increased by
7. For each of the following samples that were given an experimental treatment, test whether they represent populations that score significantly higher than the general population: (a) a sample of 100 with a mean of 82, (b) a sample of 10 with a mean of 84. The general population of individuals has
6. For each of the following samples that were given an experimental treatment, test whether the samples represent populations that are different from the general population: (a) a sample of 10 with a mean of 44, (b) a sample of 1 with a mean of 48. The general population of individuals has a mean
5. ADVANCED TOPIC: Figure the 99% confidence interval (that is, the lower and upper confidence limits) for each part of problem 3. Assume that in each case the researcher’s sample has a mean of 10 and that the population of individuals is known to follow a normal curve.
4. ADVANCED TOPIC: Figure the 95% confidence interval (that is, the lower and upper confidence limits) for each part of problem 2. Assume that in each case the researcher’s sample has a mean of 100 and that the population of individuals is known to follow a normal curve.
3. For a population that has a standard deviation of 20, figure the standard deviation of the distribution of means for samples of size (a) 2, (b) 3, (c) 4, and (d) 9.
2. For a population that has a standard deviation of 10, figure the standard deviation of the distribution of means for samples of size (a) 2, (b) 3, (c) 4, and (d) 9.
4. Describe how to change the Z scores to raw scores to find the confidence interval.These problems involve figuring. Most real-life statistics problems are done with special statistical software. Even if you have such software, do these problems by hand to ingrain the method in your mind.All data
3. Mention that you next find the Z scores that go with the confidence interval that you want.
2. Explain that the first step in figuring a confidence interval is to estimate the population mean (for which the best estimate is the sample mean), and figure the standard deviation of the distribution of means.
1. Explain that a confidence interval is an estimate (based on your sample’s mean and the standard deviation of the distribution of means) of the range of values that is likely to include the true population mean for the group studied(Population 1). Be sure to mention that the 95% (or 99%)
5. Explain how and why the scores from Steps ❸ and ❹ of the hypothesis-testing process are compared. Explain the meaning of the result of this comparison with regard to the specific research and null hypotheses being tested.
4. Describe how and why you figure the Z score of the sample mean on the comparison distribution.
3. Describe the logic and process for determining (using the normal curve) the cutoff sample score(s) on the comparison distribution at which the null hypothesis should be rejected.
2. Explain the concept of the comparison distribution. Be sure to mention that, with a sample of more than one, the comparison distribution is a distribution of means because the information from the study is a mean of a sample. Mention that the distribution of means has the same mean as the
1. Describe the core logic of hypothesis testing in this situation. Be sure to explain the meaning of the research hypothesis and the null hypothesis in this situation where we focus on the mean of a sample and compare it to a known population mean. Explain the concept of support being provided for
20. Bohnert and colleagues (2007) conducted a study comparing various aspects of social adjustment to college of male and female students during the summer before their first year of college (Time 1) and 10 months later (Time 2).Table 4 shows the results of the study. The “t(83)” column gives
19. Pecukonis (1990), as part of a larger study, measured ego development (a measure of overall maturity) and ability to empathize with others among a group of 24 aggressive adolescent girls in a residential treatment center. The girls were divided into high- and low-ego development groups, and the
18. A researcher predicts that listening to music while solving math problems will make a particular brain area more active. To test this, a research participant has her brain scanned while listening to music and solving math problems, and the brain area of interest has a percentage signal change
17. A family psychologist developed an elaborate training program to reduce the stress of childless men who marry women with adolescent children. It is known from previous research that such men, one month after moving in with their new wife and her children, have a stress level of 85 with a
16. A researcher wants to test whether a certain sound will make rats do worse on learning tasks. It is known that an ordinary rat can learn to run a particular maze correctly in 18 trials, with a standard deviation of 6. (The number of trials to learn this maze is normally distributed.) The
13. For each of the following, (a) state which two populations are being compared,(b) state the research hypothesis, (c) state the null hypothesis, and (d) say whether you should use a one-tailed or two-tailed test and why.i. In an experiment, people are told to solve a problem by focusing on the
12. When a result is significant, explain why it is wrong to say the result “proves”the research hypothesis.
11. List the five steps of hypothesis testing, and explain the procedure and logic of each.
10. Reber and Kotovsky (1997), in a study of problem solving, described one of their results comparing a specific group of participants within their overall control condition as follows: “This group took an average of 179 moves to solve the puzzle, whereas the rest of the control participants
2. When a result is not extreme enough to reject the null hypothesis, explain why it is wrong to conclude that your result supports the null hypothesis.
