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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
A hypothesis test produces a t statistic of t 5 2.30. If the researcher is using a two-tailed test with a 5 .05, how large does the sample have to be in order to reject the null hypothesis?a. at least n 5 8b. at least n 5 9c. at least n 5 10d. at least n 5 11
A sample is selected from a population and a treatment is administered to the sample. For a hypothesis test with a t statistic, if there is a 5-point difference between the sample mean and the original population mean, which set of sample characteristics is most likely to lead to a decision that
A sample of n 5 25 is selected from a population with m 5 40, and a treatment is administered to each individual in the sample. After treatment, the sample mean is M 5 44 with a sample variance of s 2 5 100.Based on this information, what is the size of the treatment effect as measured by Cohen’s
A sample is selected from a population with a mean of m 5 75, and a treatment is administered to the individuals in the sample. The researcher intends to use a t statistic to evaluate the effect of the treatment. If the sample mean is M 5 79, then which of the following outcomes would produce the
A sample of n 5 4 scores is selected from a population with an unknown mean. The sample has a mean of M 5 40 and a variance of s 2 5 16.Which of the following is the correct 90% confidence interval for m?a. m 5 40 6 2.353(4)b. m 5 40 6 1.638(4)c. m 5 40 6 2.353(2)d. m 5 40 6 1.638(2)
A researcher uses a sample of n 5 25 individuals to evaluate the effect of a treatment. The hypothesis test uses a 5 .05 and produces a significant result with t 5 2.15. How would this result be reported in the literature?a. t(25) 5 2.15, p , .05b. t(24) 5 2.15, p , .05c. t(25) 5 2.15, p . .05d.
A sample is selected from a population with a mean of m 5 30 and a treatment is administered to the sample. If the treatment is expected to increase scores and a t statistic is used for a one-tailed hypothesis test, then which of the following is the correct null hypothesis?a. m # 30b. m , 30c. m $
A researcher predicts that a treatment will increase scores. To test the treatment effect, a sample of n 5 16 is selected from a population with m 5 80 and a treatment is administered to the individuals in the sample. After treatment, the sample mean is M 5 78 with s 2 5 16.If the researcher uses a
A researcher fails to reject the null hypothesis with a regular two-tailed test using a 5 .05. If the researcher used a directional (one-tailed) test with the same data and the same alpha level, then what decision would be made?a. De nitely reject the null hypothesisb. De nitely reject the null
Under what circumstances is a t statistic used instead of a z-score for a hypothesis test?
A sample of n 5 16 scores has a mean of M 5 56 and a standard deviation of s 5 20.a. Explain what is measured by the sample standard deviation.b. Compute the estimated standard error for the sample mean and explain what is measured by the standard error.
Find the estimated standard error for the sample mean for each of the following samples.a. n 5 9 with SS 5 1152b. n 5 16 with SS 5 540c. n 5 25 with SS 5 600
The following sample of n 5 4 scores was obtained from a population with unknown parameters. Scores:2, 2, 6, 2a. Compute the sample mean and standard deviation.(Note that these are descriptive values that summarize the sample data.)b. Compute the estimated standard error for M. (Note that this is
The following sample was obtained from a population with unknown parameters. Scores: 13, 7, 6, 12, 0, 4a. Compute the sample mean and standard deviation.(Note that these are descriptive values that summarize the sample data.)b. Compute the estimated standard error for M. (Note that this is an
Explain why t distributions tend to be flatter and more spread out than the normal distribution.
