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statistics
essentials of statistics for the behavioral sciences
Essentials Of Statistics For The Behavioral Sciences 10th Edition Frederick J Gravetter, Larry B. Wallnau, Lori Ann B. Forzano, James E. Witnauer - Solutions
The following data are from a repeated-measures study examining the effect of a treatment by measuring a group of n = 11 participants before and after they receive the treatment.a. Calculate the difference scores and MD.b. Compute SS, sample variance, and estimated standard error.c. Is there a
How does the numerator of the repeated-measures t-statistic compare to the numerator of the singlesample t-statistic?
The stimulant Ritalin has been shown to increase attention span and improve academic performance in children with ADHD (Evans et al., 2001). To demonstrate the effectiveness of the drug, a researcher selects a sample of n = 20 children diagnosed with the disorder and measures each child’s
Callahan (2009) demonstrated that Tai Chi can significantly reduce symptoms for individuals with arthritis. Participants were 18 years old or older with doctordiagnosed arthritis. Self-reports of pain and stiffness were measured at the beginning of an eight-week Tai Chi course and again at the
Solve the following problems.a. A repeated-measures study with a sample of n = 6 participants produces a mean difference of MD = 4 with SS5 30. Use a two-tailed hypothesis test with α = .05 to determine whether this sample provides evidence of a significant treatment effect.b. Now assume that SS =
Gamification refers to the application of game design and development to social, industrial, and educational settings. For example, a gamification program might award points or achievements to people for reaching specific goals. A recent experiment on gamification in the workplace revealed that
Exercise is known to produce positive psychological effects. Interestingly, not all exercise is equally effective. It turns out that exercising in a natural environment (e.g., jogging in the woods) produces better psychological outcomes than exercising in urban environments or in homes (Mackay
A repeated-measures, a matched-subjects, and an independent-measures study all produce a t statistic with df = 10. How many participants were used in each study?
Suppose that you conduct three different t-tests to analyze the results of an experiment with three independent samples. Each individual t-test uses α = .05. What is the probability of a Type 1 error occurring in any of the hypothesis tests? Is it greater than, equal to, or less than .05?
Calculate SStotal, SSbetween, and SSwithin for the following set of data: Treatment 1 Treatment 2 Treatment 3 n = 10 n = 10 T = 105 T = 110 SS = 350.5 424 n = 10 T = 180 SS = 190.0 SS = N = 30 G = 395 X² = 6,517
What value is expected for the F-ratio, on average, if the null hypothesis is true in an ANOVA? Explain why.
Describe some of the reasons that group means might be different from each other in an analysis of variance. Describe some of the reasons that individual scores might be different from each other.
A researcher uses an ANOVA to compare six treatment conditions with a sample of n = 12 in each treatment. For this analysis, find dftotal, dfbetween, and dfwithin.
The following values are from an independent-measures study comparing three treatment conditions. a. Compute the variance for each sample.b. Compute MSwithin, which would be the denominator of the F-ratio for an ANOVA. Because the samples are all the same size, you should find that MSwithin is
A researcher reports an F-ratio with dfbetween = 3 and dfwithin = 40 for an independent-measures ANOVA.a. How many treatment conditions were compared in the experiment?b. How many subjects participated in the experiment?c. Use Appendix B to find the critical value for F. Use α = .05.d. What is the
A researcher conducts an experiment comparing three treatment conditions with a separate sample of n = 6 in each treatment. An ANOVA is used to evaluate the data, and the results of the ANOVA are presented in the following table. Complete all missing values in the table. Source Between
A researcher reports an F-ratio with df = 4, 62 from an independent-measures research study.a. How many treatment conditions were compared in the study? b. What was the total number of participants in the study?c. Use Appendix B to find the critical value for F. Use α = .05.d. What is the
The following summary table presents the results from an ANOVA comparing five treatment conditions with n = 5 participants in each condition. Complete all missing values. Source Between treatments Within treatments Total SS 1500 df MS 125 F =
A developmental psychologist is examining the development of language skills from age 2 to age 4. Three different groups of children are obtained, one for each age, with n = 16 children in each group. Each child is given a language-skills assessment test. The resulting data were analyzed with an
A research study comparing three treatment conditions produces T = 20 with n = 4 for the first treatment, T = 10 with n = 5 for the second treatment, and T = 30 with n = 6 for the third treatment. Calculate SSbetween treatments for these data.
