Statistics For The Behavioral Sciences, 9th Edition Solution Manual

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Solutions-page280Solutions forEnd-of-Chapter ProblemsNote: Many of the problems in the text require several stages of computation. At each stagethere is an opportunity for rounding answers. Depending on the exact sequence of operationsused to solve a problem, different individuals will round their answers at different times and indifferent ways. As a result, you or your students may obtain answers that are slightly differentfrom those presented here. To help minimize this problem, we have tried to include thenumerical values obtained at different stages of complex problems rather than presenting a singlefinal answer.

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Solutions-Chapter 1-page281Chapter 1: Introduction to Statistics1.a. The population is the entire set of adolescent boys who are taking medication fordepression.b. The sample is the group of 30 boys who were tested in the study.2.A parameter is a characteristic, usually a numerical value, that describes a population. Astatistic is a characteristic, usually numerical, that describes a sample.3Descriptive statistics are used to simplify and summarize data. Inferential statistics usesample data to make general conclusions about populations.4. a. If treatments 1 and 2 affect individuals differently, then the scores in the first sample willbe different from the scores in the second sample.b. Even if the two treatments have exactly the same effect, you do not expect the individualsin one condition to behave exactly the same as the individuals in the other treatment. Thetwo groups will produce different scores with different means. In this case, the differencesare the result of sampling error.5. A correlational studyhas only one group of individuals andmeasures two(or more)differentvariables for each individual. Other research methods evaluating relationships between variablescompare two (or more) different groups of scores.6. The goal of an experiment is to demonstrate the existence of a cause-and-effect relationshipbetween two variables. To accomplish the goal, an experiment must manipulate an independentvariable and control other, extraneous variables.7. The independent variable is holding a pen in your teeth versus holding the pen in your lips.The dependent variable is the rating given to each cartoon.8. This is not an experiment because no independent variable is manipulated. They arecomparing two preexisting groups of individuals.9. a. This is a nonexperimental study. The researcher is simply observing, not manipulating,two variables.b. This is an experiment. The researcher is manipulating the type of drink and should controlother variables by beginning with equivalent groups of participants.10.a. The dependent variable is the number of colds each participant has during the winter.b. discretec. ratio scale (zero means none)

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Solutions-Chapter 1-page28211. This is not an experiment because there is no manipulation. Instead, the study is comparingtwo preexisting groups (American and Canadian students).12. The independent variable is the substance that is inhaled, either oxytocin or the inactiveplacebo. The dependent variable ishow likelythe people were to give their money to the trustee.13.a. continuous. The variable is the amount of time and time is infinitely divisible.b. discrete.Family size consists of whole-number categories that cannot be divided.c. discrete.There are two separate and distinct categories (analog and digital).d. continuous.The variable is knowledge of statistics, which is measured with quiz scores.It could be a 5-point quiz, a 10-point quiz, or a 50-point quiz, which indicates thatknowledge can be divided indefinitely.14.a.An ordinal scale provides information about the direction of difference (greater or less)between two measurements.b.An interval scale provides information about the magnitude of the difference betweentwo measurements.c. A ratio scale provides information about the ratio of two measurements.15. a. The independent variable is humorous versus nonhumorous.b. The independent variable is measured on a nominal scale.c. The dependent variable is the number of sentences recalled.d. The dependent variable is measured on a ratio scale.16. Shyness is an internal attribute or characteristic that cannot be observed or measureddirectly. Shyness could be operationally defined by identifying and observing external behaviorsassociated with shyness. Or, participants could be given a questionnaire asking how they behaveor feel in situations for which shyness might have an influence.17. a.The independent variable is whether or not the motivational signs were posted, and thedependent variable is amount of use of the stairs.b. Posting versus not posting is measured on a nominal scale.18.a.X= 12b.X2= 46c.(X)2= (12)2= 144d.(X–1) = 819. a.X= 15b.X2= 65c.(X+ 1) = 20d.(X+ 1)2= 100

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Solutions-Chapter 1-page28320. a.X=–8b.X2= 22c.(X+ 4) = 1221. a.X= 11b.Y= 25c.XY= 5422. a. Σ(X+ 1)b. Σ(X+ 1)2c. (ΣX)2–323. a.X2= 30b. (X)2= 64c.(X–2) = 0d.(X–2)2= 14

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Solutions-Chapter 2-page284Chapter 2: Frequency Distributions1.Xf────103968472635141────2.Xfp%────────────920.1010%830.1515%750.2525%640.2020%530.1515%420.1010%310.055%────────────3. a.n= 12b. ΣX= 40c. ΣX2= 1484. a.n= 145. a.Xfb.Xfb. ΣX= 3528-29125-298c. ΣX2= 10726-27420-24 1024-25715-19322-23410-14220-2125-9118-19216-17114-15012-13110-1118-91

