Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

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670 APPENDIX C | Solutions for Odd-Numbered Problems in the TextCHAPTER 9Introduction to the t Statistic1. A z-score is used when the population standard deviation(or variance) is known. The t statistic is usedwhen the population variance or standard deviation isunknown. The t statistic uses the sample variance orstandard deviation in place of the unknown populationvalues.3. a. The sample variance is 144 and the estimatedstandard error is 4.b. The sample variance is 36 and the estimatedstandard error is 1.5.c. The sample variance is 25 and the estimatedstandard error is 1.5. a. t = ±3.182b. t = ±2.145c. t = ±2.0697. a. M = 3 and s = Ï4 = 2.b. s M= 1.9. a. 4.5 pointsb. The sample variance is 27 and the estimatedstandard error is s M= 1.5.c. For these data, t = 3.00. With df = 11 thecritical value is t = ±2.201. Reject H 0andconclude that there is a significant effect.11. a. With n = 16, s M= 0.75 and t = 1.30.75 = 1.73. Thisis not greater than the critical value of 2.131, sothere is no significant effect.b. With n = 36, s M= 0.50 and t = 1.30.50 = 2.60. Thisvalue is greater than the critical value of 2.042(using df = 30), so we reject the null hypothesisand conclude that there is a significant treatmenteffect.c. As the sample size increases, the likelihood ofrejecting the null hypothesis also increases.13. a. With a two-tailed test, the critical boundaries are±2.306 and the obtained value of t = 3.31.5 = 2.20is not sufficient to reject the null hypothesis.b. For the one-tailed test the critical value is 1.860,so we reject the null hypothesis and concludethat participants significantly overestimated thenumber who noticed.15. a. With df = 15, the critical values are ±2.947. Forthese data, the sample variance is 16, the estimatedstandard error is 1, and t = 8.21 = 8.20. Reject thenull hypothesis and conclude that there has been asignificant change in the level of anxiety.b. With df = 15, the t values for 90% confidence are±1.753, and the interval extends from 21.547 to25.053.c. The data indicate a significant change in the levelof anxiety, t(15) = 8.20, p < .01, 90% CI[21.547, 25.053].17. a. The estimated standard error is 1.9, andt = −4.5/1.9 = −2.37. For a two-tailed test, thecritical value is 2.306. Reject the null hypothesis,scores for students with e-books are significantlydifferent.b. For 90% confidence, use t = ±1.860. The intervalis 77.2 ± (1.860)1.9 and extends from 73.666 to80.734.c. The results show that exam scores weresignificantly different for students using e-booksthan for other students, t(8) = 2.37, p < .05,90%CI[73.666, 80.734]. 0.637.19. a. With n = 9 the estimated standard error is 4 andt = 4 4 = 1. r2 = 1 49 = 0.111. Cohen’s d = 12= 0.333.b. With n = 16 the estimated standard error is 3 andt = 4 3 = 1.33. r2 = 1.77416.77 = 0.106. Cohen’s d = 12= 0.333.c. The sample size does not have any influence onCohen’s d and has only a minor effect on r 2 .21. a. H 0: μ ≤ 4 (not greater than neutral). The estimatedstandard error is 0.26 and t = 2.04. With acritical value of 1.753, reject H 0and conclude thatthe males with a great sense of humor were ratedsignificantly higher than neutral.b. H 0: μ ≥ 4 (not lower than neutral). The estimatedstandard error is 0.295 and t = −2.37. With acritical value of −1.753, reject H 0and concludethat the males with a no sense of humor were ratedsignificantly lower than neutral.23. a. H 0: μ = 50. With df = 9 the critical valuesare t = ±3.250. For these data, M = 55.5,SS = 162.5, s 2 = 18.06, the standard error is 1.34,and t = 4.10. Reject H 0and conclude that mathematicalachievement scores for children with ahistory of daycare are significantly different fromscores for other childrenb. Cohen’s d = 5.54.25 = 1.29.c. The results indicate that mathematics test scoresfor children with a history of daycare are significantlydifferent from scores for children withoutdaycare experience, t(9) = 4.10, p < .01,d = 1.29.