A research study comparing three treatment conditions produces T = 28 with n = 7 for the first treatment, T = 32 with n = 8 for the second treatment, and T = 108 with n = 9 for the third treatment. Calculate SSbetween treatments for these data.
A research report from an independent-measures study states that there are significant differences between treatments, F(4, 40) = 3.45, p < .05.a. How many treatment conditions were compared in the study?b. What was the total number of participants in the study?c. Would the result be significant
A researcher used ANOVA and computed F = 4.25 for the following data.a. If the mean for Treatment III were changed to M = 25, what would happen to the size of the F-ratio (increase or decrease)? Explain your answer.b. If the SS for Treatment I were changed to SS = 1,400, what would happen to the
For the data in the following matrix: a. Which two means are compared to describe the treatment main effect?b. Which two means are compared to describe the main effect of age?c. Is there an interaction between age and treatment? Explain your answer.
Explain what happens during each of the two stages of the two-factor ANOVA.
The following matrix presents the results from an independent-measures, two-factor study with a sample of n = 10 participants in each treatment condition. Note that one treatment mean (“M = ?”) is missing.a. What value for the missing mean would result in no main effect for factor A?b. What
Suppose that a researcher was interested in the effect of caffeine on memory. She measured memory performance either immediately after studying (0-day delay) or after a 10-day delay. Half of the participants in each delay group received either a cup of decaffeinated coffee or a cup of regular,
The following matrix presents the results of a two-factor study with n = 10 scores in each of the six treatment conditions. Note that one of the treatment means is missing.a. What value for the missing mean would result in no main effect for factor A?b. What value for the missing mean would result
The following table summarizes the results from a two-factor study with two levels of factor A and three levels of factor B using a separate sample of n = 5 participants in each treatment condition. Fill in the missing values. Source Between treatments Factor A Factor B A X B Interaction Within
In a classic study of the effect of memory on caffeine, Loke (1988) studied the effect of caffeine on the serial position effect. In memory tests, the serial position effect refers to the observation that memory for items at the beginning and end of a list are remembered better than items in the
The diathesis stress approach to mental illness proposes that neither environmental stress alone nor genetic factors alone are enough to produce mental illness. Instead, both environmental stress and genetic predisposition to mental illness are required for mental illnesses like schizophrenia and
The following results are from an independent-measures, two-factor study with n = 5 participants in each treatment condition.a. Use a two-factor ANOVA with α = .05 to evaluate the main effects and the interaction.b. Test the simple effect of factor A at level B2. Factor
Suppose that a researcher conducts an independent samples experiment comparing three treatments. Participants serve in the experiment either online or by visiting the researcher’s lab. Scores for this hypothetical experiment are listed below.a. Use a one-way ANOVA with α = .05 to evaluate the
Calculate SP (the sum of products of deviations) for the following scores. Both means are whole numbers, so the definitional formula works well. X 4 3 9 0 Y 00 8 11 8 00 1
In Chapter 10 presented data demonstrating that participants who binge-watched a television series enjoyed the show less than participants who watched the series in daily sessions. In the study, one group watched the complete television series in a single session and the other group watched the
A set of n = 15 pairs of scores (X and Y values) produces a regression equation of Y = 3X + 8. Find the predicted Y value for each of the following X scores: 1, 2, 3, and 6.
For the following set of data, compute the Pearson correlation statistic and find the linear regression equation for predicting Y from X: X 1 20324 4 Y 5 10 9 12 11 13
The regression equation is computed for a set of n = 18 pairs of X and Y values with a correlation of r = +0.50 and SSY = 48.a. Find the standard error of estimate for the regression equation.b. How big would the standard error be if the sample size were n = 66?
Solve the following problems.a. One set of 10 pairs of scores, X and Y values, produces a correlation of r = 0.60. If SSY = 200, find the standard error of estimate for the regression line.b. A second set of 10 pairs of X and Y values produces a correlation of r = 0.40. If SSY = 200, find the
Judge and Cable (2010) demonstrated a positive relationship between weight and income for a group of men. The following are data similar to those obtained in the study. To simplify the weight variable, the men are classified into five categories that measure actual weight relative to height, from 1
A set of n = 18 pairs of scores (X and Y values) has SSX = 16, SSY = 64, and SP = 20. If the mean for the X values is MX = 6 and the mean for the Y values is MY = 8:a. Calculate the Pearson correlation for the scores.b. Find the regression equation for predicting Y from the X values.
