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essentials of statistics

Essentials Of Statistics For The Behavioral Sciences 9th Edition Frederick J Gravetter, Larry B. Wallnau, Lori Ann B. Forzano - Solutions

Solve the following problems.a. A repeated-measures study with a sample of n 5 16 participants produces a mean difference of MD 5 4 with a standard deviation of s 5 8.Use a two-tailed hypothesis test with a 5 .05 to determine whether it is likely that this sample came from a population with mD 5
A sample of difference scores from a repeatedmeasures experiment has a mean of MD 5 3 with a standard deviation of s 5 4.a. If n 5 4, is this sample sufficient to reject the null hypothesis using a two-tailed test with a 5 .05?b. Would you reject H0 if n 5 16? Again, assume a two-tailed test with a
Participants enter a research study with unique characteristics that produce different scores from one person to another. For an independent-measures study, these individual differences can cause problems. Identify the problems and briefly explain how they are eliminated or reduced with a
Swearing is a common, almost reflexive, response to pain. Whether you knock your shin into the edge of a coffee table or smash your thumb with a hammer, most of us respond with a streak of obscenities.One question, however, is whether swearing has any effect on the amount of pain that you feel. To
The previous problem demonstrates that removing individual differences can substantially reduce variance and lower the standard error. However, this benefit only occurs if the individual differences are consistent across treatment conditions. In Problem 20, for example, the participants with the
Nothing has changed. With a 5 .05, is there a significant difference between the two treatment conditions?b. Now assume that the data are from a repeatedmeasures study using the same sample of n 5 9 participants in both treatment conditions. Compute the variance for the sample of difference scores,
Explain the difference between a matched-subjects design and a repeated-measures design.
A researcher conducts an experiment comparing two treatment conditions with 10 scores in each treatment condition.a. If an independent-measures design is used, how many participants are needed for the study?b. If a repeated-measures design is used, how many participants are needed for the study?c.
A repeated-measures, a matched-subjects, and an independent-measures study all produce a t statistic with df 5 16.How many participants were used in each study?
Describe parametric and nonparametric hypothesis tests.
Describe the data (observed frequencies) for a chi-square test for goodness of t.
Describe the hypotheses for a chi-square test for goodness of t, explain how the expected frequencies are obtained, and nd the expected frequencies for a specic research example.
Dene the degrees of freedom for the chi-square test for goodness of t and locate the critical value for a specic alpha level in the chi-square distribution.
Conduct a chi-square test for goodness of t and report the results as they would appear in the scientic literature.
Dene the degrees of freedom for the chi-square test for independence and locate the critical value for a specic alpha level in the chi-square distribution.
Describe the hypotheses for a chi-square test for independence and explain how the expected frequencies are obtained.
Conduct a chi-square test for independence and report the results as they would appear in the scientic literature.
Compute Cohen’s w to measure effect size for both chi-square tests.
Compute the phi-coefcient or Cramér’s V to measure effect size for the chisquare test for independence.
Identify the basic assumptions and restrictions for chi-square tests.
Explain the similarities and the differences between the chi-square test for independence and the Pearson correlation.
Explain the similarities and the differences between the chi-square test for independence and the independent-measures t test or ANOVA.
Which of the following is a characteristic of nonparametric tests?a. They require a numerical score for each individual.b. They require assumptions about the population distribution(s).c. They evaluate hypotheses about population means or variances.d. None of the above is a characteristic of a
Which of the following accurately describes the observed frequencies for a chisquare test for goodness of fit?a. They are always positive whole numbers.b. They are always positive but can include fractions or decimals.c. They can be positive or negative but are always whole numbers.d. They can be
A researcher uses a sample of n 5 60 participants to test whether people have any preferences among three kinds of apples. Each person tastes all three types and then picks a favorite. What are the expected frequencies for the chi-square test for goodness of fit?a. 1 3, 1 3, 1 3b. 10, 10, 10c. 20,
A researcher is conducting a chi-square test for goodness of fit to evaluate preferences among three different designs for a new automobile. With a sample of n 5 30 the researcher obtains a chi-square statistic of x2 5 4.81. What is the appropriate statistical decision for this outcome?a. Reject
Which of the following is the correct equation to compute df for the chi-square test for goodness of fit?a. n 2 1b. n 2 2c. n 2 C (where C is the number of categories)d. None of the above
A researcher uses a sample of 20 college sophomores to determine whether they have any preference between two cell phones. Each student uses each phone for one day and then selects a favorite. If 14 students select the first phone and only 6 choose the second, then what is the value for x2?a.
