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Statistics For The Behavioral Sciences 9th Edition Frederick J Gravetter, Larry B. Wallnau - Solutions

In studies examining the effect of humor on interpersonal attractions, McGee and Shevlin (2009) found 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
A psychologist would like to determine whether there is a relationship between depression and aging. It is known that the general population averages μ = 40 on a standardized depression test. The psychologist obtains a sample of n = 9 individuals who are all more than 70 years old. The depression
Find the estimated standard error for the sample mean for each of the following samples. a. n = 4 with SS = 48 b. n = 6 with SS = 270 c. n = 12 with SS = 132 Discuss.
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 α = .05 for each of the following sample sizes: a. n = 6 b. n = 12 c. n = 24
The following sample of n = 6 scores was obtained from a population with unknown parameters. Scores: 7, 1, 6, 3, 6, 7a. 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
The following sample was obtained from a population with unknown parameters. Scores: 6, 12, 0, 3, 4 a. 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
To evaluate the effect of a treatment, a sample is obtained from a population with a mean of μ = 75, and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M = 79.6 with a standard deviation of s = 12. a. If the sample consists of n = 16
To evaluate the effect of a treatment, a sample of n = 9 is obtained from a population with a mean of μ = 40, and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M = 33. a. If the sample has a standard deviation of s = 9, are the data
Describe the basic characteristics of an independent measures, or a between-subjects, research study?
For each of the following, assume that the two samples are selected from populations with equal means and calculate how much difference should be expected, on average, between the two sample means. a. Each sample has n = 5 scores with s2 = 38 for the first sample and s2 = 42 for the second. (Note:
For each of the following, calculate the pooled variance and the estimated standard error for the sample mean difference a. The first sample has n = 4 scores and a variance of s2 = 55, and the second sample has n = 6 scores and a variance of s2 = 63. b. Now the sample variances are increased so
A researcher conducts an independent-measures study comparing two treatments and reports the t statistic as t(30) = 2.085. a. How many individuals participated in the entire study? b. Using a two-tailed test with α = .05, is there a significant difference between the two treatments? c. Compute r2
Hallam, Price, and Katsarou (2002) investigated the influence of background noise on classroom performance for children aged 10 to 12. In one part of the study, calming music led to better performance on an arithmetic task compared to a no-music condition. Suppose that a researcher selects one
Do you view a chocolate bar as delicious or as fattening? Your attitude may depend on your gender. In a study of American college students, Rozin, Bauer, and Catanese (2003) examined the importance of food as a source of pleasure versus concerns about food associated with weight gain and health.
In a study examining overweight and obese college football players, Mathews and Wagner (2008) found that on average both offensive and defensive linemen exceeded the at-risk criterion for body mass index (BMI). BMI is a ratio of body weight to height squared and is commonly used to classify people
Functional foods are those containing nutritional supplements in addition to natural nutrients. Examples include orange juice with calcium and eggs with omega-3. Kolodinsky, et al. (2008) examined attitudes toward functional foods for college students. For American students, the results indicated
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 fast
Numerous studies have found that males report higher self-esteem than females, especially for adolescents (Kling, Hyde, Showers, & Buswell, 1999). Typical results show a mean self-esteem score of M = 39.0 with SS = 60.2 for a sample of n = 10 male adolescents and a mean of M = 35.4 with SS = 69.4
A researcher is comparing the effectiveness of two sets of instructions for assembling a child's bike. A sample of eight fathers is obtained. Half of the fathers are given one set of instructions and the other half receives the second set. The researcher measures how much time is needed for each
Describe what is measured by the estimated standard error in the bottom of the independent-measures t statistic?
When people learn a new task, their performance usually improves when they are tested the next day, but only if they get at least 6 hours of sleep (Stickgold, Whidbee, Schirmer, Patel, & Hobson, 2000). The following data demonstrate this phenomenon. The participants learned a visual discrimination
Steven Schmidt (1994) conducted a series of experiments examining the effects of humor on memory. In one study, participants were given a mix of humorous and non-humorous sentences and significantly more humorous sentences were recalled. However, Schmidt argued that the humorous sentences were not
Downs and Abwender (2002) evaluated soccer players and swimmers to determine whether the routine blows to the head experienced by soccer players produced long-term neurological deficits. In the study, neurological tests were administered to mature soccer players and swimmers and the results
Research has shown that people are more likely to show dishonest and self-interested behaviors in darkness than in a well-lit environment (Zhong, Bohns, & Gino, 2010). In one experiment, participants were given a set of 20 puzzles and were paid $0.50 for each one solved in a 5-minute period.
If other factors are held constant, explain how each of the following influences the value of the independent-measures t statistic and the likelihood of rejecting the null hypothesis: a. Increasing the number of scores in each sample. b. Increasing the variance for each sample?
