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nonparametric statistical inference

Questions and Answers of Nonparametric Statistical Inference

11. Consider the assumptions underlying the 11. F test for one-way analysis of variance(Section 16.12). Given the following data, do you believe the F test is defensible?(Explain.)X s n Group 1 75 21
10. Which case, Problem 7 or Problem 8, calls for the application of Tukey’s HSD test?(Explain.)
8. Study the following ANOVA summary, and then provide the missing information for the 8.cells designated a–f:Source SS df MS F p Between-groups 1104 (a) (b) 3.00 (c)Within-groups (d) (e) 184 Total
6. Determine 6. F.05 and F.01 from Table C for each situation below:
5. Consider s2 within and s2 between in Problem 4d.(a) Which is an estimate of inherent variation, and which is an estimate of differential treatment effects?(b) Explain, within the context of this
4. A researcher randomly assigns six students with behavioral problems to three treatment 4.conditions (this, of course, would be far too few participants for practical study). At the end of three
3. You have designed an investigation involving the comparison of four groups. 3.(a) Express H0 in symbolic form.(b) Why can’t H1 be expressed in symbolic form?(c) List several possible ways in
15. Recall the very low correlation between matched pairs in Problem 6 (r12 04). Reanalyze these data as if the scores were from two independent groups of eight participants each.(a) Compare the two
13. Parents of 14 entering 13. first graders eagerly volunteer their children for the tryout of a new experimental reading program announced at a PTA meeting. To obtain an “equivalent” group for
12. You wish to see whether students perform differently on essay tests and on multiplechoice tests. You select a sample of eight students enrolled in an introductory biology course and have each
11. An exercise physiologist compares two cardiovascular fitness programs. Ten matched pairs of out-of-shape adult volunteers are formed on the basis of a variety of factors such as sex, age, weight,
10. A psychological testing firm wishes to determine whether college applicants can improve their college aptitude test scores by taking the test twice. To investigate this question, a sample of 40
9. Is one Internet search engine more ef 9. ficient than another? You ask each of seven student volunteers to find information on a specific topic using one search engine (search 1) and then to find
8. Consider Problem 5: 8.(a) Without performing any calculations, what one value do you know for certain would not fall in a 95% confidence interval for μ1 − μ2? (Explain.)(b) Construct and
7. Consider Problem 6:(a) Without performing any calculations, what one value do you know for certain would fall in a 99% confidence interval for μ1 − μ2? (Explain.)(b) Construct and interpret a
6. The sales manager of a large educational software company compares two training programs 6.offered by competing firms. She forms eight matched pairs of sales trainees on the basis of their verbal
5. Professor Civiello wishes to investigate problem-solving skills under two conditions: solv-ing a problem with and without background music. In a carefully controlled experiment involving six
4. Repeat Problem 3c, except use the direct-difference method.(a) What are the statistical hypotheses?(b) Compute D, SSD, and sD.(c) Test H0.(d) Draw final conclusions.(e) Give the symbols for the
3. The following are scores for 3. five participants in an investigation having a pretest–posttest design:Participant ABCDE Pretest 12 6 8 5 9 Posttest 9 8 6 1 6(a) Compute SSpre, SSpost, and
21. Suppose the following statement were made on the basis of the significant difference reported in Problem 13: “Statistics show that women are higher in emotional intelligence than men.”(a) Is
20. Is randomization the same as random sampling? (Explain.)
19. Examine Problems 8, 9, 10, 14, and 16. In which would it be easiest to clarify causal 19.relationships? (Explain.)
18. Compare the investigation described in Problem 9 with that in Problem 14. Suppose a significant difference had been found in both—in favor of the children who attended preschool in Problem 9
17. From the data given in Problem 16:(a) Compute and interpret the effect size, d; evaluate its magnitude in terms of Cohen’s criteria and in terms of the normal curve.(b) Calculate and interpret
16. The director of Academic Support Services wants to test the efficacy of a possible intervention for undergraduate students who are placed on academic probation. She randomly assigns 28 such
15. (a) Suppose you constructed a 95% confidence interval for μ1 −μ2, given the data in Problem 14. What one value do you already know will reside in that interval?(Explain.)(b) Now construct a
14. A high school social studies teacher decides to conduct action research in her classroom 14.by investigating the effects of immediate testing on memory. She randomly divides her class into two
13. You read the following in a popular magazine: 13. “A group of college women scored significantly higher, on average, than a group of college men on a test of emotional intelligence.” (Limit
12. Parametric statistical tests are tests that are based on one or more assumptions about the nature of the populations from which the samples are selected. What assumptions are required in the t
11. From the data given in Problem 10:(a) Compute and interpret the effect size, d; evaluate its magnitude in terms of Cohen’s criteria and in terms of the normal curve.(b) Calculate and interpret
10. You are investigating the possible differences between eighth-grade boys and girls 10.regarding their perceptions of the usefulness and relevance of science for the roles they see themselves
9. An educational psychologist is interested in knowing whether the experience of attending preschool is related to subsequent sociability. She identifies two groups of first graders: those who had
8. Does familiarity with an assessment increase test scores? You hypothesize that it does.You identify 11 fifth-grade students to take a writing assessment that they had not experienced before. Six
7. For each of the following cases, give the critical value( 7. s) of t:(a) H1: μ1 −μ2 0, n1 6, n2 12, α 05(b) H1: μ1 −μ2 0, n1 12, n2 14, α 01(c) H1: μ1 −μ2 0, n1 14, n2 16, α 05(d)
6. From the data given in Problem 5: 6.(a) Compute and interpret the effect size, d; evaluate its magnitude in terms of Cohen’s criteria and in terms of the normal curve.(b) Calculate and interpret
5. The following results are for two samples, one from Population 1 and the other from 5.Population 2:
4. Assume H0: μ1 − μ2 0 is true. What are the three defining characteristics of the sampling distribution of differences between means?