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Solutions-Chapter 2-page2856.Xf60-64155-59250-54245-491Younger drivers, especially those 20 to 2940-442years old, tend to get more tickets.35-39330-34325-29520-24815-1937. a. 2 points wide and around 8 intervalsb. 5 points wide and around 12 intervals or 10 points wide and around 6 intervalsc. 10 points wide and around 9 intervals8. A regular table reports the exact frequency for each category on the scale of measurement.After the categories have been grouped into class intervals, the table reports only the overallfrequency for the interval but does not indicate how many scores are in each of the individualcategories.9. A bar graph leaves a space between adjacent bars and is used with data from nominal orordinal scales. In a histogram, adjacent bars touch at the real limits. Histograms are used todisplay data from interval or ratio scales.10. a.Xf101908173615245342211

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Solutions-Chapter 2-page286b.5│┌───┐│││4│┌───┤│││││3││││┌───┐││││││2│┌───┤│├───┐││f││││││││1│┌───┤│││├───┤├───┐┌───┐││││││││││││└─┴───┴───┴───┴───┴───┴───┴───┴───┴───┴───┴───X123456789101111.7│7│6│┌───┐6│5│││5│4│┌───┤│4│f3│││├───┐3│2│││││2│1│┌───┤││├───┬───┐1│└┴───┴───┴───┴───┴───┴───┴──└23456723456712. a. histogram or polygon (ratio scale)b. bar graph (ordinal scale)c. bar graph (nominal scale)d.histogram or polygon (ratio scale)e. bar graph (ordinal scale)

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Solutions-Chapter 2-page28713. a. A bar graph should be used for measurements from an ordinal scale.b.140││120││100││f80││60││40││20││───────────────────────────────────SMLXLXXLT-shirt size14. A bar graph is appropriate for scores measured on an ordinal scale.160││140││120││f100││80││60││40││───────────────────────────────────ABCDFGrade15. a.────Xf────918174655742────b. positively skewed

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Solutions-Chapter 2-page28816.────Xf────8274The distribution in negatively skewed.655342312211────17. a.─────Xf─────1019282726453423221─────b.│4││3│f│2││1││└─────────────────────────────────X12345678910c. It is a fairly symmetrical distribution centered at X = 6. The scores are scattered across thescale.

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Solutions-Chapter 2-page28918.65○○---○ Unhappyf 4——Happy3○2○○1○○————————————————————————12345678910Number of FriendsYes, it appears that the happy people tend to have more friends than the unhappy peopledo.19.──────────────Xfcfc%──────────────7225100632392562080491456345202114──────────────a. The percentile rank forX= 2.5 is 4%b. The percentile rank forX= 6.5 is 92%c. The 20thpercentile is X = 3.5.d. The 80thpercentile is X = 5.5.20.──────────────Xfcfc%──────────────50-5912010040-493199530-396168020-295105010-1935250-92210──────────────

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Solutions-Chapter 2-page290a. The percentile rank forX= 9.5 is 10%b. The percentile rank forX= 39.5 is 80%c. The 25thpercentile is X = 19.5.d. The 50thpercentile is X = 29.5.21.──────────────Xfcfc%──────────────10250100954896884386715357061020405610204448──────────────a. The percentile rank forX= 6 is 30%.b. The percentile rank forX= 9is 91%c. The 25thpercentile is X = 5.75.d. The 90thpercentileis X = 8.9.22. a. The percentile rank forX=15 is 17.5%.b.The percentile rank forX= 18 is 77.5%.c. The 15thpercentile is X = 14.75.d. The 90thpercentile is X = 19.23. a. The percentile rank forX=5 is 8%.b.The percentile rank forX= 12 is 85%.c. The 25thpercentile is X = 7.d. The 70thpercentile is X = 10.24. a. The 30thpercentile is X = 72.b. The 88thpercentile is X = 93.5.c. The percentile rank for X = 77 is40%.d. The percentile rank for X = 90 is 81%.25.1│7962│08412920358263│0948624│5435│36816│4

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Solutions-Chapter 2-page29126. a. 4b. 72, 71, 78, and 74c. 2d. 46 and 4027.2│804723│490694│5439765│43193826│55057│248│1