The results of a recent study showed that children who routinely drank reduced fat milk (1% or skim) were more likely to be overweight or obese at ages 2 and 4 compared to children who drank whole or 2% milk (Scharf, Demmer, & DeBoer, 2013).a. Is this an example of an experimental or a
Deters and Mehl (2013) studied the effect of Facebook status updates on feelings of loneliness. Eighty-six participants were randomly assigned to two groups. One group was instructed to post more social media status updates and the other group was not. The researchers measured participants’
Define the terms population and sample, and explain the role of each in a research study.
We know that the average IQ of everyone in the United States is 100. We randomly select 10 people and observe that their average IQ is 105.a. The value of 105 is a .b. The value of 100 is a .
Define the terms statistic and parameter and explain how these terms are related to the concept of sampling error.
Explain why honesty is a hypothetical construct instead of a concrete variable. Describe how honesty might be measured and defined using an operational definition.
In your most recent checkup, your physician listed that your height is 70 inches, rounded to the nearest whole inch. Why is it unlikely that your height is exactly 70 inches? What are the upper and lower real limits of your height?
Your friend measures the temperature of her coffee to be 70° Celsius. Your friend also notices that the temperature outside is 35° Celsius. Why is it incorrect to say that the coffee is twice as warm as the temperature outside?
Dwyer, Figuerooa, Gasalla, and Lopez (2018) showed that learning of flavor preferences depends on the relative value of the reward with which a flavor is paired. In their experiment, rats received pairings of a cherry flavor with 8% sucrose solution after exposure to 32% sucrose solution, which
Doebel and Munakata (2018) discovered that delay of gratification by children is influenced by social context. All children were told that they were in the “green group” and were placed in a room with a single marshmallow. Participants were told that they could either eat the single marshmallow
In 2016, the 50th percentile score for household in come in the United States was $59,039. What statistic for central tendency is this?
For the following set of scores: a. Construct a frequency distribution table to organize the scores. Include cumulative frequency and cumulative percent.b. What is the percentile rank of the upper real limit of X = 5?c. What is the upper real limit of the score that cor responds to the 50th
For each of the following, list the class intervals that would be best for a grouped frequency distribution. a. Lowest X = 3, highest X 5 84b. Lowest X = 17, highest X = 32c. Lowest X = 52, highest X = 97
For the following set of scores: a. Construct a frequency distribution table.b. Sketch a histogram showing the distribution.c. What is the shape of the distribution? 756 4 4 3 8 9 4 7 5 5 6 9 4 7 5 10 6 8 5 6 3 4 8 5
A local fast-food restaurant normally sells coffee in three sizes—small, medium, and large—at three different prices. Recently they had a special sale, charging only $1 for any sized coffee. During the sale, an employee recorded the number of each coffee size that was purchased on Wednesday
Your instructors, your parents, and your feelings of stress during finals week all tell you that cramming is a bad way to prepare for exams. Participants in Kornell’s (2009) research study received two sets of flash cards with vocabulary questions that they studied multiple times. One stack of
A sample of n = 9 scores has ∑X = 108. What is the sample mean? f 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 X
A sample of n = 12 scores has ∑X = 72. What is the sample mean? 5 4 3 2 0 1 2 3 4 5 6 7 8 9 10 X
Find the mean for the following set of scores: 2, 7, 9, 4, 5, 3, 0, 6 f 6 5 4 3 2 1 0 1 2 3 4 50 6 7 8 9 10 X
Find the mean for the following set of scores: 8, 2, 5, 7, 12, 9, 11, 3, 6 f 5 4 3 2 1 0 12 3 4 5 6 7 8 9 10 X
Using the following informal histogram, what is the value of the mean? Explain your answer. f 5 4 3 2 1 1 2 3 4 5 6 7 89 10 X
Which statistic is equivalent to dividing the sum of scores equally across all members of a sample?
A sample with a mean of M = 8 has ∑X = 56. How many scores are in the sample?