APPENDIX C | Solutions for Odd-Numbered Problems in the Text 671CHAPTER 10 The t Test for Two Independent SamplesThere are several possible solutions to the matchstickpuzzle in Problem 15 but all involve destroying two of theexisting squares. One square is destroyed by removing twomatchsticks from one of the corners and a second square isdestroyed by removing one matchstick. The three removedmatchsticks are then used to build a new square using a linethat already exists in the figure as the fourth side. One solutionis shown in the following figure.Figure C3Original pattern with 5 squares (arrows note matchsticks to remove)New pattern with 4 squares (arrows note new locations for matchsticks)1. An independent-measures study uses a separatesample for each of the treatments or populations beingcompared.3. a. The first sample has s 2 = 12 and the secondhas s 2 = 6. The pooled variance is 54 6 = 9(halfway between).b. The first sample has s 2 = 12 and the second hass 2 = 3. The pooled variance is 54 9 = 6 (closer tothe variance for the larger sample).5. a. The pooled variance is 120.b. The estimated standard error is 4.00.c. A mean difference of 8 would produce t = 8 4 =2.00. With df = 28 the critical values are ±2.048.Fail to reject H 0.7. The null hypothesis says that there is no mean differencebetween the two populations of students. Thepooled variance is 20, the estimated standard erroris 2, and t = 8 2 = 4.00. With df = 18, the criticalboundaries are ±2.878. Reject the null hypothesisand conclude that there is a significant difference inthe high school performance of students who watchedSesame Street as children and those who did not.
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EDITION10Statistics for theBehavior
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Statistics for the Behavioral Scien
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CONTENTSCHAPTER 1 Introduction to S
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CONTENTSvii5.4 Using z-Scores to St
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CONTENTSixCHAPTER 10 The t Test for
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CONTENTSxiCHAPTER 15 Correlation 48
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PREFACEMany students in the behavio
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PREFACExv3. The former Chapter 19,
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PREFACExviiTo the StudentA primary
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ABOUT THE AUTHORSFREDERICK J GRAVET
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PREVIEWBefore we begin our discussi
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4 CHAPTER 1 | Introduction to Stati
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10 CHAPTER 1 | Introduction to Stat
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PREVIEWThere is some evidence that
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36 CHAPTER 2 | Frequency Distributi
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Central TendencyCHAPTER3Tools You W
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SECTION 3.1 | Overview 69DEFINITION
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SECTION 3.2 | The Mean 71research r
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SECTION 3.2 | The Mean 73the distri
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SECTION 3.2 | The Mean 75TABLE 3.1S
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SECTION 3.2 | The Mean 77Table 3.2
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SECTION 3.3 | The Median 793.3 The
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SECTION 3.3 | The Median 81To find
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SECTION 3.4 | The Mode 832. What is
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SECTION 3.4 | The Mode 85FIGURE 3.7
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SECTION 3.5 | Selecting a Measure o
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SECTION 3.6 | Central Tendency and
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FOCUS ON PROBLEM SOLVING 95of centr
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PROBLEMS 976. A population of N = 1
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VariabilityCHAPTER4Tools You Will N
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SECTION 4.1 | Introduction to Varia
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SECTION 4.2 | Defining Standard Dev
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SECTION 4.3 | Measuring Variance an
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SECTION 4.4 | Measuring Standard De
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SECTION 4.5 | Sample Variance as an
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SECTION 4.6 | More about Variance a
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SUMMARY 1252. A population has a me
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FOCUS ON PROBLEM SOLVING 127VAR0000
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PROBLEMS 1299. For the following se
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z-Scores: Location of Scoresand Sta
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SECTION 5.1 | Introduction to z-Sco
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SECTION 5.2 | z-Scores and Location
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SECTION 5.2 | z-Scores and Location
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SECTION 5.3 | Other Relationships B
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SECTION 5.4 | Using z-Scores to Sta
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SECTION 5.4 | Using z-Scores to Sta
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SECTION 5.5 | Other Standardized Di
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SECTION 5.5 | Other Standardized Di
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SECTION 5.6 | Computing z-Scores fo
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SECTION 5.7 | Looking Ahead to Infe
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SUMMARY 153LEARNING CHECK1. In N =
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DEMONSTRATION 5.2 155sure that your
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PROBLEMS 15716. A distribution of e
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PREVIEWHow likely is it that you wi
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162 CHAPTER 6 | Probabilitythe prob
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164 CHAPTER 6 | Probability(Note: W
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166 CHAPTER 6 | ProbabilityFIGURE 6
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168 CHAPTER 6 | Probability■ The
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170 CHAPTER 6 | ProbabilityFinding
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172 CHAPTER 6 | Probabilityand exac
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174 CHAPTER 6 | ProbabilityFinally,
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176 CHAPTER 6 | ProbabilityXz-score