If a chi-square test for independence has df 5 3, then how many cells are in the matrix of observed frequencies?a. 4b. 5c. 6d. 8
Which of the following can be evaluated with a chi-square test for independence?a. The relationship between two variablesb. Differences between two or more population frequency distributionsc. Either the relationship between two variables or the differences between distributionsd. Neither the
A researcher classifies a group of people into three age groups and measures whether each person used Facebook during the previous week (yes/no). The researcher uses a chi-square test for independence to determine if there is a significant relationship between the two variables. If the researcher
Which of the following is an appropriate measure of effect size for the chisquare test for goodness of fit?a. Cohen’s wb. The phi-coefcientc. Cramér’s Vd. Either the phi-coefcient or Cramér’s V
A researcher obtains x2 5 4.0 for a test for independence using observed frequencies in a 2 3 3 matrix. If the sample contained a total of n 5 100 people, then what is the value of Cramér’s V?a. 0.04b. 0.16c. 0.20d. 0.40
Under what circumstances should the chi-square statistic not be used?a. When the expected frequency is greater than 5 for any cellb. When the expected frequency is less than 5 for any cellc. When the expected frequency equals the observed frequency for any celld. None of the above
Because a chi-square test for independence can be used to evaluate the relationship between two variables, it can be described as being similar to what other statistical procedure?a. An independent-measures t testb. A repeated-measures t testc. A single-sample t testd. A Pearson correlation
Because a chi-square test for independence can be used to evaluate differences between separate populations, it can be described as being similar to what other statistical procedure?a. An independent-measures t testb. A repeated-measures t testc. A single-sample t testd. A Pearson correlation
The student population at the state college consists of 60% females and 40% males.a. The college theater department recently staged a production of a modern musical. A researcher recorded the gender of each student entering the theater and found a total of 37 females and 18 males.Is the gender
A developmental psychologist would like to determine whether infants display any color preferences. A stimulus consisting of four color patches (red, green, blue, and yellow) is projected onto the ceiling above a crib. Infants are placed in the crib, one at a time, and the psychologist records how
Data from the Department of Motor Vehicles indicate that 80% of all licensed drivers are older than age 25.a. In a sample of n 5 50 people who recently received speeding tickets, 33 were older than 25 years and the other 17 were age 25 or younger. Is the age distribution for this sample
A psychologist examining art appreciation selected an abstract painting that had no obvious top or bottom.Hangers were placed on the painting so that it could be hung with any one of the four sides at the top. The painting was shown to a sample of n 5 50 participants, and each was asked to hang the
A professor in the psychology department would like to determine whether there has been a significant change in grading practices over the years. It is known that the overall grade distribution for the department in 1985 had 14% As, 26% Bs, 31% Cs, 19% Ds, and 10%Fs. A sample of n 5 200 psychology
Automobile insurance is much more expensive for teenage drivers than for older drivers. To justify this cost difference, insurance companies claim that the younger drivers are much more likely to be involved in costly accidents. To test this claim, a researcher obtains information about registered
A communications company has developed three new designs for a cell phone. To evaluate consumer response, a sample of 120 college students is selected and each student is given all three phones to use for one week. At the end of the week, the students must identify which of the three designs they
In Problem 8, a researcher asked college students to evaluate three new cell phone designs. However, the researcher suspects that college students may have criteria that are different from those used by older adults. To test this hypothesis, the researcher repeats the study using a sample of n 5 60
Earlier in the chapter, we introduced the chi-square test of independence with a study examining the relationship between personality and color preference.The following table shows the frequency distribution for a group of n 5 200 students who were classified in terms of personality (introvert,
Liu et al. (2015) recently reported the results of a study examining whether happy people live longer.The study followed a large sample of British women, aged 50 to 69 over a 10-year period. At the beginning of the study the women were asked several questions, including how often they felt happy.