Find the t values that form the boundaries of the critical region for a two-tailed test with a 5 .05 for each of the following sample sizes:a. n 5 4b. n 5 15c. n 5 24
Find the t value that forms the boundary of the critical region in the right-hand tail for a one-tailed test with a 5 .01 for each of the following sample sizes.a. n 5 10b. n 5 20c. n 5 30
A random sample of n 5 12 individuals is selected from a population with m 5 70, and a treatment is administered to each individual in the sample. After treatment, the sample mean is found to be M 5 74.5 with SS 5 297.a. How much difference is there between the mean for the treated sample and the
A random sample of n 5 4 individuals is selected from a population with m 5 35, and a treatment is administered to each individual in the sample. After treatment, the sample mean is found to be M 5 40.1 with SS 5 48.a. How much difference is there between the mean for the treated sample and the
Infants, even newborns, prefer to look at attractive faces compared to less attractive faces (Slater, et al., 1998). In the study, infants from 1 to 6 days old were shown two photographs of women’s faces. Previously, a group of adults had rated one of the faces as significantly more attractive
The spotlight effect refers to overestimating the extent to which others notice your appearance or behavior, especially when you commit a social faux pas.Effectively, you feel as if you are suddenly standing in a spotlight with everyone looking. In one demonstration of this phenomenon, Gilovich,
To evaluate the effect of a treatment, a sample is obtained from a population with a mean of m 5 40, and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M 5 44.5 with a variance of s 2 5 36.a. If the sample consists of n 5 4
To evaluate the effect of a treatment, a sample of n 5 6 is obtained from a population with a mean of m 5 80, and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M 5 72.a. If the sample variance is s 2 5 54, are the data sufficient to
Weinstein, McDermott, and Roediger (2010) report that students who were given questions to be answered while studying new material had better scores when tested on the material compared to students who were simply given an opportunity to reread the material.In a similar study, a group of students
To evaluate the effect of a treatment, a sample is obtained from a population with a mean of m 5 20, and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M 5 21.3 with a variance of s 2 5 9.a. Assuming that the sample consists of n 5 16
To evaluate the effect of a treatment, a sample of n 5 8 is obtained from a population with a mean of m 5 50, and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M 5 55.a. Assuming that the sample variance is s 2 5 32, use a two-tailed
Standardized measures seem to indicate that the average level of anxiety has increased gradually over the past 50 years (Twenge, 2000). In the 1950s, the average score on the Child Manifest Anxiety Scale was m 5 15.1. A sample of n 5 16 of today’s children produces a mean score of M 5 23.3 with
Ackerman and Goldsmith (2011) found that students who studied text from printed hardcopy had better test scores than students who studied from text presented on a screen. In a related study, a professor noticed that several students in a large class had purchased the e-book version of the course
Oishi and Shigehiro (2010) report that people who move from home to home frequently as children tend to have lower than average levels of well-being as adults. To further examine this relationship, a psychologist obtains a sample of n 5 12 young adults who each experienced 5 or more different homes
McGee and Shevlin (2009) demonstrated that an individual’s sense of humor had a significant effect on how the individual was perceived by others. In one part of the study, female college students were given brief descriptions of a potential romantic partner.The fictitious male was described
Belsky, Weinraub, Owen, and Kelly (2001) reported on the effects of preschool child care on the development of young children. One result suggests that children who spend more time away from their mothers are more likely to show behavioral problems in kindergarten. Using a standardized scale, the
An example of the vertical-horizontal illusion is shown in the figure. Although the two lines are exactly the same length, the vertical line appears to be much longer. To examine the strength of this illusion, a researcher prepared an example in which both lines were exactly 10 inches long. The
De ne independent-measures designs and repeated-measures designs and identify examples of each.
Describe the hypotheses for an independent-measures t test.
Describe the structure of the independent-measures t statistic and explain how it is related to the single-sample t.
Calculate the pooled variance for two samples and the estimated standard error for the sample mean difference, and explain what each one measures.
Calculate the complete independent-measures t statistic and its degrees of freedom.
Use the data from two samples to conduct an independent-measures t test evaluating the signi cance of the difference between two population means.
Conduct a directional (one-tailed) hypothesis test using the independent-measures t statistic.
Describe the basic assumptions underlying the independent-measures t hypothesis test, especially the homogeneity of variance assumption, and explain how the homogeneity assumption can be tested.
Measure effect size for an independent-measures t test using either Cohen’s d or r2, the percentage of variance accounted for.