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178 CHAPTER 6 | ProbabilityBOX 6.1
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180 CHAPTER 6 | ProbabilityEXAMPLE
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182 CHAPTER 6 | ProbabilityFIGURE 6
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184 CHAPTER 6 | Probability6.5 Look
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186 CHAPTER 6 | Probability2. For a
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188 CHAPTER 6 | ProbabilityDEMONSTR
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190 CHAPTER 6 | Probability6. Draw
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Probability and Samples: TheDistrib
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SECTION 7.1 | Samples, Populations,
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SECTION 7.1 | Samples, Populations,
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SECTION 7.2 | The Distribution of S
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SECTION 7.3 | Probability and the D
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SECTION 7.3 | Probability and the D
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SECTION 7.4 | More about Standard E
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SECTION 7.4 | More about Standard E
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FOCUS ON PROBLEM SOLVING 219SUMMARY
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PROBLEMS 221STEP 2Compute the z-sco
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Introduction toHypothesis TestingCH
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SECTION 8.1 | The Logic of Hypothes
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SECTION 8.2 | Uncertainty and Error
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SECTION 8.2 | Uncertainty and Error
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SECTION 8.3 | More about Hypothesis
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SECTION 8.3 | More about Hypothesis
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SECTION 8.4 | Directional (One-Tail
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SECTION 8.5 | Concerns about Hypoth
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SECTION 8.5 | Concerns about Hypoth
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SECTION 8.6 | Statistical Power 255
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FOCUS ON PROBLEM SOLVING 2618. The
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PROBLEMS 263In this distribution, o
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PROBLEMS 26513. A random sample is
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Introduction to the t StatisticCHAP
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SECTION 9.1 | The t Statistic: An A
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SECTION 9.2 | Hypothesis Tests with
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SECTION 9.2 | Hypothesis Tests with
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SECTION 9.3 | Measuring Effect Size
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SECTION 9.4 | Directional Hypothese
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SUMMARY 2913. A researcher rejects
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DEMONSTRATION 9.1 293One-Sample Sta
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PROBLEMS 295PROBLEMS1. Under what c
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PROBLEMS 297b. Construct the 90% co
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The t Test for TwoIndependent Sampl
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SECTION 10.1 | Introduction to the
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SECTION 10.2 | The Null Hypothesis
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SECTION 10.3 | Hypothesis Tests wit
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SECTION 10.4 | Effect Size and Conf
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SECTION 10.5 | The Role of Sample V
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KEY TERMS 325SUMMARY1. The independ
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FOCUS ON PROBLEM SOLVING 327Group S
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PROBLEMS 329The t Statistic Finally
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PROBLEMS 331c. Write a sentence dem
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PROBLEMS 33319. If other factors ar
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PREVIEWIt’s the night before an e
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338 CHAPTER 11 | The t Test for Two
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PREVIEWYour job interview is tomorr
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Repeated-MeasuresAnalysis of Varian
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SECTION 13.1 | Overview of the Repe
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SECTION 13.2 | Hypothesis Testing a
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SPSS ® 4375. When the obtained F-r
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DEMONSTRATION 13.1 439you must also
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PROBLEMS 441PROBLEMS1. How does the
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PROBLEMS 44313. The following summa
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PROBLEMS 44523. The following data
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Two-FactorAnalysis of Variance(Inde
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SECTION 14.1 | An Overview of the T
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SECTION 14.3 | More about the Two-F
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SUMMARY 473SUMMARY1. A research stu
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FOCUS ON PROBLEM SOLVING 475Descrip
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DEMONSTRATION 14.1 477STEP 2STAGE 1
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PROBLEMS 479PROBLEMS1. Define each
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PROBLEMS 48115. Research results in
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PROBLEMS 483EasyFactorA TaskDifficu
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PREVIEWA recent report describing t
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488 CHAPTER 15 | CorrelationDEFINIT
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490 CHAPTER 15 | CorrelationDEFINIT
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492 CHAPTER 15 | CorrelationSubstit
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494 CHAPTER 15 | Correlationeither
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496 CHAPTER 15 | Correlationreliabl
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498 CHAPTER 15 | Correlation60Numbe
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500 CHAPTER 15 | CorrelationOne of
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502 CHAPTER 15 | CorrelationBOX 15.