Many businesses use some type of customer loyalty program to encourage repeat customers. A common example is the buy-ten-get-one-free punch card. Drèze and Nunes (2006) examined a simple variation of this program that appears to give customers a head start on completing their cards. One group of
In a classic study, Loftus and Palmer (1974) investigated the relationship between memory for eyewitnesses and the questions they are asked. In the study, participants watched a film of an automobile accident and then were questioned about the accident. One group was asked how fast the cars were
In a study investigating freshman weight gain, the researchers also looked at gender differences in weight (Kasparek, Corwin, Valois, Sargent, & Morris, 2008). Using self-reported heights and weights, they computed the Body Mass Index (BMI) for each student. Based on the BMI scores, the students
Research results suggest that IQ scores for boys are more variable than IQ scores for girls (Arden &Plomin, 2006). A typical study looking at 10-year-old children classifies participants by gender and by low, average, or high IQ. Following are hypothetical data representing the research results. Do
Gender differences in dream content are well documented (see Winget & Kramer, 1979). Suppose a researcher studies aggression content in the dreams of men and women. Each participant reports his or her most recent dream. Then each dream is judged by a panel of experts to have low, medium, or high
Many parents allow their underage children to drink alcohol in limited situations when an adult is present to supervise. The idea is that teens will learn responsible drinking habits if they first experience alcohol in a controlled environment. Other parents take a strict nodrinking approach with
A recent study indicates that people tend to select video game avatars with characteristics similar to those of their creators (Bélisle & Onur, 2010). Participants who had created avatars for a virtual community game completed a questionnaire about their personalities.An independent group of
Research indicates that people who volunteer to participate in research studies tend to have higher intelligence than nonvolunteers. To test this phenomenon, a researcher obtains a sample of 200 high-school students. The students are given a description of a psychological research study and asked
Research has demonstrated strong gender differences in teenagers’ approaches to dealing with mental health issues (Chandra & Minkovitz, 2006). In a typical study, eighth-grade students are asked to report their willingness to use mental health services in the event they were experiencing
Describe the information provided by the sign (1/2) and the numerical value of a correlation.
Calculate the sum of products of deviations (SP) for a set of scores using the de-nitional and the computational formulas.
Calculate the Pearson correlation for a set of scores and explain what it measures.
Explain how the value of the Pearson correlation is affected when a constant is added to each of the X scores and/or the Y scores, and when the X and/or Y scores are all multiplied by a constant.
Explain why a cause-and-effect explanation is not justied by a correlation between two variables.
Explain how a correlation can be inuenced by a restricted range of scores or by outliers.
Dene the coefcient of determination and explain what it measures.
Conduct a hypothesis test evaluating the signicance of a correlation.
Explain how ranks are assigned to a set of scores, especially tied scores.
Compute the Spearman correlation for a set of data and explain what it measures.
Describe the circumstances in which the point-biserial correlation is used and explain what it measures.
Describe the circumstances in which the phi-coefcient is used and explain what it measures.
Dene the equation that describes a linear relationship between two variables.
Compute the regression equation (slope and Y-intercept) for a set of X and Y scores.
Compute the standard error of estimate for a regression equation and explain what it measures.
Conduct an analysis of regression to evaluate the signicance of a regression equation.
Which of the following is a justified conclusion if a correlation is positive?a. Increases in X tend to be accompanied by increases in Y.b. Increases in X tend to be accompanied by decreases in Y.c. Increases in X are always accompanied by increases in Y.d. Increases in X are always accompanied by
Which of the following correlations indicates the least consistent relationship between X and Y?a. 0.80b. 0.40c. 20.10d. 20.90
What is the value of SP for a set of n 5 5 pairs of X and Y values with SX 5 10, SY 5 20, and SXY 5 60?a. 220b. 228c. 20d. 60
A set of n 5 5 pairs of X and Y scores has SSX 5 18, SSY 5 8, SX 5 5, SY 5 15, and SXY 5 18.What is the Pearson correlation for these scores?a. 18 12 5 1.50b. 18 144 5 0.125c. 3 12 5 0.25d. 3 144 5 0.21
A set of n 5 15 pairs of X and Y values has a Pearson correlation of r 5 0.40.If 2 points were added to each of the X values, then what is the correlation for the resulting data?a. 0.40b. 20.40c. 0.60d. 20.60
A researcher obtains a strong positive correlation between aggressive behavior for six-year-old children and the amount of violence they watch on television. Based on this correlation, which of the following conclusions is justified?a. Decreasing the amount of violence that the children see on TV
A set of n 5 5 pairs of X and Y scores produces a Pearson correlation of r 5 20.10. The X values vary from 0 to 5 and the Y values vary from 2 to 6.If one new individual with X 5 12 and Y 5 14 is added to the sample, then what is the most likely value for the new correlation?a. 20.60b. 20.20c.