Describe the homogeneity of variance assumption and explain why it is important for the independent measures t test?
One sample has SS = 48 and a second sample has SS = 32. a. If n = 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 = 70 and a second sample has SS = 42. a. If n = 8 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
As noted on page 320, 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 (1 = (2 and calculate how much difference
Two separate samples, each with n = 12 individuals, receive two different treatments. After treatment, the first sample has SS = 1740 and the second has SS = 1560. a. Find the pooled variance for the two samples. b. Compute the estimated standard error for the sample mean difference. c. If the
Two separate samples receive two different treatments. The first sample has n = 9 with SS = 710, and the second has n = 6 with SS = 460. 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 difference is
For the following studies, indicate whether a repeated measures t test is the appropriate analysis. Explain your answers. a. A researcher is comparing the amount of time spent playing video games each week for college males versus college females. b. A researcher is comparing two new designs for
Research has shown that losing even one night's sleep can have a significant effect on performance of complex tasks such as problem solving (Linde & Bergstroem, 1992). To demonstrate this phenomenon, a sample of n = 25 college students was given a problem solving task at noon on one day and
Strack, Martin, and Stepper (1988) reported that people rate cartoons as funnier when holding a pen in their teeth (which forced them to smile) than when holding a pen in their lips (which forced them to frown). A researcher attempted to replicate this result using a sample of n = 25 adults between
How would you react to doing much worse on an exam than you expected? There is some evidence to suggest that most individuals believe that they can cope with this kind of problem better than their fellow students (Igou, 2008). In the study, participants read a scenario of a negative event and were
Research results indicate that physically attractive people are also perceived as being more intelligent (Eagly, Ashmore, Makhijani, & Longo, 1991). As a demonstration of this phenomenon, a researcher obtained a set of 10 photographs, 5 showing men who were judged to be attractive and 5 showing men
Researchers have noted a decline in cognitive functioning as people age (Bartus, 1990). However, the results from other research suggest that the antioxidants in foods such as blueberries may reduce and even reverse these age-related declines (Joseph et al., 1999). To examine this phenomenon,
The following data are from a repeated-measures study examining the effect of a treatment by measuring a group of n = 4 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
A researcher for a cereal company wanted to demonstrate the health benefits of eating oatmeal. A sample of 9 volunteers was obtained and each participant ate a fixed diet without any oatmeal for 30 days. At the end of the 30-day period, cholesterol was measured for each individual. Then the
A variety of research results suggest that visual images interfere with visual perception. In one study, Segal and Fusella (1970) had participants watch a screen, looking for brief presentations of a small blue arrow. On some trials, the participants were also asked to form a mental image (for
One of the primary advantages of a repeated-measures design, compared to independent measures, is that it reduces the overall variability by removing variance caused by individual differences. The following data are from a research study comparing two treatment conditions.a. Assume that the data
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 18, for example, the first two participants
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. Briefly explain how these problems are eliminated or reduced with a repeated-measures study .
A researcher uses a matched-subjects design to investigate whether single people who own pets are generally happier than singles without pets. A mood inventory questionnaire is administered to a group of 20- to 29-year-old non-pet owners and a similar age group of pet owners. The pet owners are
There is some evidence suggesting that you are likely to improve your test score if you rethink and change answers on a multiple-choice exam (Johnston, 1975).To examine this phenomenon, a teacher gave the same final exam to two sections of a psychology course. The students in one section were told
The teacher from the previous problem also tried a different approach to answering the question of whether changing answers helps or hurts exam grades. In a separate class, students were encouraged to review their final exams and change any answers they wanted to before turning in their papers.
At the Olympic level of competition, even the smallest factors can make the difference between winning and losing. For example, Pelton (1983) has shown that Olympic marksmen shoot much better if they fire between heartbeats, rather than squeezing the trigger during a heartbeat. The small vibration
The Preview section of this chapter presented a repeated-measures research study demonstrating that swearing can help reduce pain (Stephens, Atkins, & Kingston, 2009).In the study, each participant was asked to plunge a hand into icy water and keep it there as long as the pain would allow. In
Explain the difference between a matched-subjects design and a repeated-measures design. Discuss.