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504 CHAPTER 15 | Correlation171615Z
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506 CHAPTER 15 | Correlation3. What
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508 CHAPTER 15 | Correlationon the
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510 CHAPTER 15 | CorrelationLEARNIN
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512 CHAPTER 15 | CorrelationScoresR
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514 CHAPTER 15 | CorrelationThe pro
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516 CHAPTER 15 | Correlationthat a
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518 CHAPTER 15 | Correlationmeasure
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520 CHAPTER 15 | CorrelationSUMMARY
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522 CHAPTER 15 | CorrelationTo comp
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524 CHAPTER 15 | CorrelationSTEP 2C
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526 CHAPTER 15 | Correlation14. Ide
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Introduction to RegressionCHAPTER16
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SECTION 16.1 | Introduction to Line
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SECTION 16.2 | The Standard Error o
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SECTION 16.3 | Introduction to Mult
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KEY TERMS 553a predicted portion an
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DEMONSTRATION 16.1 555DEMONSTRATION
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PROBLEMS 557Alzheimer’s disease.
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The Chi-Square Statistic:Tests for
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SECTION 17.1 | Introduction to Chi-
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SECTION 17.2 | An Example of the Ch
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SECTION 17.4 | Effect Size and Assu
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SECTION 17.4 | Effect Size and Assu
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SECTION 17.5 | Special Applications
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SECTION 17.5 | Special Applications
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SUMMARY 591With df = 2 and α = .05
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SPSS ® SPSS ® 593General instruct
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DEMONSTRATION 17.1 595FOCUS ON PROB
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PROBLEMS 597Finally, we can add the
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PROBLEMS 599response, a sample of 1
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PROBLEMS 601a researcher obtains a
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PREVIEWIn 1960, Gibson and Walk des
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606 CHAPTER 18 | The Binomial Testp
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608 CHAPTER 18 | The Binomial Test2
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610 CHAPTER 18 | The Binomial Test
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612 CHAPTER 18 | The Binomial Test
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614 CHAPTER 18 | The Binomial TestT
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616 CHAPTER 18 | The Binomial Testt
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618 CHAPTER 18 | The Binomial TestB
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Page 647 and 648: Basic Mathematics ReviewAPPENDIXAPR
Page 649 and 650: APPENDIX A | Basic Mathematics Revi
Page 667: APPENDIX A | Basic Mathematics Revi
Page 670 and 671: 648 APPENDIX B | Statistical Tables
Page 686 and 687: 664 APPENDIX C | Solutions for Odd-
Page 706 and 707: 684 APPENDIX D | General Instructio
Page 709 and 710: Hypothesis Tests for OrdinalData: M
Page 711 and 712: APPENDIX E | Hypothesis Tests for O
Page 721: APPENDIX E | Hypothesis Tests for O
Page 724 and 725: 702 Statistics Organizer: Finding t
Page 739 and 740: ReferencesAckerman, R. (2011). Meta
Page 741 and 742: REFERENCES 719Alzheimer’s disease
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REFERENCES 721of aging and estrogen
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724 NAME INDEXKaell, A., 622Kahn, K
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726 SUBJECT INDEXConfidence interva
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728 SUBJECT INDEXIndependent random
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730 SUBJECT INDEXResearch studies,
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732 SUBJECT INDEXTwo-factor ANOVA (
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