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Essentials Of Statistics For The Behavioral Sciences 8th Edition Frederick J Gravetter, Larry B. Wallnau - Solutions

Researchers at a National Weather Center in the northeastern United States recorded the number of 90° days each year since records first started in 1875. The numbers form a normal shaped distribution with a mean of µ = 9.6 and a standard deviation of s = 1.9. To see if the data showed any
Montarello and Martens (2005) found that fifth-grade students completed more mathematics problems correctly when simple problems were mixed in with their regular math assignments. To further explore this phenomenon, suppose that a researcher selects a standardized mathematics achievement test that
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 can reduce and even reverse these age-related declines, at least in laboratory rats (Joseph et al., 1999).
A researcher plans to conduct an experiment evaluating the effect of a treatment. A sample of n = 9 participants is selected and each person receives the treatment before being tested on a standardized dexterity task. The treatment is expected to lower scores on the test by an average of 30 points.
A sample of n = 40 is selected from a normal population with µ = 75 msec. and s = 12, and a treatment is administered to the sample. The treatment is expected to increase scores by an average of 4 msec.a. If the treatment effect is evaluated with a twotailed hypothesis test using a = .05, what is
Briefly explain how increasing sample size influences each of the following. Assume that all other factors are held constant. a. The size of the z-score in a hypothesis test. b. The size of Cohen's d. c. The power of a hypothesis test.
Define the alpha level and the critical region, and explain how they are related.
A researcher is investigating the effectiveness of a new medication for lowering blood pressure for individuals with systolic pressure greater than 140. For this population, systolic scores average µ = 160 with a standard deviation of s = 20, and the scores form a normal-shaped distribution. The
A researcher is evaluating the influence of a treatment using a sample selected from a normally distributed population with a mean of µ = 80 and a standard deviation of s = 20. The researcher expects a 12-point treatment effect and plans to use a two-tailed hypothesis test with a = .05.a. Compute
Although there is a popular belief that herbal remedies such as Ginkgo biloba and Ginseng may improve learning and memory in healthy adults, these effects are usually not supported by well-controlled research (Persson, Bringlov, Nilsson, & Nyberg, 2004). In a typical study, a researcher obtains a
Childhood participation in sports, cultural groups, and youth groups appears to be related to improved self-esteem for adolescents (McGee, Williams, Howden-Chapman, Martin, & Kawachi, 2006). In a representative study, a sample of n = 100 adolescents with a history of group participation is given a
A local college requires an English composition course for all freshmen. This year they are evaluating a new online version of the course. A random sample of n = 16 freshmen is selected and the students are placed in the online course. At the end of the semester, all freshmen take the same English
A random sample is selected from a normal population with a mean of µ = 30 and a standard deviation of s = 8. After a treatment is administered to the individuals in the sample, the sample mean is found to be µ = 33. a. If the sample consists of n = 16 scores, is the sample mean sufficient to
A random sample of n = 25 scores is selected from a normal population with a mean of µ = 40. After a treatment is administered to the individuals in the sample, the sample mean is found to be µ = 44. a. If the population standard deviation is s = 5, is the sample mean sufficient to conclude that
Brunt, Rhee, and Zhong (2008) surveyed 557 undergraduate college students to examine their weight status, health behaviors, and diet. Using body mass index (BMI), they classified the students into four categories: underweight, healthy weight, overweight, and obese. They also measured dietary
A random sample is selected from a normal population with a mean of µ = 100 and a standard deviation of s = 20. After a treatment is administered to the individuals in the sample, the sample mean is found to be µ = 96. a. How large a sample is necessary for this sample mean to be statistically
Under what circumstances is a t statistic used instead of a z-score for a hypothesis test?