3. Consider two large populations of observations, A and B. Suppose you have unlimited 3.time and resources.(a) Describe how, through a series of sampling experiments, you could construct a fairly
2. A graduate student wishes to compare the high school grade-point averages (GPAs) of males and females. He identifies 50 brother/sister pairs, obtains the GPA for each individual, and proceeds to
1. Translate each of the following into words, and then express each in symbols in terms 1.of a difference between means relative to zero:(a) μA μB(b) μA μB(c) μA μB(d) μA μB
25. How do you explain the considerable width of the resulting confidence intervals in Problem 24?
24. From the data in Problems 8a and 8b, determine and interpret the respective 95% 24.confidence intervals for μ.
23. Suppose the director in Problem 22 is criticized for conducting a t test in which there is evidence of nonnormality in the population.(a) How do these sample results suggest population
22. Fifteen years ago, a complete survey of all undergraduate students at a large university 22.indicated that the average student smoked X 8 3 cigarettes per day. The director of the student health
21. The expression “p 001” occurs in the results section of a journal article. Does this indicate that the investigator used the very conservative level of significance α 001 to test the null
20. Suppose 20. α 0 5 and the researcher reports that the sample mean “approached significance.”(a) What do you think is meant by this expression?(b) Translate the researcher’s statement into
19. Translate each of the following statements into symbolic form involving a p value:(a) “The results did not reach significance at the .05 level.”(b) “The sample mean fell significantly below
18. Repeat Problem 17, this time assuming that the investigator has in mind α 01.
17. For each of the following sample 17. t ratios, report the p value relative to a suitable “landmark” (as discussed in Section 13.8). Select among the landmarks .10, .05, and .01, and assume
16. The following are the times (in seconds) that a sample of 16. five 8-year-olds took to complete a particular item on a spatial reasoning test: X 12 3 and s 9 8. The investigator wishes to use
15. Using the data in Problem 8b, an investigator tests H0: μ 11 25 against H1: μ 11 25.(a) Determine t.01.(b) Perform the statistical test.(c) Draw final conclusions.
14. Consider the data in Problem 8a. Suppose the researcher wants to test the hypothesis 14.that the population mean is equal to 72; she is interested in sample departures from this mean in either
13. The task in a particular concept-formation experiment is to discover, through trial and error, the correct sequence in which to press a row of buttons. It is determined from the nature of the
12. For each of the following instances, locate the regions of rejection and the sample results 12.on a rough distribution sketch; perform the test; and give final conclusions about the value of
11. From Table B and for df 25, find the proportion of t values that would be:(a) less than t −1 316(b) less than t 1 316(c) between t −2 060 and t 2 060(d) between t −1 708 and t 2 060
10. From Table B, identify the centrally located limits, for 10. df 8, that would include:(a) 90% of t values(b) 95% of t values(c) 99% of t values
9. From Table B, identify the value of t that for df 15:(a) is so high that only 1% of the t values would be higher(b) is so low that only 10% of the t values would be lower
8. Compute the best estimate of 8. σ and σX for each of the following samples:(a) percentage correct on a multiple-choice exam: 72, 86, 75, 66, 90(b) number of points on a performance assessment:
7. Comment on the following statement: For small samples selected from a normal population, the sampling distribution of means follows Student’s t distribution.
6. Suppose that 6. df 3. How do the tails of the corresponding t distribution compare with the tails of the normal curve? Support your answer by referring to Tables A and B in Appendix C (assume α
5. Why is the t distribution a whole family rather than a single distribution?
4. You select a random sample of 10 observations and compute s, the estimate of σ. Even though there are 10 observations, s is really based on only nine independent pieces of information. (Explain.)
3. A random sample of 3. five observations is selected. The deviation scores for the first four observations are −5, 3, 1, and −2.(a) What is the fifth deviation score?(b) Compute SS and sX for
2. When would S (Formula 5.2) and s (Formula 13.1) be very similar? very different?(Explain.)
1. Ben knows that the standard deviation of a particular population of scores equals 16. 1.However, he does not know the value of the population mean and wishes to test the hypothesis H0: μ 100. He
10. For a random sample,X 83 and n 625; assume σ 15.(a) Test H0: μ 80 against H1: 80 α 05 . What does this tell you about μ?(b) Construct the 95% confidence interval for μ. What does this tell
9. (a) If a hypothesized value of μ falls outside a 99% confidence interval, will it also fall outside the 95% confidence interval for the same sample results?(b) If a hypothesized value of μ falls
8. The 99% con 8. fidence interval for μ is computed from a random sample. It runs from 43.7 to 51.2.(a) Suppose for the same set of sample results H0: μ 48 were tested using α 01(two-tailed).