Use the data from two separate samples to compute a con dence interval describing the size of the mean difference between two treatment conditions or two populations.
Describe the relationship between a hypothesis test with an independent-measures t statistic using a 5 .05 and the corresponding 95% con dence interval for the mean difference.
Describe how the results of an independent-measures t test and measures of effect size are reported in the scienti c literature.
Describe how sample size and sample variance in uence the outcome of a hypothesis test and measures of effect size for the independent-measures t statistic.
Which of the following is most likely to be an independent-measures design?a. A study comparing self-esteem for children from single-parent homes and children from two-parent homesb. A study comparing classroom learning with and without background musicc. A study comparing blood pressure before and
Which of the following is most likely to be a repeated-measures design?a. A study comparing motor-skills performance for left-handed adolescents and right-handed adolescentsb. A study comparing cholesterol levels before and after a diet featuring oatmealc. A study comparing self-esteem for
An independent-measures study comparing two treatment conditions uses _____________ groups of participants and obtains _____________ score(s) for each participant.a. 1, 1b. 1, 2c. 2, 1d. 2, 2
Which of the following is the correct null hypothesis for an independentmeasures t test?a. There is no difference between the two sample means.b. There is no difference between the two population means.c. The difference between the two sample means is identical to the difference between the two
Which of the following does not accurately describe the relationship between the formulas for the single-sample t and the independent-measures t?a. The single-sample t has one sample mean and the independent-measures t has two.b. The single-sample t has one population mean and the
One sample has n 5 4 and a second sample has n 5 8.If the pooled variance for the two samples is 24, then what is the estimated standard error for the sample mean difference?a. 9b. 4c. 3d. 2
A researcher obtains M 5 34 with SS 5 190 for a sample of n 5 10 girls and M 5 29 with SS 5 170 for a sample of n 5 10 boys. If the two samples are used to evaluate the mean difference between the two populations, what value will be obtained for the t statistic?a. 5 4 5 1.25b. 5 2 5 2.50c. 5Ï2 5
What is the value of the independent-measures t statistic for a study with n 5 10 participants in each treatment if the data produce M 5 38 and SS 5 200 for the first treatment and M 5 33 and SS 5 160 for the second treatment?a. t 5 1.25b. t 5 2.50c. t 5 0.25d. t 5 5Ï20 5 1.12
A researcher uses two samples, each with n 5 15 participants, to evaluate the mean difference in performance scores between 8-year-old and 10-year-old children. The prediction is that the older children will have higher scores. The sample mean for the older children is five points higher than the
Hartley’s F-max test is used to evaluate the homogeneity of variance assumption. What is the null hypothesis for this test?a. The two sample variances are equal.b. The two sample variances are not equal.c. The two population variances are equal.d. The two population variances are not equal.
A researcher obtains a mean of M 5 26 for a sample in one treatment condition and M 5 28 for a sample in another treatment. The pooled variance for the two samples is 16.What value would be obtained if Cohen’s d were used to measure the effect size?a. 2 16b. 4 16c. 2 4d. There is not enough
Which of the following is not an accurate description of a confidence interval for a mean difference using the independent-measures t statistic?a. The sample mean difference, M1 2 M2, will be located in the center of the interval.b. If other factors are held constant, the width of the interval will
Which of the following accurately describes the 95% confidence interval for an independent-measures study for which a hypothesis test concludes that there is no significant mean difference with a 5 .05.a. The con dence interval will include the value 0.b. The con dence interval will not include the
The results of a hypothesis test with an independent-measures t statistic are reported as follows: t(22) 5 2.48, p , .05, d 5 0.27. Which of the following is an accurate description of the study and the result?a. The study used a total of 24 participants and the null hypothesis was rejected.b. The
Which of the following accurately describes how the outcome of a hypothesis test and measures of effect size with the independent-measures t statistic are affected when sample size is increased?a. The likelihood of rejecting the null hypothesis and measures of effect size both increase.b. The
Which of the following accurately describes how the outcome of a hypothesis test and measures of effect size with the independent-measures t statistic are affected when sample variance increases?a. The likelihood of rejecting the null hypothesis and measures of effect size both increase.b. The
Which of the following sets of data would produce the largest value for an independent-measures t statistic?a. Two sample means of 10 and 12 with sample variances of 20 and 25b. Two sample means of 10 and 12 with variances of 120 and 125c. Two sample means of 10 and 20 with variances of 20 and 25d.