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Solutions-Chapter 3-page292Chapter 3: Central Tendency1.The purpose of central tendency is to identify a single score that serves as the bestrepresentative for an entire distribution, usually a score from the center of the distribution.2. No single method for computing a measure of central tendency works well in all situations.With three different methods, however, at least one usually works well3. The mean is 29/10 = 2.9, the median is 2.5, and the mode is 2.4. For this sample, the mean is 94/12 = 7.83, the median is 8, and the mode is 8.5. The mean is 69/12 = 5.75, the median is 6, and the mode is 7.6. The mean is 107/15 = 7.13, the median is 7, and the mode is 6.7. a. Median = 2.83 (2.5 + 0.33)b. Median = 38.X= 63.9.N= 2510. The original sample hasn= 8 andΣX= 80. The new sample hasn= 9 and ΣX= 81. Thenew mean isM= 9.11. The original sample hasn= 5 and ΣX= 60. The new sample hasn= 4 and ΣX= 52. Thenew mean isM= 13.12. With the new score,n= 12, ΣX= 60, andM= 5.13. After the score is removed, n =8, ΣX= 88, andM= 11.14. After the score is changed, N = 20, ΣX= 320, and μ = 16.15. After the score is changed,n= 7, ΣX= 49, andM= 7.16. The original sample hasn= 7 and ΣX= 35. The new sample hasn= 8 and ΣX= 48. Thenew score must beX= 13.17. The original sample hasn= 16 and ΣX= 320. The new sample hasn= 15 and ΣX= 285.The score that was removed must beX= 35.

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Solutions-Chapter 3-page29318. a. The new mean isM= 6.b. The new mean is (12 + 56)/10 = 6.8.c. The newmean is (28 + 24)/10 = 5.2.19. a. The new mean is 75/10 = 7.5.b. The new mean is (20 + 60)/10 = 8c. The new mean is (30 + 40)/10 = 720.With a skewed distribution, the extreme scores in the tail can displace the mean out towardthe tail. The result is that the mean is often not a very representative value.21.The median is used instead of the mean when there is a skewed distribution (a few extremescores), an open-ended distribution, undetermined scores, or an ordinal scale.22. a. With one extreme score, the median would be better than the mean.b. With a nominal scale, the mode is the only option.c. With numerical scores, the mean is usually best.23. a. Mode = 2b. Median = 2c. You cannot findthe total number of fast-food visits (ΣX) for this sample.24.a.5││4│┌───┐│││3│┌───┬───┤││││││2│┌───┐│││├───┐┌───┐f││││││││││1│┌───┬───┤├───┤│││├───┤│││││││││││││└─┴───┴───┴───┴───┴───┴───┴───┴───┴───┴───┴─X10+1+2+3+4+5+6+7+8Weight change (in pounds) during the first semester of freshman yearb. The mean difference in weight isM= 79/20 = +3.95 pounds. On average, the studentsgained 3.95 points during the semester.c. Yes, nearly all the students showed some weight gain.25.a. For weekdaysM= 0.99 inches and for weekend days isM= 1.67 inches.b. There does appear to be more rain on weekend days than there is on weekdays.

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Solutions-Chapter 4-page294Chapter 4: Variability1.a.SSis the sum of squared deviation scores.b. Variance is the mean squared deviation.c.Standard deviation is the square root of the variance. It provides a measure of thestandard distance from the mean.2.SScannot be less than zero because it is computed by adding squared deviations. Squareddeviations are always greater than or equal to zero.3. Standard deviation and variance are measures of distance and are always greater than or equalto zero.4.A standard deviation of zero indicates there is no variability. In this case, all of the scores inthe sample have exactly the same value.5. Without some correction, the sample variance underestimates the variance for the population.Changing the formula for sample variance (usingn–1 instead ofN) is the necessary correction.6. a. No.X= 70 is 10 points away from the mean, only ½ of the standard deviation.b. Yes. Withs= 5, 10 points is equal to a distance of 2 standard deviations.7. a.s= 2 is better (you are above the mean by 3 standard deviations).b.s= 10 is better (you are below the mean by less than half a standard deviation).8.a. The mean is μ = 35 and the standard deviation is still σ = 5.b. The new mean is μ = 90 and the new standard deviation is σ = 15.9.a. The original mean isM= 80 and the standard deviation iss= 8.b. The original mean isM= 12 and the standard deviation iss= 3.10. The mean isM= 86 and the standard deviation iss=3.11. a. The range is either 11 or 12, and the standard deviation is σ = 4.b. After adding 2 points to each score, the range is still either 11 or 12, and the standarddeviation is still σ = 4. Adding a constant to every score does not affect measures ofvariability.12.a.The definitional formula is easy to use when the mean is a whole number and there arerelatively few scores.b. The computational formula is preferred when the mean is not a whole number.

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