Basic Statistics For The Behavioral Sciences 5th Edition Gary Heiman - Solutions

2. How do you create independent samples?
1. A scientist has conducted a two-sample experiment, (a) What two parametric procedures are available to him? (b) What is the deciding factor for selecting between them?
25. (a) Why must a relationship be significant to be important? (b) Why can a rela¬ tionship be significant and still be unimportant?
24. In a two-tailed test, A is 35. (a) Is the of -f 2.019 significant? (b) Is the of -t-4.10 significant?
23. You wish to compute the 95% confidence interval for a sample with a df of 80. Using interpolation, determine the that you should use.
22. While reading a published research report, you encounter the following state¬ ments. For each, identify the N, the procedure performed and the outcome, the relationship, and the type of error possibly being made, (a) “When we examined the perceptual skills data, the mean of 55 for the sample
21. (a) How would you report your results if a = .05, N = 43, and = +6.12 is significant? (b) How would you report your results if ot = .05, A = 6, and= —1.72 is not significant?
20. A newspaper article claims that the academic rank of a college is negatively re¬ lated to the rank of its football team. From a sample of 28 colleges, you obtain a correlation coefficient of —.32. (a) Which type of correlation coefficient did you compute? (b) What are Hq and (c) With a =
19. We ask whether a computer word processing program leads to more or fewer grammatical errors. On a typing test without a computer, p, = 12. A sample using a computer has scores of 8, 12, 10, 9, 6, and 7. Perform all parts of the /-test and draw the appropriate conclusions.
18. Foofy computes the correlation between an individual’s physical strength and his or her college grade point average. Using a computer, the correlation for a sample of 2000 people is r(1998) = +.08, p < .0001. She claims this is a useful tool for predicting which college applicants are likely
17. A scientist suspects that as a person’s stress level changes, so does the amount of his or her impulse buying. With N = 72, his r is -I-.38. (a) What are Hq and(b) With a = .05, what is (c) Report these results using the correct format.(d) What conclusions should he draw? (e) What other
16. Eventually, for the study in question 15, Poindexter reported that r(18) = -1-.41, p> .05. (a) What should he conclude about this relationship? (b) What other computations should he perform to describe the relationship in these data?(c) What statistical principle should he be concerned with?
15. Poindexter examined the relationship between the quality of sneakers worn by volleyball players and their average number of points scored per game. Studying 20 people who owned sneakers of good to excellent quality, he computed r == -I-.41. Without further ado, he immediately claimed to have
14. In question 13, (a) What statistical principle should Foofy be concerned with?(b) Identify three problems with her study from a statistical perspective.(c) Why would correcting these problems improve her study?
13. Foofy studies if hearing an argument in favor of an issue alters participants’ atti¬ tudes toward the issue one way or the other. She presents a 30-secon(^argument to 8 people. In a national survey about this issue, p, = 50. She obtains X = 53.25 and s\ = 569.86. (a) What are //q and (b)
12. A researcher predicts that smoking cigarettes decreases a person’s sense of smell. On a test of olfactory sensitivity, the p. for nonsmokers is 18.4. A sample of peo¬ ple who smoke a pack a day produces these scores:16 14 19 17 16 18 17 15 18 19 12 14(a) What are and for this study? (b)
11.You ask whether this textbook is beneficial or detrimental to students learning statistics. On a national statistics exam, p- = 68.5 for students using other text¬ books. A sample of students using this book has the following scores:64 69 92 77 71 99 82 74 69 88(a) What are Hq and for this
10.(a) What are the three aspects of maximizing the power of a r-test? (b) What are the three aspects of maximizing the power of a correlation coefficient?
9. (a) What is power? (b) What outcome should cause you to worry about having sufficient power? (c) Why? (d) At what stage do you build in power?
8. Say that you have a sample mean of 44 in a study, (a) Estimate the corresponding p, using point estimation, (b) What would a confidence interval for this (jl tell you? (c) Why is computing a confidence interval better than using a point estimate?
7. What is the final step when results are significant in any study?
6. Summarize the steps involved in analyzing the results of a one-sample experiment.
5. Summarize the steps involved in analyzing a Pearson correlational study.
4. (a) Why are there different values of when samples have different Nsl (b) What must you compute in order to find
3. (a) What is the difference between and cr^? (b) How is their use the same?