A researcher conducts an experiment comparing two treatment conditions and obtains data with 10 scores for each treatment condition. a. If the researcher used an independent-measures design, how many subjects participated in the experiment? b. If the researcher used a repeated-measures design, how
A sample of n = 9 individuals participates in a repeated measures study that produces a sample mean difference of MD = 6.5 with SS = 200 for the difference scores. a. Calculate the standard deviation for the sample of difference scores. Briefly explain what is measured by the standard deviation.
a. A repeated-measures study with a sample of n = 25 participants produces a mean difference of MD = 3 with a standard deviation of s = 4. Based on the mean and standard deviation, you should be able to visualize (or sketch) the sample distribution. Use a two-tailed hypothesis test with α = .05 to
a. A repeated-measures study with a sample of n = 9 participants produces a mean difference of MD = 3 with a standard deviation of s = 6. Based on the mean and standard deviation, you should be able to visualize (or sketch) the sample distribution. Use a two tailed hypothesis test with α = .05 to
A sample of difference scores from a repeated-measures experiment has a mean of MD = 4 with a standard deviation of s = 6.a. If n = 4, is this sample sufficient to reject the null hypothesis using a two-tailed test with α = .05?b. Would you reject H0 if n = 16? Again, assume a two-tailed test with
As mentioned in Chapters 2 and 3 (pp. 38 and 81), Steven Schmidt (1994) reported a series of studies examining the effect of humor on memory. In one part of the study, participants were presented with a list containing a mix of humorous and non humorous sentences, and were then asked to recall as
People tend to evaluate the quality of their lives relative to others around them. In a demonstration of this phenomenon, Frieswijk, Buunk, Steverink, and Slaets (2004) conducted interviews with frail elderly people. In the interview, each person was compared with fictitious others who were worse
In the problems at the end of Chapter 8, we presented a study indicating that people with visible tattoos are viewed more negatively than people without visible tattoos (Resenhoeft, Villa, & Wiseman, 2008). Suppose that a researcher intends to examine this phenomenon by asking participants to rate
The stimulant Ritalin has been shown to increase attention span and improve academic performance in children with ADHD (Evans, Pelham, Smith, 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
Explain why the F-ratio is expected to be near 1.00 when the null hypothesis is true. Discuss.
For the preceding problem you should find that there are significant differences among the three treatments. One reason for the significance is that the sample variances are relatively small. To create the following data, we started with the values from problem 9 and increased the variability (the
Binge drinking on college campuses has been a hot topic in the popular media and in scholarly research. Flett, Goldstein, Wall, Hewitt, Wekerle, and Azzi (2008) report the results of a study relating perfectionism to binge drinking. In the study, students were classified into three groups based on
A researcher reports an F-ratio with df = 3, 36 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?
A research report from an independent-measures study states that there are significant differences between treatments, F(2, 54) = 3.58, p < .05. a. How many treatment conditions were compared in the study? b. What was the total number of participants in the study?
There is some evidence that high school students justify cheating in class on the basis of poor teacher skills or low levels of teacher caring (Murdock, Miller, and Kohlhardt, 2004). Students appear to rationalize their illicit behavior based on perceptions of how their teachers view cheating. Poor
The following summary table presents the results from an ANOVA comparing three treatment conditions with n = 8 participants in each condition. Complete all missing values. (Hint: Start with the df column.)
A pharmaceutical company has developed a drug that is expected to reduce hunger. To test the drug, two samples of rats are selected with n = 20 in each sample. The rats in the first sample receive the drug every day and those in the second sample are given a placebo. The dependent variable is the
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
The following data were obtained from an independent-measures research study comparing three treatment conditions. Use an ANOVA with Î± = .05 to determine whether there are any significant mean differences among the treatments.
The following values summarize the results from an independent-measures study comparing two treatment conditions.a. Use an independent-measures t test with Î± = .05 to determine whether there is a significant mean difference between the two treatments.b. Use an ANOVA with Î± = .05 to determine
Describe the similarities between an F-ratio and a t statistic.
The following data represent the results from an independent-measures study comparing two treatment conditions.a. Use an independent-measures t test with Î± = .05 to determine whether there is a significant mean difference between the two treatments.b. Use an ANOVA with Î± = .05 to determine
One possible explanation for why some birds migrate and others maintain year round residency in a single location is intelligence. Specifically, birds with small brains, relative to their body size, are simply not smart enough to find food during the winter and must migrate to warmer climates where
There is some research indicating that college students who use Facebook while studying tend to have lower grades than non-users (Kirschner & Karpinski, 2010). A representative study surveys students to determine the amount of Facebook use during the time they are studying or doing homework.
New research suggests that watching television, especially medical shows such as Grey's Anatomy and House can result in more concern about personal health (Ye, 2010). Surveys administered to college students measure television viewing habits and health concerns such as fear of developing the
Several factors influence the size of the F-ratio. For each of the following, indicate whether it would influence the numerator or the denominator of the F-ratio, and indicate whether the size of the F-ratio would increase or decrease. a. Increase the differences between the sample means. b.
Why should you use ANOVA instead of several t tests to evaluate mean differences when an experiment consists of three or more treatment conditions? Discuss.
