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statistics for engineers and scientists

Questions and Answers of Statistics For Engineers And Scientists

11. A psychologist conducts a study of perceptual illusions under two different lighting conditions. Twenty participants were each tested under both of the two different conditions. The experimenter
9. About how many participants are needed for 80% power in each of the following planned studies that will use a t test for dependent means with p 6 .05?
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
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
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
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
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
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
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
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
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
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
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)
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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
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
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
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)
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
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
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
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
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
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
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
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
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 22e -x2>2 where f1x2 is the height of the curve at point x and and e are the usual mathematical
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
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
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
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,
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
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
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%
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%,
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
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)
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.
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
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
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)
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)
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
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
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
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
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
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
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
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)
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.
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
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

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