Describe the basic characteristics that define an independent-measures, or a between-subjects, research study.
Describe what is measured by the estimated standard error in the bottom of the independent-measures t statistic.
One sample has SS 5 36 and a second sample has SS 5 24.a. If n 5 5 for both samples, find each of the sample variances and compute the pooled variance. Because the samples are the same size, you should find that the pooled variance is exactly halfway between the two sample variances.b. Now assume
One sample has SS 5 60 and a second sample has SS 5 48.a. If n 5 7 for both samples, find each of the sample variances, and calculate the pooled variance.Because the samples are the same size, you should find that the pooled variance is exactly halfway between the two sample variances.b. Now assume
Two separate samples, each with n 5 9 individuals, receive different treatments. After treatment, the first sample has SS 5 546 and the second has SS 5 606.a. Find the pooled variance for the two samples.b. Compute the estimated standard error for the sample mean difference.c. If the sample mean
Two separate samples receive different treatments.After treatment, the first sample has n 5 6 with SS 5 236, and the second has n 5 12 with SS 5 340.a. Compute the pooled variance for the two samples.b. Calculate the estimated standard error for the sample mean difference.c. If the sample mean
Research results suggest a relationship between the TV viewing habits of 5-year-old children and their future performance in high school. For example, Anderson, Huston, Wright, and Collins (1998) report that high school students who regularly watched Sesame Street as children had better grades in
Does posting calorie content for menu items affect people’s choices in fast-food restaurants? According to results obtained by Elbel, Gyamfi, and Kersh(2011), the answer is no. The researchers monitored the calorie content of food purchases for children and adolescents in four large fast-food
A long history of psychology research has demonstrated that memory is usually improved by studying material on multiple occasions rather than one time only. This effect is commonly known as distributed practice or spacing effects. In a recent paper examining this effect, Cepeda et al. (2008) looked
Recent research has shown that creative people are more likely to cheat than their less-creative counterparts (Gino & Ariely, 2011). Participants in the study first completed creativity assessment questionnaires and then returned to the lab several days later for a series of tasks. One task was a
Recent research has demonstrated that music-based physical training for elderly people can improve balance, walking efficiency, and reduce the risk of falls (Trombetti et al., 2011). As part of the training, participants walked in time to music and responded to changes in the music’s rhythm
McAllister et al. (2012) compared varsity football and hockey players with varsity athletes from noncontact sports to determine whether exposure to head impacts during one season have an effect on cognitive performance. In the study, tests of new learning performance were significantly poorer for
Zhou and Vohs (2009) published a study showing that handling money reduces the perception pain.In the experiment, a group of college students was told that they were participating in a manual dexterity study. Half of the students were given a stack of money to count and the other half got a stack
In a classic study in the area of problem solving, Katona (1940) compared the effectiveness of two methods of instruction. One group of participants was shown the exact, step-by-step procedure for solving a problem and was required to memorize the solution. Participants in a second group were
A researcher conducts an independent-measures study comparing two treatments and reports the t statistic as t(18) 5 2.15.a. How many individuals participated in the entire study?b. Using a two-tailed test with a 5 .05, is there a significant difference between the two treatments?c. Compute r 2to
In a recent study, Piff, Kraus, Côté, Cheng, and Keltner (2010) found that people from lower socioeconomic classes tend to display greater prosocial behavior than their higher-class counterparts. In one part of the study, participants played a game with an anonymous partner. Part of the game
Describe the homogeneity of variance assumption and explain why it is important for the independentmeasures t test.