1. Define the following terms in your own words: (a) hypothesis-testing procedure,(b) .05 significance level, and (c) two-tailed test.
4. You can also request the Z scores directly from SPSS. However, SPSS figures the standard deviation based on the dividing by N - 1 formula for the variance.Thus, the Z scores figured directly by SPSS will be different from the Z scores as you learn to figure them. Here are the steps for figuring
3. Frick (1998) argued that in most cases psychology researchers should not think in terms of samples and populations at all. Rather, he argues, researchers should think of themselves as studying processes. An experiment examines some process in a group of individuals. Then the researcher evaluates
2. The exact percentage of scores between any two Z scores can also be calculated using statistics or spreadsheet software (for example, using the normal curve function in Excel).
1. The formula for the normal curve (when the mean is 0 and the standard deviation is 1) is f(x) =1 22 e -x2>2 where f1x2 is the height of the curve at point x and and e are the usual mathematical constants (approximately 3.14 and 2.72, respectively). However, psychology researchers almost never
26. You apply to 20 graduate programs, 10 of which are in clinical psychology, 5 of which are in counseling psychology, and 5 of which are in social work. You get a message from home that you have a letter from one of the programs you applied to, but nothing is said about which one. Give the
25. You are conducting a survey at a college with 800 students, 50 faculty members, and 150 administrators. Each of these 1,000 individuals has a single email address listed in the online campus directory. Suppose you were to select one email address at random. What is the probability it would be
24. Suppose that you were going to conduct a survey of visitors to your campus.You want the survey to be as representative as possible. (a) How would you select the people to survey? (b) Why would that be your best method?
23. A large study evaluating a national mass media smoking cessation campaign in the United States recruited participants using a “. . . random-digit-dial method, from February 5 through April 15, 2008, prior to the national launch of the . . . media campaign” (Vallone et al., 2011, p. S39).
22. Suppose you want to conduct a survey of the attitude of psychology graduate students studying clinical psychology toward psychoanalytic methods of psychotherapy.One approach would be to contact every psychology graduate student you know and ask them to fill out a questionnaire about it. (a)
21. Suppose that you are designing an instrument panel for a large industrial machine.The machine requires the person using it to reach 2 feet from a particular position. The reach from this position for adult women is known to have a mean of 2.8 feet with a standard deviation of .5. The reach for
20. In the example in problem 18, assume that the mean is 300 and the standard deviation is 25. Using a normal curve table, what scores would be the top and bottom scores to find (a) the middle 50% of architects, (b) the middle 90% of architects, and (c) the middle 99% of architects?
19. In the example in problem 18, using a normal curve table, what is the minimum Z score an architect can have on the creativity test to be in the (a) top 50%,(b) top 40%, (c) top 60%, (d) top 30%, and (e) top 20%?
18. Suppose that the scores of architects on a particular creativity test are normally distributed. Using a normal curve table, what percentage of architects have Z scores (a) above .10, (b) below .10, (c) above .20, (d) below .20, (e) above 1.10,(f) below 1.10, (g) above -.10, and (h) below -.10 ?
17. Using the information in problem 16 and the 50%-34%-14% figures, what is the longest time to recover that a person can take and still be in the bottom(a) 2%, (b) 16%, (c) 50%, (d) 84%, and (e) 98%?
16. The amount of time it takes to recover physiologically from a certain kind of sudden noise is found to be normally distributed with a mean of 80 seconds and a standard deviation of 10 seconds. Using the 50%-34%-14% figures, approximately what percentage of scores (on time to recover) will be
15. A person scores 81 on a test of verbal ability and 6.4 on a test of quantitative ability.For the verbal ability test, the mean for people in general is 50 and the standard deviation is 20. For the quantitative ability test, the mean for people in general is 0 and the standard deviation is 5.
14. On a standard measure of hearing ability, the mean is 300 and the standard deviation is 20. Give the Z scores for persons who score (a) 340, (b) 310, and(c) 260. Give the raw scores for persons whose Z scores on this test are (d) 2.4,(e) 1.5, (f) 0, and (g) -4.5.