A set of n 5 10 pairs of X and Y values produces a Pearson correlation of r 5 20.40. How much of the variability in the Y scores can be predicted from the relationship with X?a. 16%b. 40%c. 0.16%d. 0.40%
A researcher selects a sample of n 5 25 high school students and measures the grade point average and the amount of time spent on Facebook for each student. The researcher plans to use a hypothesis test to determine whether there is a significant relationship between the two variables. Which of the
The Pearson correlation is calculated for a sample of n 5 25 individuals. What value of df should be used to test the significance of the correlation?a. 23b. 24c. 25d. Cannot be determined without additional information
If the following scores are converted to ranks (1 5 smallest), then what rank is assigned to the score X 5 7? Scores: 4, 5, 5, 6, 6, 6, 7, 9, 10a. 4b. 5c. 6d. 7
What is the Spearman correlation for the following set of ranked data?a. 0.8b. 20.8c. 0.375d. 20.375
Which of the following correlations can be computed for data that are also suitable for an independent-measures t test?a. Pearsonb. Spearmanc. Point-biseriald. Phi-coefcient
A researcher would like to measure the relationship between gender (male/female) and voter registration (yes/no). Which of the following correlations would be appropriate?a. Pearsonb. Spearmanc. Point-biseriald. Phi-coefcient
In the general linear equation Y 5 bX 1a, what is measured by the value of a?a. The point at which the line crosses the X-axisb. The point at which the line crosses the Y-axisc. The amount that X changes each time Y increases by 1 pointd. The amount that Y changes each time X increases by 1 point
A set of n 5 25 pairs of X and Y values has MX 5 4, SSX 5 10, MY 5 6, SSY 5 40, and SP 5 20.What is the regression equation for predicting Y from X?a. Y 5 2X 2 2b. Y 5 2X 2 8c. Y 5 0.5X 1 4d. Y 5 0.5X 1 1
What is measured by the standard error of estimate for a regression equation?a. The standard distance between a predicted Y value and the mean for the Y scoresb. The standard distance between a predicted Y value and the center of the regression linec. The standard distance between a predicted Y
A researcher computes the regression equation for predicting Y for a sample of n 5 25 pairs of X and Y values. If the significance of the equation is evaluated with an analysis of regression, then what are the df values for the F-ratio?a. 1, 24b. 1, 23c. 2, 23d. 2, 22
Calculate SP (the sum of products of deviations) for the following scores. Note: Both means are whole numbers, so the definitional formula works well.X Y 4 5 0 2 1 1 3 4
Calculate SP (the sum of products of deviations) for the following scores. Note: Both means are decimal values, so the computational formula works well.X Y 0 4 1 1 0 5 4 1 2 1 1 3
For the following scores, X Y 2 7 5 4 4 7 7 5 2 6 4 7a. Sketch a scatter plot showing the six data points.b. Just looking at the scatter plot, estimate the value of the Pearson correlation.c. Compute the Pearson correlation.
For the following scores, X Y 0 4 2 9 1 6 1 9a. Sketch a scatter plot and estimate the Pearson correlation.b. Compute the Pearson correlation.
For the following scores, X Y 4 0 1 5 1 0 4 5a. Sketch a scatter plot and estimate the Pearson correlation.b. Compute the Pearson correlation.
For the following scores, X Y 3 6 5 5 6 0 6 2 5 2a. Sketch a scatter plot and estimate the value of the Pearson correlation.b. Compute the Pearson correlation.
With a small sample, a single point can have a large effect on the magnitude of the correlation. To create the following data, we started with the scores from Problem 8 and changed the first X value from X 5 3 to X 5 8.X Y 8 6 5 5 6 0 6 2 5 2a. Sketch a scatter plot and estimate the value of the
For the following set of scores, X Y 4 5 6 5 3 2 9 4 6 5 2 3a. Compute the Pearson correlation.b. Add 2 points to each X value and compute the correlation for the modified scores. How does adding a constant to every score affect the value of the correlation?c. Multiply each of the original X values
At the beginning of this chapter we discussed a study by Judge and Cable (2010) demonstrating 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
For a two-tailed test with a 5 .05, use Table B.6 to determine how large a Pearson correlation is necessary to be statistically significant for each of the following samples.a. A sample of n 5 6b. A sample of n 5 12c. A sample of n 5 24
It appears that there is a significant relationship between cognitive ability and social status, at least for birds. Boogert, Reader, and Laland (2006) measured social status and individual learning ability for a group of starlings. The following data represent results similar to those obtained in

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