Essential Statistics for the Behavioral Sciences Brief Edition Solution Manual

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1Problem SolutionsCHAPTER 11.Descriptive statistics are procedures used to summarize, organize,and make sense of a set of scores or observations, whereas inferen-tial statistics are procedures that allow researchers to infer or gener-alize observations made with samples to the larger population fromwhich they were selected.2.Data describe a set of measurements (made up of raw scores); a rawscore describes individual measurements.3.Samples are selected from populations of interest. Hence, samplesconsist of a portion of individuals in a population of interest.4.Experimental, quasi-experimental, and correlational research methods.5.(a) Independent variable. (b) Dependent variable.6.The four scales of measurement are nominal, ordinal, interval, andratio. Ratio scale measurements are the most informative.7.Yes. Nominal values are often coded (i.e., converted to numericvalues) when entered into statistical software.8.Interval variablesdo nothave a true zero, and ratio variablesdohave a true zero.9.Amount; Class.10.Continuous and discrete variables.11.(a) Descriptive statistics. (b) Inferential statistics. (c) Descriptive statistics.12.(a) False. (b) True. (c) True.13.No, it is not necessary to make inferences, becauseallindividuals inthe population were observed.14.The statistics class has apopulationof 25 students enrolled, but asampleof only 23 students attended.15.By definition, samples will always be smaller than the population.Samples constitute a subset (or a smaller set of values) than those inthe population.16.An experimental research method because the researcher claims tohave demonstratedcause.17.A correlational research method because pairs of scores (height,income) were measured and compared for each participant.18.(a) Quasi-independent variable. (b) Quasi-independent variable.(c) Independent variable. (d) Independent variable. (e) Quasi-independent variable. (f) Independent variable.19.(a) Sleeping pill (real or fake). (b) Time spent sleeping.•••

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2Statistics for the Behavioral Sciences20.(a) Cocaine use (dependent vs. inexperienced). (b) Impulsive behavior.21.(a) Nominal. (b) Yes, it is appropriate to numerically code “months”because it is a nominal scale variable.22.Nominal, ordinal, interval, and ratio.23.The main disadvantage of measuring qualitative data is that the dataare on a nominal scale, which limits the types of conclusions thatresearchers can draw. For this reason, quantitative variables are moreoften measured because they are more informative in terms of order,differences, and ratios.24.(a) Qualitative. (b) Quantitative. (c) Quantitative. (d) Qualitative.25.(a) Continuous. (b) Discrete. (c) Continuous. (d) Discrete.26.VariableQualitative vs.QuantitativeContinuous vs.DiscreteType ofMeasurementSexQualitativeDiscreteNominalSeasonsQualitativeDiscreteNominalTime of dayQuantitativeContinuousRatioRating scale scoreQuantitativeDiscreteIntervalMovie ratings (1 to 4 stars)QuantitativeDiscreteOrdinalNumber of students in yourclassQuantitativeDiscreteRatioTemperature (degreesFahrenheit)QuantitativeContinuousIntervalTime (in minutes) to preparedinnerQuantitativeContinuousRatioPosition standing in lineQuantitativeDiscreteOrdinal27.(a) Descriptive statistics. (b) Overall, gun ownership really has notchanged in the last 40 years with the percent of gun owners in 1972being identical to the percent of gun owners in 2012.28.An operational definition.29.No, an experimental method is not possible because the variable (sex)is a preexisting variable; it is a quasi-independent variable.30.(a) Continuous. (b) Quantitative. (c) Ratio scale.31.The 91,373 nineteen-year-old-men likely represent a sample of all19-year-old men in a much larger population.32.Equidistant scales. Variables on an interval scale have equidistantscales, meaning that differences on this scale are informative.