To evaluate the effect of a treatment, a sample of n = 8 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 µ = 35. a. If the sample variance is s2 = 32, are the data sufficient
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,
Many animals, including humans, tend to avoid direct eye contact and even patterns that look like eyes. Some insects, including moths, have evolved eye-spot patterns on their wings to help ward off predators. Scaife (1976) reports a study examining how eye-spot patterns affect the behavior of
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 µ = 15.1. A sample of n = 16 of today's children produces a mean score of µ = 23.3 with
The librarian at the local elementary school claims that, on average, the books in the library are more than 20 years old. To test this claim, a student takes a sample of n = 30 books and records the publication date for each. The sample produces an average age of µ = 23.8 years with a variance of
For several years researchers have noticed that there appears to be a regular, year-by-year increase in the average IQ for the general population. This phenomenon is called the Flynn effect after the researcher who first reported it (Flynn, 1984, 1999), and it means that psychologists must
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, an instructor in a
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
A random sample of n = 16 scores is obtained from a population with a mean of µ = 45. After a treatment is administered to the individuals in the sample, the sample mean is found to be µ = 49.2. a. Assuming that the sample standard deviation is s = 8, compute r2 and the estimated Cohen's d to
A random sample is obtained from a population with a mean of µ = 45. After a treatment is administered to the individuals in the sample, the sample mean is M = 49 with a standard deviation of σ = 12. a. Assuming that the sample consists of n = 9 scores, compute r2 and the estimated Cohen's d to
A sample of n = 25 scores has a mean of µ = 83 and a standard deviation of σ = 15. 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.
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
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
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 = 12 young adults who each experienced = or more different homes
Research examining the effects of preschool childcare has found that children who spent time in day care, especially high-quality day care, perform better on math and language tests than children who stay home with their mothers (Broberg, Wessels, Lamb, & Hwang, 1997). In a typical study, a
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
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 = .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.b. Compute the estimated standard error for M.
The following sample was obtained from a population with unknown parameters. Scores: 6, 12, 0, 13, 4, 7 a. Compute the sample mean and standard deviation. b. Compute the estimated standard error for M.
A random sample of n = 25 individuals is selected from a population with µ = 20, and a treatment is administered to each individual in the sample. After treatment, the sample mean is found to be µ = 22.2 with SS = 384. a. How much difference is there between the mean for the treated sample and
To evaluate the effect of a treatment, a sample is obtained from a population with a mean of µ = 30, and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be µ = 31.3 with a standard deviation of s = 3. a. If the sample consists of n = 16
Two separate samples receive different treatments. After treatment, the first sample has n = 9 with SS = 462, and the second has n = 7 with SS = 420. 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
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 = 4 scores with s2 = 68 for the first sample and s2 = 76 for the second. b.
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(25) = 2.071. a. How many individuals participated in the entire study? b. Using a two-tailed test with a = .05, is there a significant difference between the two treatments? c. Compute r2
In a recent study, Piff, Kraus, Cote, Cheng, and Keitner (2010) found that people from lower social economic 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
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
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 adversity. 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
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
Describe what is measured by the estimated standard error in the bottom of the independent-measures t statistic.
Recent research has shown that creative people are more likely to cheat than their less creative counterparts (Gino & Ariely, 2010). 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
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
Recent research has demonstrated that music-based physical training for elderly people can improve balance and 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
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 independentmeasures t statistic and the likelihood of rejecting the null hypothesis: a. An increase in the mean difference between the samples. b. An increase in the number of scores in each sample. c.
Describe the homogeneity of variance assumption and explain why it is important for the independentmeasures t test.