2. In this chapter, you learned about four different statistical procedures (plus power). List them.
1. A scientist has conducted a one-sample experiment, (a) What two parametric pro¬ cedures are available to her? (b) What is the deciding factor for selecting between them? (c) What are the other assumptions of the t-test?
27. A report indicates that brand X toothpaste significantly reduced tooth decay rela¬ tive to other brands, with p < .44. (a) What does “significant” indicate about the researcher’s decision about brand X? (b) What makes you suspicious of the claim that brand X works better than other
26. Researcher A finds a significant relationship between increasing stress level and ability to concentrate. Researcher B replicates this study but finds a nonsignifi¬ cant relationship. Identify the statistical error that each researcher may have made.
25. A researcher suggests that males and females are the same when it comes to intelligence. Why is this hypothesis impossible to test?
24. We measure the self-esteem scores of a sample of statistics students, reasoning that this course may lower their self-esteem relative to that of the typical college student (p. = 55 and = 11.35). We obtain these scores:44 55 39 17 27 38 36 24 36(a) Is this a one-tailed or two-tailed test? Why?
23. Bubbles reads that in study A z^bt = +1-97, p < .05. She also reads that in study B the Zobt +14.21, p < .0001. (a) She concludes that the results of study B are way beyond the critical value used in study A, falling into a region of rejection containing only .0001 of the sampling distribution.
22. Poindexter claims that the real cheating occurs when we increase power by increasing the likelihood that results will be significant. He reasons that if we are more likely to reject Hq, then we are more likely to do so when Hq is true. Therefore, we are more likely to make a Type I error. Why
21. Foofy claims that a one-tailed test is cheating because we use a smaller and therefore it is easier to reject Hq than with a two-tailed test. If the independent variable doesn’t work, she claims, we are more likely to make a Type I error. Why is she correct or incorrect?
20. (a) In question 18, what is the probability that we made a Type I error? What would be the error in terms of the independent and dependent variables? (b) What is the probability that we made a Type II error? What would be the error in terms of the independent and dependent variables?
19. (a) In question 17, what is the probability that we made a Type I error? What would be the error in terms of the independent and dependent variables? (b) What is the probability that we made a Type II error? What would be the error in terms of the independent and dependent variables?
18. We ask whether attending a private school leads to higher or lower performance on a test of social skills. A sample of 100 students from a private school produces a mean of 71.30 on the test, and the national mean for students from public schools is 75.62 (a^ = 28.0). (a) Should we use a
17. Listening to music while taking a test may be relaxing or distracting. We test 49 participants while listening to music, and they produce an X = 54.63. The mean of the population taking this test without music is 50 (a^ = 12). (a) Is this a one- tailed or two-tailed test? Why? (b) What are our
16. For the following, should the researcher perform parametric or nonparametric procedures? (a) When ranking the intelligence of a group of people given a smart pill, (b) When comparing the median income for a group of college professors to that of the national population of all incomes, (c) When
15. What is the difference between a real relationship in nature and one that results from sampling error?
14. For each study in question 13, indicate whether a one- or a two-tailed test should be used and state the Hq and Assume that p. = 50 when the amount of the independent variable is zero.
13. Describe the experimental hypotheses and the independent and dependent vari¬ ables when we study: (a) whether the amount of pizza consumed by college students during finals week increases relative to the rest of the semester,(b) whether breathing exercises alter blood pressure, (c) whether
12. (a) Why is obtaining a significant result a goal of research? (b) Why is declaring the results significant not the final step in conducting research?
11. (a) What is power? (b) Why do researchers want to maximize power? (c) What result makes us worry whether we have sufficient power? (d) Why is a one-tailed test more powerful than a two-tailed test?
10. (a) What are the advantage and disadvantage of two-tailed tests? (b) What are the advantage and disadvantage of one-tailed tests?
9. (a) Why should you prefer parametric procedures? (b) Why can you use para¬ metric procedures even if you do not perfectly meet their assumptions?(c) What happens if you seriously violate the assumptions of a procedure?