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Problem Solutions3CHAPTER 21.Step 1: Find the real range. Step 2: Find the interval width. Step 3:Construct the frequency distribution.2.Grouped data are distributed in intervals; ungrouped data are not.3.(a) No. (b) Yes.4.To ensure that a single score cannot be counted in more than oneinterval.5.A percentile rank.6.Ungrouped data sets with only a few different scores, and qualitative orcategorical variables.7.Rule 1: A vertical rectangle represents each interval, and the heightof the rectangle equals the frequency recorded for each interval. Rule2: The base of each rectangle begins and ends at the upper and lowerboundaries of each interval. Rule 3: Each rectangle touches adjacentrectangles at the boundaries of each interval.8.Midpoint; Upper boundary.9.When the data are discrete. Histograms are only used with continuousdata.10.Discrete/categorical data.11.(a)Intervalsf(x)18–22513–1738–1273–75(b)Interval: 8–12.12.(a)Classesf(x)L9C16R5(b)Yes, the rat did press the center lever the most.13.The intervals overlap at the upper and lower boundaries, which mightlead to some scores being counted in more than one interval.14.Three errors are (1) the intervals overlap, (2) the class width for eachinterval is not equal, and (3) the distribution includes an open interval.

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4Statistics for the Behavioral Sciences15.The lower boundaries are 35, 46, 57, and 68.16.The upper boundaries are 3, 6, 9, 12, 15, and 18.17.No, the data should remain ungrouped because the data are categorical.18.The interval width for each interval is 3.19.(a)Number of DreamsPercentile Rank4100%388%260%124%010%(b) Two Dreams20.Sixty children qualify for the new cognitive-behavioral therapy.21.(a) A bar chart or pie chart if distributing the letter grades along thex-axis. A histogram or frequency polygon if distributing the numericvalues on a 4.0 grading scale. (b) A bar chart or pie chart. (c) A barchart or pie chart distributing the frequencies for each behavioral ther-apy. (d) A histogram or frequency polygon.22.(a) Histogram. (b) Bar chart. (c) Histogram. (d) Bar chart.23.A = 8, B = 3, C = 1224.(a) A = 78, B = 86, C = 68, D = 13. (b) Yes, this was a difficult testbecause half the class would fail.25.(a) 35 students. (b) 6 students. (c) 15 students.26.100%Cumulative PercentIntervals90%80%70%60%50%40%30%20%10%0%24681012

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Problem Solutions527. (a)0510152025300FrequencyIntervals87654321(b)10FrequencySeason of Birth9876543210SpringSummerFallWinterSpringSummerFallWinter28.

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6Statistics for the Behavioral Sciences29.The interval of 60–79 has the largest portion of students (20% of stu-dents fall in this interval).30.The percentile point for the 50th percentile is 74.5 minutes.31.(a) Real range = 56. (b) 30%.32.(a) While more men earned a bachelor’s degree in psychology in 1970–1971, women earn more than three times the number of bachelor’sdegrees in psychology as of 2005–2006. (b) Ungrouped data, becauseyears are not distributed consecutively.33.(a) A relative percent distribution. (b) About 576 Americans.CHAPTER 31.(a)N. (b)n. (c)μ. (d)MorX.2.Measures of central tendency are statistical measures used to locate asingle score that is most representative or descriptive of all scores in adistribution.3.The median is the score in the middle of a distribution. It is always atthe center of a distribution.4.A population mean is the mean for a set of scores in an entire popula-tion, whereas the sample mean is the mean for a sample, or subset ofscores from a population.5.Five characteristics of the mean are as follows: (1) Changing an exist-ing score will change the mean; (2) adding a new score or completelyremoving an existing score will change the mean, unless that valueequals the mean; (3) adding, subtracting, multiplying, or dividing eachscore in a distribution by a constant will cause the mean to change bythat constant; (4) the sum of the differences of scores from their meanis zero; and (5) the sum of the squared differences of scores from theirmean is minimal.6.The weighted mean equals the arithmetic mean when the sample sizesor “weights” for a set of scores are the same or equal.7.Data that are normally distributed on an interval or ratio scale of mea-surement.8.Data that are skewed and ordinal data.9.The mode is used with other measures of central tendency for anymodal distribution and for nominal data.10.(a) Median. (b) Mean. (c) Mean.11.Mean = 4, median = 2, mode = 0.12.(a) College students: mean = 25, median = 18, mode = 21. Parents:mean = 14, median = 18, mode = 21. (b) Because both distributions areskewed, the median would be the appropriate measure of central ten-dency. This might be misleading, though, because the median indicatesthat texting was the same between groups (the median was 18 in bothsamples), even though differences exist in regard to the mean.