Posttests are done after an ANOVA. a. What is the purpose of posttests? b. Explain why you do not need posttests if the analysis is comparing only two treatments. c. Explain why you do not need posttests if the decision from the ANOVA is to fail to reject the null hypothesis.
An independent-measures research study compares three treatment conditions with a sample of n = 10 in each condition. The sample means are M1 = 2, M2 = 3,and M3 = 7. a. Compute SS for the set of 3 treatment means. (Use the three means as a set of n = 3 scores and compute SS.) b. Using the result
The following data summarize the results from an independent-measures study comparing three treatment conditions.a. Use an ANOVA with Î± = .05 to determine whether there are any significant differences among the three treatment means.b. Calculate Î·2 to measure the effect size for this study.c.
For the preceding problem you should find that there are significant differences among the three treatments. The primary reason for the significance is that the mean for treatment I is substantially smaller than the means for the other two treatments. To create the following data, we started with
The following data summarize the results from an independent-measures study comparing three treatment conditions.a. Calculate the sample variance for each of the three samples.b. Use an ANOVA with Î± = .05 to determine whether there are any significant differences among the three treatment means.
How does the denominator of the F-ratio (the error term) differ for a repeated-measures ANOVA compared to an independent-measures ANOVA? Discuss.
For the data in problem 9,a. Compute SStotal and SS between treatments.b. Eliminate the mean differences between treatments by adding 2 points to each score in treatment I, adding 1 point to each score in treatment II, and subtracting 3 points from each score in treatment III. (All three treatments
The following data were obtained from a repeated measures study comparing three treatment conditions.Use a repeated-measures ANOVA with Î± = .05 to determine whether these data are sufficient to demonstrate significant differences between the treatments.
In Problem 11 the data show large and consistent differences between subjects. For example, subject A has the largest score in every treatment and subject D always has the smallest score. In the second stage of the ANOVA, the large individual differences are subtracted out of the denominator of the
One of the primary advantages of a repeated-measures design, compared to an independent-measures design, is that it reduces the overall variability by removing variance caused by individual differences. The following data are from a research study comparing three treatment conditions.a. Assume that
The following data are from an experiment comparing three different treatment conditions:a. If the experiment uses an independent-measures design, can the researcher conclude that the treatments are significantly different? Test at the .05 level of significance.b. If the experiment is done with a
A researcher is evaluating customer satisfaction with the service and coverage of two phone carriers. Each individual in a sample of n = 25 uses one carrier for two weeks and then switches to the other. Each participant then rates the two carriers. The following table presents the results from the
The following summary table presents the results from a repeated-measures ANOVA comparing three treatment conditions with a sample of n = 11 subjects. Fill in the missing values in the table. (Hint: Start with the df values.)
The following summary table presents the results from a repeated-measures ANOVA comparing four treatment conditions, each with a sample of n = 12 participants. Fill in the missing values in the table. (Hint: Start with the df values.)
A recent study indicates that simply giving college students a pedometer can result in increased walking (Jackson & Howton, 2008). Students were given pedometers for a 12 week period, and asked to record the average number of steps per day during weeks 1, 6, and 12. The following data are
A repeated-measures experiment comparing only two treatments can be evaluated with either a t statistic or an ANOVA. As we found with the independent measures design, the t test and the ANOVA produce equivalent conclusions, and the two test statistics are related by the equation F t2. The following
The repeated-measures ANOVA can be viewed as a two-stage process. What is the purpose of the second stage? Discuss.
For either independent-measures or repeated-measures designs comparing two treatments, the mean difference can be evaluated with either a t test or an ANOVA. The two tests are related by the equation F = t2. For the following data,a. Use a repeated measures t test with Î± = .05 to determine
In the Preview section for this chapter, we presented an example of a delayed discounting study in which people are willing to settle for a smaller reward today in exchange for a larger reward in the future. The following data represent the typical results from one of these studies. The
The endorphins released by the brain act as natural painkillers. For example, Gintzler (1970) monitored endorphin activity and pain thresholds in pregnant rats during the days before they gave birth. The data showed an increase in pain threshold as the pregnancy progressed. The change was gradual
A researcher conducts an experiment comparing three treatment conditions with n = 10 scores in each condition. a. If the researcher uses an independent-measures design, how many individuals are needed for the study and what are the df values for the F-ratio? b. If the researcher uses a
A researcher conducts a repeated-measures experiment using a sample of n = 8 subjects to evaluate the differences among four treatment conditions. If the results are examined with an ANOVA, what are the df values for the F-ratio?
A researcher uses a repeated-measures ANOVA to evaluate the results from a research study and reports an F-ratio with df = 2, 30. a. How many treatment conditions were compared in the study? b. How many individuals participated in the study? Discuss.

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