8. What does significant convey about (a) The results of an experiment? What does significant indicate about (b) When you compared the obtained and critical val¬ ues? (c) Whether your results are in the region of rejection? (d) The likelihood of obtaining your sample mean when Hq is true?
7. (a) When do you use a one-tailed test? (b) When do you use a two-tailed test?
6. (a) What does Hq communicate? (b) What does H^ communicate?
5. What are experimental hypotheses?
4. What four things must a researcher do prior to collecting data for a study?
5.What does a stand for, and what two things does it determine?
2. What are inferential statistics used for?
1. Why does the possibility of sampling error present a problem to researchers when inferring a relationship in the population?
25. (a) In question 24, if a particular sample does not represent the population of average bowlers, what is your best estimate of the p- of the population it does represent? (b) Explain the logic behind this conclusion.
24. On a standard test of motor coordination, a sports psychologist found that the population of average bowlers had a mean score of 24, with a standard deviation of 6. She tested a random sample of 30 bowlers at Fred’s Bowling Alley and found a sample mean of 26. A second random sample of 30
23. In a study you obtain the following data representing the aggressive tendencies of some football players:40 30 39 40 41 39 31 28 33(a) Researchers have found that in the population of nonfootball players, p- is 30 (a^ = 5). Using both tails of the sampling distribution, determine whether your
22. Suppose that for question 16 you obtained a sample mean of 46. Using the .05 criterion with the region of rejection in both tails of the distribution, should you consider the sample to be representative of the population in which|jL = 50? Why?
21. Suppose that for question 15 you obtained a sample mean of 24. Using the .05 criterion with the region of rejection in both tails of the sampling distribution, should you consider the sample to be representative of the population in which |jL = 18? Why?
20. We obtain a X = 46.8 {N = 15) which may represent the population where jjL = 50 = 11). Using the criterion of .05 and the lower tail of the sampling distribution: (a) What is our critical value? (b) Is this sample in the region of rejection? How do you know? (c) What should we conclude about
19. The mean of a population of raw scores is 33 (a^ = 12). Use the criterion of .05 and the upper tail of the sampling distribution to test whether a sample with X = 36.8 {N = 30) represents this population, (a) What is the critical value?(b) Is the sample in the region of rejection? How do you
18. In a population, p. = 100 and = 25. A sample {N = 150) has X = 102.Using two tails of the sampling distribution and the .05 criterion: (a) What is the critical value? (b) Is this sample in the region of rejection? How do you know?(c) What does this indicate about the likelihood of this sample
17. In the population of typical college students, p, = 75 on a statistics final exam (a^ = 6.4). For 25 students who studied statistics using a new technique, X = 72.1. Using two tails of the sampling distribution and the .05 criterion:(a) What is the critical value? (b) Is this sample in the
16. The mean of a population of raw scores is 50 (cr^ = 18). What is the probability of randomly selecting a sample of 40 scores having a mean below 46?
15. The mean of a population of raw scores is 18 (a^ = 12). What is the probability of randomly selecting a sample of 30 scores having a mean above 24?
14. Foofy computes the X from data that her professor says is a random sample from population Q. She correctly computes that this mean has a z-score of +41 on the sampling distribution for population Q. Foofy claims she has proven that this could not be a random sample from population Q. Do you
13. For a distribution in which X = 43 and = 8, what is the probability of randomly selecting the following? (a) A score of 27 or below; (b) a score of 51 or above; (c) a score between 42 and 44; (d) a score below 33 or above 49 _
12. (a) Why does random sampling produce representative samples? (b) Why does random sampling produce imrepresentative samples?
11. Foofy conducts a survey to learn who will be elected class president and concludes that Poindexter will win. It turns out that Dorcas wins. What is the statistical explanation for Foofy’s erroneous prediction?
10. Four airplanes from different airlines have crashed in the past two weeks. This terrifies Bubbles, who must travel on a plane. Her travel agent claims that the probability of a plane crash is minuscule. Who is correctly interpreting the situation? Why?
9.Poindexter’s uncle is building a house on land that has been devastated by hurricanes 160 times in the past 200 years. However, there hasn’t been a major storm there in 13 years, so his uncle says this is a safe investment. His nephew argues that he is wrong because a hurricane must be due
8. What is the difference between using both tails versus one tail of the sampling distribution in terms of (a) the size of the region of rejection? (b) The critical value?