13. On a measure of artistic ability, the mean for college students in New Zealand is 150 and the standard deviation is 25. Give the Z scores for New Zealand college students who score (a) 100, (b) 120, (c) 140, and (d) 160. Give the raw scores for persons whose Z scores on this test are (e) -1,
5. Using the information in problem 4 and the 50%-34%-14% figures, what is the minimum score a person has to have to be in the top (a) 2%, (b) 16%,(c) 50%, (d) 84%, and (e) 98%?
2. On an intelligence test, the mean number of raw items correct is 231 and the standard deviation is 41. What are the raw (actual) scores on the test for people with IQs of (a) 107, (b) 83, and (c) 100? To do this problem, first figure the Z score for the particular IQ score; then use that Z score
1. On a measure of anxiety, the mean is 79 and the standard deviation is 12. What are the Z scores for each of the following raw scores? (a) 91, (b) 68, and (c) 103.
5. Note that if you request the variance from SPSS, you can convert it to the variance as we figure it in this chapter by multiplying the variance from SPSS by N - 1 (that is, the number of scores minus 1) and then dividing the result by N (the number of scores). That is, the variance as we are
4. It is important to remember that the standard deviation in most cases is not exactly the average amount that scores differ from the mean. To be precise, the standard deviation is the square root of the average of scores’ squared deviations from the mean. This squaring, averaging, and then
3. Why don’t statisticians use the deviation scores themselves, make all deviations positive, and just use their average? In fact, the average of the deviation scores(treating all deviations as positive) has a formal name—the average deviation or mean deviation. This procedure was actually used
2. This section focuses on the variance and standard deviation as indicators of spread, or variability. Another way to describe the spread of a group of scores is in terms of the range—the highest score minus the lowest score. Suppose that in a particular class the oldest student is 39 years of
1. In more formal, mathematical statistics writing, the symbols can be more complex. This complexity allows formulas to handle intricate situations without confusion. However, in books on statistics for psychologists, even fairly advanced texts, the symbols are kept simple. The simplified form
21. Selwyn (2007) conducted a study of gender-related perceptions of information and communication technologies (such as video game systems, DVD players, and cell phones). The researcher asked 406 college students in Wales to rate 8 technologies in terms of their level of masculinity or femininity.
20. A study involves measuring the number of days absent from work for 216 employees of a large company during the preceding year. As part of the results, the researcher reports, “The number of days absent during the preceding year 1M = 9.21; SD = 7.342 was . . . .” Explain what is written in
19. You figure the variance of a distribution of scores to be –4.26. Explain why your answer cannot be correct.
18. Describe and explain the location of the mean, mode, and median of a distribution of scores that is strongly skewed to the left.
17. A developmental psychologist studies the number of words that seven infants have learned at a particular age. The numbers are 10, 12, 8, 0, 3, 40, and 18.Figure the (a) mean, (b) median, and (c) standard deviation for the number of words learned by these seven infants. (d) Explain what you have
16. A psychologist interested in political behavior measured the square footage of the desks in the official office of four U.S. governors and of four chief executive officers (CEOs) of major U.S. corporations. The figures for the governors were 44, 36, 52, and 40 square feet. The figures for the
15. Make up three sets of scores: (a) one with the mean greater than the median,(b) one with the median and the mean the same, and (c) one with the mode greater than the median. (Each made-up set of scores should include at least five scores.)
14. For the following scores, find the (a) mean, (b) median, (c) sum of squared deviations, (d) variance, and (e) standard deviation:8, -5, 7, -10, 5
13. For the following scores, find the (a) mean, (b) median, (c) sum of squared deviations, (d) variance, and (e) standard deviation:3.0, 3.4, 2.6, 3.3, 3.5, 3.2
12. For the following scores, find the (a) mean, (b) median, (c) sum of squared deviations, (d) variance, and (e) standard deviation:1,112; 1,245; 1,361; 1,372; 1,472
11. For the following scores, find the (a) mean, (b) median, (c) sum of squared deviations, (d) variance, and (e) standard deviation:2, 2, 0, 5, 1, 4, 1, 3, 0, 0, 1, 4, 4, 0, 1, 4, 3, 4, 2, 1, 0
10. (a) Describe the variance and standard deviation. (b) Explain why the standard deviation is more often used as a descriptive statistic than the variance.
9. (a) Describe and explain the difference between the mean, median, and mode.(b) Make up an example (not in your lectures) in which the median would be the preferred measure of central tendency.
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