One sample has SS = 36 and a second sample has SS = 18. a. If n = 4 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 283, 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 μ1 = μ2 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 = 4, the second has n = 6, and the pooled variance is 60. b. One sample has n = 12, the second has n = 15, and the
Two separate samples, each with n = 15 individuals, receive different treatments. After treatment, the first sample has SS = 1740 and the second has SS = 1620. a. Find the pooled variance for the two samples. b. Compute the estimated standard error for the sample mean difference. c. If the sample
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 again
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
Masculine-themed words (such as competitive, independent, analyze, strong) are commonly used in job recruitment materials, especially for job advertisements in male-dominated areas (Gaucher, Friesen, & Kay, 2011). The same study found that these words also make the jobs less appealing to women. In
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, = showing men who were judged to be attractive and = 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 = 6 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
Research indicates that the color red increases men€™s attraction to women (Elliot & Niesta, 2008). In the original study, men were shown women€™s photographs presented on either a white or a red background. Photographs presented on red were rated significantly more attractive
One of the primary advantages of a repeatedmeasures 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 are
Problem 18 shows 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 (top two rows)
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
A researcher uses a matched-subjects design to investigate whether single people with pets are happier than singles without pets. A mood inventory survey is given to a group of 20- to 29-year-old non€“pet owners and a similar age group of pet owners. The pet owners are matched one to one
Some evidence suggests 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 course. Students in one section were told to turn in their exams
The teacher from Problem 21 also tried a different approach to determining whether changing answers helps or hurts exam grades. In another class, students were told to review their final exams and change any answers they wanted to before turning them in. However, the students had to indicate both
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
Example 11.1 in this chapter presented a repeatedmeasures research study demonstrating that swearing can help reduce ratings of 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.
A researcher conducts an experiment comparing two treatment conditions with 20 scores in each treatment condition. a. If an independent-measures design is used, how many subjects are needed for the experiment? b. If a repeated-measures design is used, how many subjects are needed for the
A sample of n = 9 individuals participates in a repeated-measures study that produces a sample mean difference of MD = 4.25 with SS = 128 for the difference scores. a. Calculate the standard deviation for the sample of difference scores. Briefly explain what is measured by the standard
a. A repeated-measures study with a sample of n = 16 participants produces a mean difference of MD = 3 with a standard deviation of σ = 4. Use a two-tailed hypothesis test with a = .05 to determine whether this sample provides evidence of a significant treatment effect. b. Now assume that the
a. A repeated-measures study with a sample of n = 9 participants produces a mean difference of MD = 3 with a standard deviation of σ = 6. Use a two-tailed hypothesis test with a = .05 to determine whether it is likely that this sample came from a population with mD = 0. b. Now assume that the
A sample of difference scores from a repeatedmeasures experiment has a mean of MD = 4 with a standard deviation of σ = 6. a. If n = 4, is this sample sufficient to reject the null hypothesis using a two-tailed test with a = .05? b. Would you reject H0 if n = 16? Again, assume a two-tailed test
When you get a surprisingly low price on a product do you assume that you got a really good deal or that you bought a low-quality product? Research indicates that you are more likely to associate low price and low quality if someone else makes the purchase rather than yourself (Yan & Sengupta,
Explain why the F-ratio is expected to be near 1.00 when the null hypothesis is true.
The following data summarize the results from an independent-measures study comparing three treatment conditions.a. Use an ANOVA with a = .05 to determine whether there are any significant differences among the three treatment means. Note: Because the samples are all the same size, MSwithin is the
To create the following data we started with the same sample means and variances that appeared in problem 10 but increased the sample size to n = 25.a. Predict how the increase in sample size should affect the F-ratio for these data compared to theF-ratio in problem 10. Use an ANOVA to check your
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
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, & Kohlhardt, 2004). Students appear to rationalize their illicit behavior based on perceptions of how their teachers view cheating.
A researcher reports an F-ratio with df = 2, 27 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(3, 48) = 2.95, p , .05. a. How many treatment conditions were compared in the study? b. What was the total number of participants in the study?
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.
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 independentmeasures research study comparing three treatment conditions. Use an ANOVA with a = .05 to determine whether there are any significant mean differences among the treatments.
Several factors influence the size of the F-ratio. For each of the following, indicate whether it influences the numerator or the denominator of the F-ratio, and indicate whether the size of the F-ratio would increase or decrease. In each case, assume that all other factors are held constant. a. An
The following values summarize the results from an independent-measures study comparing two treatment conditions.a. Use an independent-measures t test with a = .05 to determine whether there is a significant mean difference between the two treatments. You should find that F = t2.b. Use an ANOVA
The following data are from an independent-measures study comparing two treatment conditions.a. Use an independent-measures t test with a = .05 to determine whether there is a significant mean difference between the two treatments.b. Use an ANOVA with a = .05 to determine whether there is a
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

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