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Problem Solutions713.The mean because the data are distributed normally.14.The mean because the data are normally distributed, and the duration(in hours) is a ratio scale measure.15.(a) Positively skewed distribution. (b) The median.16.The median because the data are negatively skewed.17.The mode because the data are nominal.18.Bimodal distribution.19.Weighted mean = 14.69.20.Weighted mean = 3.65.21.(a) The mean, because time is a ratio measurement. (b) The mode,because blood types are nominal data. (c) The median, because collegerankings are ordinal data.22.(a)M= 22 points. (b)M= 10 points. (c)M= 24 points. (d)M= 6points.23.M= 6 new friends.24.The sum of the differences of scores from the mean is 0.25.The mean will decrease.26.The mean will increase.27.(a) The mean will increase. (b) The mean will not change. (c) The meanwill decrease.28.The new mean weight is 190 pounds.29.Yes, the mean would be appropriate because the data are approximatelynormally distributed (the mean and median do not differ greatly).30.(a) Heavy-drinking men have higher mean self-esteem scores thanheavy-drinking women.31.(a) The mode for nonsmoking Black participants was concern abouta family member; the mode for nonsmoking White participants wasconcern for a friend.32.Yes, participants consumed the most candies in the proximate and vis-ible condition.33.The median because these data are negatively skewed.CHAPTER 41.No. A data set can vary (variability is greater than 0) or not vary (vari-ability is equal to 0). A negative variability is meaningless.2.Two scores; the largest and smallest score in a distribution.3.The IQR is the range of data after the top and bottom 25% of scoresare removed.4.The variance is preferred because it includes all scores to estimate vari-ability.

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8Statistics for the Behavioral Sciences5.Deviations are squared for three reasons: (1) The sum of the differencesof scores from their mean will always equal 0. To avoid having 0 in thenumerator, each deviation is squared. (2) The sum of the squared dif-ferences of scores from their mean is minimal. Hence, the solution weobtain is the smallest possible positive value—or the value with min-imal error. (3) Squaring scores can be corrected by taking the squareroot of the variance.6.The variance of the sample will equal the variance of the populationfrom which the sample was selected, on average.7.(n− 1).8.The standard deviation measures the average distance that scores devi-ate from their mean.9.The empirical rule states that 68% of all scores lie within 1SDof themean, 95% of all scores lie within 2SDof the mean, and 99.7% of allscores lie within 3SDof the mean.10.The standard deviation is always positive; is used to describe quantita-tive variables, typically reported with the mean; and is affected by thevalue of every score in a distribution.11.(a) R = 98 − 24 = 74. (b) IQR = 94 − 77 = 17. (c) SIQR = 8.5. (d)σ2=448.64. (e)σ= 21.18.12.(a) R = 98 − 77 = 21. (b) IQR = 96 − 85 = 11. (c) SIQR = 5.5. (d)s2=55.41. (e)SD= 7.44.13.Yes, Sample 2 has a larger range because the data deviate further fromtheir mean.14.(a)df= 30. (b)s212030== 4.0,SD=4 = 2.15.(a)df= 1,200. (b)s210 8001 200=,,= 9.0,SD=9 = 3.16.No, in both cases, the standard deviation is the square root of the vari-ance. Hence, the population and the sample standard deviation will be93 0=. .17.No, in both cases, the variance is the square of the standard deviation.So the population and sample variance will be 122= 144.18.(a) Decrease. (b) Increase. (c) No effect.19.(a) Increase. (b) No effect. (c) Decrease.20.36.21.6.22.sSD224060 14 074 072 02====−.;...23.Yes, we would divide byN:σ2= 240/60 = 4;σ=4 = 2.00.24.(a)SD= 4. (b)SD= 8.25.SS= 69.60,s2= 7.73,SD= 2.78.26.SS= 37.50,s2= 5.36,SD= 2.31.27.(a)Population:SS= 1,755,σ2= 109.69,σ= 10.47.(b)Sample:SS= 1,755,s2= 117.00,SD= 10.82.