7. What does comparing the critical value to a sample’s z-score indicate?
6. When testing the representativeness of a sample mean, (a) what is the criterion? (b) What is the region of rejection? (c) What is the critical value?
5. What does the term sampling error indicate?
4. (a) When are events independent? (b) When are they dependent?
3. (a) What is sampling with replacement? (b) What is sampling without replace¬ ment? (c) How does sampling without replacement affect the probability of events, compared to sampling with replacement?
2. What is random sampling?
1. (a) What does probability convey about an event’s occurence in a sample?(b) What is the probability of a random event based on?
25.Dorcas complains that it is unfair to use SAT scores to determine college admittance because she might do much better in college than predicted, (a) What statistic(s) will indicate whether her complaint is likely to be correct? (b) In reality, the positive correlation coefficient between SAT
24. A researcher measures how positive a person’s mood is and how creative he or she is, obtaining the following interval scores:Participant Mood XCreativity Y1 10 72 86 39 11 46 45 55 63 77 74 82 59 46 10 14(a) Compute the statistic that summarizes this relationship, (b) What is the predicted
23. In question 21 of the Application Questions in Chapter 7, we correlated “burnout” scores (X) with absenteeism scores (F)- Using those data: (a) Compute the linear regression equation, (b) Compute the standard error of the estimate.(c) For a burnout of 4, what absence score is predicted? (d)
22. (a) For the relationship in question 21, what is the proportion of variance accounted for? (b) What is the proportion of variance not accounted for?(c) Why is or is not this a valuable relationship?
21. You measure how much people are initially attracted to a person of the opposite sex and how anxious they become during their first date. For the following ratio data, answer the questions below.Participant Attraction XAnxiety Y1 28 26 14 31 54 38 56 10 69 15 76 88 68 94 710 26(a) Compute the
20. A researcher finds that variable A accounts for 15% of the variance in variable B. Another researcher finds that variable C accounts for 25% of the variance in variable B. Why is variable C scientifically more important?
19. (a) In question 18 what advanced statistical procedures can Poindexter employ to improve his predictions about test errors even more? (b) Say that the resulting correlation coefficient is .67. Using the proportion of variance accounted for, explain what this means.
18. Poindexter finds r = —.80 when correlating number of hours studied and number of errors made on a statistics test. He also finds r = +.40 between speed of taking the test and number of errors on the test. He concludes that hours studied forms twice as strong a relationship and is therefore
17. Bubbles has a statistics grade of 70, and Foofy has a grade of 98. (a) Based on question 16, who is predicted to have a higher grade on the admissions test? Why? (b) Subsequently, Bubbles received the higher admissions test score. How can this be explained?
16. A researcher determined that the correlation between statistics grades and scores on a graduate school admissions test is r = +.41. (a) The Sy = 3.90. Compute the standard error of the estimate, (b) If the researcher predicts the overall mean on the admissions test for each student, using
15. What do you know about a research project when you read that it employed multiple correlation and regression procedures?
14. (a) Explain conceptually why the proportion of variance accounted for equals 1.0 with a perfect correlation, (b) Why should you expect most relationships to account for only about 9% to 25% of the variance?
13. Explain how colleges use SAT scores to predict the future grades of college-bound students.
12. What research steps must you go through to use the relationship between a person’s intelligence and grade average in high school so that, if you know a person’s IQ, you can more accurately predict the person’s grade average?
11. (a) What are the two statistical names for r^? (b) How do you interpret r^?
10. When are multiple regression procedures used?
9. How is the value of Sy, related to the size of r? Why?
8. (a) What two assumptions must you make about the data in order for the standard error of the estimate to be accurate, and what does each mean? (b) How does heteroscedasticity lead to an inaccurate description of the data?
7. (a) What is the name for SyT! (b) What does Sy’ tell you about the spread in the Y scores? (c) What does Sy, tell you about your errors in prediction?
6. Distinguish between the predictor variable and the criterion variable in linear regression.
5. (a) What does the Y intercept indicate? (b) What does the slope indicate?

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Basic Statistics For The Behavioral Sciences 5th Edition Gary Heiman - Solutions

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