If other factors are held constant, explain how each of the following influences the value of the independentmeasures t statistic, the likelihood of rejecting the null hypothesis, and the magnitude of measures of effect size:a. Increasing the number of scores in each sampleb. Increasing the
As noted on page 275, when the two population means are equal, the estimated standard error for the independent-measures t test provides a measure of how much difference to expect between two sample means. For each of the following situations, assume that m1 5 m2 and calculate how much difference
Two samples are selected from the same population.For each of the following, calculate how much difference is expected, on average, between the two sample means.a. One sample has n 5 4, the second has n 5 6, and the pooled variance is 60.b. One sample has n 5 12, the second has n 5 15, and the
For each of the following, assume that the two samples are obtained from populations with the same mean, and calculate how much difference should be expected, on average, between the two sample means.a. Each sample has n 5 4 scores with s 2 5 68 for the first sample and s 2 5 76 for the second.
For each of the following, calculate the pooled variance and the estimated standard error for the sample mean differencea. The first sample has n 5 4 scores and a variance of s2 5 17, and the second sample has n 5 8 scores and a variance of s 2 5 27.b. Now the sample variances are increased so that
It appears that there is some truth to the old adage“That which doesn’t kill us makes us stronger.” Seery, Holman, and Silver (2010) found that individuals with some history of adversity report better mental health and higher well-being compared to people with little or no history of
In 1974, Loftus and Palmer conducted a classic study demonstrating how the language used to ask a question can influence eyewitness memory. In the study, college students watched a film of an automobile accident and then were asked questions about what they saw. One group was asked, “About how
Explain how a z-score identi es a precise location in a distribution for either a population or a sample of scores.
Using either the z-score de nition or the z-score formula, transform X values into z-scores and transform z-scores into X values for both populations and samples.
Explain how z-scores establish a relationship among X, the mean, the standard deviation, and the value of z, and use that relationship to nd an unknown mean when given a z-score, a score, and the standard deviation; or nd an unknown standard deviation when given a z-score, a score, and the mean.
Describe the effects of standardizing a distribution by transforming the entire set of scores into z-scores and explain the advantages of this transformation.
Use z-scores to transform any distribution into a standardized distribution with a predetermined mean and a predetermined standard deviation.
Explain how z-scores can help researchers use the data from a sample to draw inferences about populations.
What location in a distribution corresponds to z 5 22.00?a. Above the mean by 2 pointsb. Above the mean by a distance equal to 2 standard deviationsc. Below the mean by 2 pointsd. Below the mean by a distance equal to 2 standard deviations
For a population with m 5 80 and s 5 12, what is the z-score corresponding to X 5 92?a. 10.50b. 11.00c. 11.20d. 112.00
For a sample with M 5 72 and s 5 4, what is the X value corresponding to z 5 22.00?a. X 5 70b. X 5 68c. X 5 64d. X 5 60
In a population with m 5 60, a score of X 5 58 corresponds to a z-score of z 5 20.50. What is the population standard deviation?a. 1b. 2c. 4d. Cannot be determined without additional information
In a sample with a standard deviation of s 5 8, a score of X 5 64 corresponds to z 5 20.50. What is the sample mean?a. M 5 56b. M 5 60c. M 5 68d. M 5 72
In a population of scores, X 5 45 corresponds to z 5 12.00 and X 5 30 corresponds to z 5 21.00. What is the population mean?a. 30b. 35c. 37.5d. 40
In a sample, X 5 70 corresponds to z 5 12.00 and X 5 65 corresponds to z 5 11.00. What are the sample mean and standard deviation?a. M 5 60 and s 5 5b. M 5 60 and s 5 10c. M 5 50 and s 5 10d. M 5 50 and s 5 5
A population with m 5 80 and s 5 15 is transformed into z-scores. After the transformation, what is the mean for the population of z-scores?a. m 5 80b. m 5 1.00c. m 5 0d. Cannot be determined from the information given
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