7. The interval width is much wider in Problem 6a than in Problem 6d. What is the principal reason for this discrepancy? Explain by referring to the calculations that Formula(12.1) entails.
6. Construct a confidence interval for μ that corresponds to each scenario in Problems 15a and 15c–15e in Chapter 11.
5. Consider Problem 4 in Chapter 11, whereX 48, n 36, and σ 10.(a) Construct a 95% confidence interval for μ.(b) Construct a 99% confidence interval for μ.
4. Repeat Problems 2a and 2b with n 9 and then with n 100. What generalization is illustrated by a comparison of the two sets of answers (i.e., n 9 versus n 100)?
3. Explain in precise terms the meaning of the interval you calculated in Problem 2b. 3.Exactly what does “95% confidence” refer to?
2. The results for Rachel 2. ’s sample in Problem 1 isX 33 10 n 36 .(a) Calculate σX .(b) Construct the 95% confidence interval for her population mean score.(c) Construct the 99% confidence
1. The national norm for third graders on a standardized test of reading achievement is a 1.mean score of 27 σ 4 . Rachel determines the mean score on this test for a random sample of third graders
20. Suppose a researcher wishes to test H0: μ 100 against H1: μ 100 using the .05 level of significance; however, if she obtains a sample mean far enough below 100 to suggest that H0 is
19. Josh wants to be almost certain that he does not commit a Type I error, so he plans to set 19.α at .00001. What advice would you give Josh?
18. What is the relationship between the level of significance and the probability of a Type I error?
17. On the basis of her statistical analysis, a researcher retains the hypothesis, H0 : μ 250.What is the probability that she has committed a Type I error? (Explain.)
16. A researcher plans to test 16. H0: μ 3 50. His alternative hypothesis is H1: 3 50. Complete the following sentences:(a) A Type I error is possible only if the population mean is _____.(b) A Type
15. Given: 15. μ 60, σ 12. For each of the following scenarios, report zα, the sample z ratio, its p value, and the corresponding statistical decision. (Note: For a one-tailed test, assume that
14. Under what conditions is a directional H1 appropriate? (Provide several examples.)
13. To which hypothesis, H0 or H1, do we restrict the use of the terms retain and reject?
12. Can you make a direct test of, say, H0 75? (Explain.)
11. Explain in general terms the roles of 11. H0 and H1 in hypothesis testing.
10. Repeat Problems 9a 10. –9c, but for H1: 500.(a) Compare these results with those of Problem 9; explain why the two sets of results are different.(b) What does this suggest about which is more
9. State the critical values for testing 9. H0: μ 500 against H1: μ 500, where(a) α 01(b) α 05(c) α 10
8. Mrs. Grant wishes to compare the performance of sixth-grade students in her district with the national norm of 100 on a widely used aptitude test. The results for a random sample of her sixth
7. Consider the generalization from Problem 6. What does this generalization mean for 7.the distinction between a statistically significant result and an important result?
6. Compare the results from Problem 5 with those of Problem 4. What generalization does 6.this comparison illustrate regarding the role of n in significance testing? (Explain.)
5. Repeat Problems 4a 5. –4e, but with n 100.
4. Let 4. ’s say the personnel director in Problem 1 obtained X 48 based on a sample of size 36. Further suppose that σ 10, α 05, and a two-tailed test is conducted.(a) Calculate σX .(b)
3. Suppose that the personnel director in Problem 1 wants to know whether the key- 3.boarding speed of secretaries at her company is different from the national mean of 50.(a) State H0.(b) Which form
2. The personnel director in Problem 1 finds her sample results to be highly inconsistent with the hypothesis that μ 50 words per minute. Does this indicate that something is wrong with her sample
1. The personnel director of a large corporation determines the keyboarding speeds, on 1.certain standard materials, of a random sample of secretaries from her company. She wishes to test the
16. A population of personality test scores is normal with μ 50 and σ 10.(a) Describe the operations you would go through to obtain a fairly accurate picture of the sampling distribution of medians
15. You randomly select a sample ( 15. n 50) from the population in Problem 14 and obtain a sample mean of X 108. Remember: Although you know that σ 15, you don’t know the value of μ.(a) Would
14. Suppose for a normally distributed population of observations you know that 14. σ 15, but you don’t know the value of μ. You plan to select a random sample (n 50) and use the sample mean to
13. Suppose you don’t know anything about the shape of the population distribution of ratings used in Problems 11 and 12. Would this lack of knowledge have any implications for solving Problem 11?
12. Repeat Problem 11h using a sample of size 100.(a) What is the effect of this larger sample on the standard error of the mean?(b) What is the effect of this larger sample on the limits within

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