One sample has a mean of M = 6, and a second sample has a mean of M = 12. The two samples are combined into a single set of scores.a. What is the mean for the combined set if both the original samples have n = 4 scores?b. What is the mean for the combined set if the first sample has n = 3 and the
Find the median for the following set of scores: 1, 4, 8, 7, 13, 26, 6
Anderson (1999) was interested in the effects of attention load on reaction time. Participants in her study received a dual-task procedure in which they needed to respond as quickly as possible to a stimulus while simultaneously paying attention to the sounds of spoken words. She recorded reaction
Briefly explain the goal for defining and measuring variability.
Describe the scores in a sample that has a standard deviation of zero.
For the following set of scores: 6, 2, 3, 0, 4a. If the scores are a population, what are the variance and standard deviation?b. If the scores are a sample, what are the variance and standard deviation?
Explain why the formula for sample variance is different from the formula for population variance. Why is it inappropriate to use the formula for population variance in calculating the variance of a sample?
For a sample of n = 12 scores, what value should be used in the denominator of the formula for variance? What value should be used in the denominator of the formula for the mean? Explain why the two formulas use different values in the denominator.
Calculate SS, variance, and standard deviation for the following sample of n = 5 scores: 2, 9, 5, 5, 9.
Solve the following problems.a. After 6 points have been added to every score in a sample, the mean is found to be M = 70 and the standard deviation is s = 13. What were the values for the mean and standard deviation for the original sample?b. After every score in a sample is multiplied by 3, the
A score of X = 75 is measured in a population with a mean of μ = 100. A z-score of z = +1.50 is calculated. Without knowing the standard deviation, explain why the z-score of z = +1.50 is incorrect.
On an exam with a mean of M = 40, you obtain a score of X = 35.a. Relative to other students, would your performance on the exam be better with a standard deviation of s = 2 or with a standard deviation of s = 8?b. If your score were X = 46, would you prefer s = 2 or s = 8? Explain your answer.
Everyone experiences “ups and downs” in life satisfaction. Boehm, Winning, Segerstrom, and Kubzansky (2015) studied whether such variability in life satisfaction is correlated with mortality rate. Over a nine-year period, 4,458 Australian older adult participants answered surveys about life
For a sample with a standard deviation of s = 15, describe the location of each of the following z-scores in terms of its position relative to the mean. For example, z = +1.00 is a location that is 15 points above the mean.a. z = -1.20b. z = +0.80c. z = +2.00d. z = -1.60
For a population with μ = 50 and σ = 6:a. Find the z-score for each of the following X values.X = 50 X = 62 X = 53X = 44 X = 47 X = 38b. Find the score (X value) that corresponds to each of the following z-scores.z = +1.00 z = +2.50 z = +1.50z = -1.50 z = -3.00 z = -2.50
For a population with μ = 80 and σ = 9, find the z-score for each of the following X values.X = 83 X = 75 X = 91X = 67 X = 85 X = 68
A sample has a mean of M = 53 and a standard deviation of s = 11. For this sample, find the z-score for each of the following X values.X = 30 X = 39 X = 70X = 48 X = 57 X = 64
Bags of Skittles™ candies include six different colors: red, orange, yellow, green, blue, and purple. If the bag has an equal number of each of the six colors, what are the probabilities for each of the following?a. Randomly selecting a green candy?b. Randomly selecting either a green or a yellow
A psychology class consists of 32 freshmen and 48 sophomores. If the professor selects names from the class list using random sampling,a. What is the probability that the first student selected will be a freshman?b. And if a random sample of n = 6 students is selected and the first five selected
Seattle, Washington, averages μ = 34 inches of annual precipitation. Assuming that the distribution of precipitation amounts is approximately normal with a standard deviation of σ = 6.5 inches, determine whether each of the following represents a fairly typical year, an extremely wet year, or an
Suppose that a researcher is interested in the effect of new smart drug on IQ. Scores from the IQ test are normally distributed with a mean of μ = 100 and σ = 15.A participant receives the smart drug and completes the IQ assessment.a. If the treatment has no effect on IQ, what is the probability
Suppose that the distribution of scores on the Graduate Record Exam (GRE) is approximately normal, with a mean of μ = 150 and a standard deviation of σ = 5.For the population of students who have taken the GRE:a. What proportion have GRE scores less than 145?b. What proportion have GRE scores
Define sampling with replacement and explain why it is used.
For a sample with a standard deviation of s = 4, a score of X = 35 corresponds to z = -1.25. What is the sample mean?
For a population with a standard deviation of σ = 12, a score of X = 115 corresponds to z = +1.25. What is the population mean?
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