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Problem Solutions928.SD= 0.5.29.(a)df= 60 for men;df= 92 for women.(b) Men are more likely to smoke at least half a pack per day because10 cigarettes is within 1SDof the mean for men but greater than 1SDfrom the mean for women.30.(a) Yes, husbands and wives show a similar distribution in their ratingsof love.(b) The ratings of love data are negatively skewed for husbands, andfor wives. Thus, most husbands, and most wives, appear to give higherratings of love, with a few giving much lower ratings.31.No, the data are likely skewed because the mean is pulled toward thelarger scores in the distribution.32.Men showed greater variability overall because the standard deviationsfor men were larger than for women.CHAPTER 51.Probability (p(x)) is calculated by dividing the number of times an out-come occurs (f(x)) by the total number of possible outcomes (samplespace).2.Two characteristics of probability: Probability varies between 0 and 1and can never be negative.3.The normal distribution is a theoretical distribution with data that aresymmetrically distributed around the mean, median, and mode.4.Normality arises naturally in many physical, behavioral, and socialmeasurement studies.5.The eight characteristics are as follows: (1) The normal distribution ismathematically defined. (2) The normal distribution is theoretical. (3)The mean, median, and mode are all located at the 50th percentile. (4)The normal distribution is symmetrical. (5) The mean can equal anyvalue. (6) The standard deviation can equal any positive value. (7) Thetotal area under the curve of a normal distribution is equal to 1.00. (8)The tails of a normal distribution are asymptotic.6.The mean equals 0, and the standard deviation equals 1.7.Azscore is a unit of measurement distributed along thex-axis of astandard normal distribution. Eachzscore reflects a standard deviationalong thex-axis.8.The standard normal transformation is the difference between a scoreand the mean, divided by the standard deviation.9.Step 1: Transform a raw score (x) into azscore. Step 2: Locate thecorresponding proportion for thezscore in the unit normal table.10.Step 1: Locate thezscore associated with a given proportion in the unitnormal table. Step 2: Transform the z score into a raw score (x).11.(a)p= .375. (b)p= .625. (c)p= 0.

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10Statistics for the Behavioral Sciences12.3,000 mothers were not satisfied.13.(a) .1587. (b) .8531. (c) .5000. (d) .9974. (e) .0250.14.(a) .6915. (b) .0934. (c) .5000. (d) .0250. (e) .4602.15.(a) .4750. (b) .0000. (c) .8664. (d) .0781. (e) .1359.16.(a) The areas are equal. (b) The first area is bigger. (c) The first area isbigger. (d) The second area is bigger. (e) The second area is bigger.17.p=.8413, Hence, 84.13% of players on the team can run the 100-meter dash in faster than 0.14 second.18.(a)z= 1.645. (b)z= −1.96. (c)z= −0.51. (d)z= 0. (e)z= 0.19.(a)p= .6826. (b)x= 26.4. (c) .0808. (d) .9192.20.Students with a 3.56 GPA or higher will be offered a scholarship.21.(a) The areas are equal. (b) The first area is bigger. (c) The second areais bigger. (d) The areas are equal. (e) The second area is bigger.22.(a) .0548. (b) .1587. (c) .4452. (d) .8413. (e) .9452.23.SD= 3.24.SD= 1.50.25.M= 136.26.M= 10.27.She knows that very few people will be highly accurate at lie detec-tion because the data are normally distributed—behaviors far from themean (e.g., highly accurate lie detection) will be associated with a lowprobability of occurrence.28.(a)z=0.(b)z= 0. (c) Thezscores are the same because both scores areat the mean in their respective distributions.29.(a)p= .9049. (b)p= .0418.30.(a)p= .1587. (b)p= .0122.31.(a)p= .7764.32.(a) Fast group. (b)Slow group.CHAPTER 61.The sampling distribution is a distribution of sample statistics thatcould be obtained from all possible samples of a given size from a pop-ulation.2.Sampling without replacement and conditional probabilities are relatedin that when we sample without replacement, the probability of eachselection is conditional or dependent on the person or item that wasselected in the previous selection.3.When order matters, each time we select participants in a differentorder, it is counted as a different possible sample. When order does notmatter, selecting participants in a different order is counted as the samesample.

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