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essentials of statistics

Essentials Of Statistics For The Behavioral Sciences 7th Edition Frederick J. Gravetter, Larry B. Wallnau - Solutions

4. Explain why you should use ANOVA instead of several t tests to evaluate mean differences when an experiment consists of three or more treatment conditions.
3. 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.
2. Describe the similarities between an F-ratio and a t statistic.
1. Explain why the expected value for an F-ratio is 1.00 when the null hypothesis is true.
21. In Chapter 11, problem 22 presented data comparing the accuracy of Olympic marksmen for shots fired during heartbeat compared to shots fired between heartbeat. The data are presented again here.During Between Participant Heartbeats Heartbeats A 93 98 B 90 94 C 95 96 D 92 91 E 95 97 F 91 97 G 92
20. Problem 16 in Chapter 11 described a study examining the effect of eating oatmeal regularly on cholesterol.Cholesterol was measured before and after adding oatmeal to the diet of a sample of n 9 participants.For this sample, cholesterol scores averaged MD 16 points lower with the oatmeal diet
19. A research study has demonstrated that self-hypnosis can be an effective treatment for allergies (Langewitz, Izakovic, & Wyler, 2005). The researchers recruited a sample of patients with moderate to severe allergic reactions. The patients were trained to focus their minds on a specific place,
18. A researcher would like to determine how physical endurance is affected by a common herbal supplement.The researcher measures endurance for a sample of n 9 participants. Each individual is then given a 30-day supply of the herbs and, 1 month later, endurance is measured again. For this sample,
17. The stimulant Ritalin has been shown to increase attention span and improve academic performance in?children with ADHD (Evans, et al., 2001). To demonstrate the effectiveness of the drug, a researcher selects a sample of n = 25 children diagnosed with the disorder, and measures each child’s
16. Problem 23 in Chapter 10 described a study demonstrating that elderly people who own dogs are less likely to pay visits to their doctors than are those who do not own pets. The data are presented again here.Number of Doctor Visits in Past Year Control Group Dog Owners 10 7 8 4 7 9 9 3 13 7 76
15. Problem 18 in Chapter 10 reported a research study in which eyewitness reports of an automobile accident were influenced by the language used to ask questions (Loftus& Palmer, 1974). One group of n = 15 witnesses was asked how fast the cars were going when they “smashed into” each other and
14. 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
13. 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
12. 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 =
11. A common test of short-term memory requires participants to repeat a random string of digits that was presented a few seconds earlier. The number of digits is increased on each trial until the person begins to make mistakes. The longest string that can be reported accurately determines the
10. 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 15.1. A sample of n 16 of today’s children produces a mean score of M 23.3 with SS
9. Problem 22 in Chapter 9 described a study reporting that a good sense of humor can have a significant effect on how people judge the attractiveness of a potential romantic partner. In the study, female college students read brief descriptions of a man. For one group, the description said that he
8. Problem 12 in Chapter 9 described a study that examined the spotlight effect, which refers to people overestimating the extent to which others notice their appearance or behavior. In the study, n = 9 participants were asked to put on a Barry Manilow T-shirt and walk into a room where other
7. A researcher obtains a sample of n = 25 asthma patients and measures the severity of each person’s symptoms before and after they complete a 3-week relaxation training course. On average, the severity of symptoms decreased by MD = 4.3 points with SS = 216 for the difference scores.a. Compute
6. A researcher obtains a sample from an unknown population and computes a sample mean of M = 43 with a standard deviation of s = 6.a. If the sample has n = 16 scores, compute an 80%confidence interval to estimate the unknown population mean.b. If the sample has n = 36 scores, compute an
5. For the following studies, state whether estimation or hypothesis testing is required. Also, is an independentor a repeated-measures t statistic appropriate?a. A researcher would like to determine how much weight the average college freshman gains during the first semester. A sample of freshmen
4. A researcher has constructed an 80% confidence interval of 45 8, using a sample of n 25 scores.a. What would happen to the width of the interval if the researcher had used a larger sample size?(Assume other factors are held constant.)b. What would happen to the width of the interval if the
3. Explain the trade off between precision and confidence for interval estimates.
2. Explain why it would not be reasonable to use estimation after a hypothesis test for which the decision was “fail to reject H0.”
1. Explain how the purpose of estimation differs from the purpose of a hypothesis test.
23. A researcher studies the effect of a drug (MAO inhibitor) on the number of nightmares occurring in veterans with post-traumatic stress disorder (PTSD).A sample of PTSD clients records each incident of a nightmare for 1 month before treatment. Participants are then given the medication for 1
22. 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
21. Placing children in time out can be an effective form of punishment. Research suggests that this same technique can also be effective for adults (Chelonis, Bastilla, Brown, & Gardner, 2007). In the study, participants were shown a series of colored shapes and had to classify each stimulus into
20. A researcher uses a matched-samples 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
19. 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
18. 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
17. 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
16. 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
15. 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
14. 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,
13. 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
12. 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
11. 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 16 adults
10. 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
9. As mentioned in Chapters 2 and 3 (pages 56 and 67), 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 nonhumorous sentences, and were then asked to recall
8. A sample of difference scores from a repeatedmeasures experiment has a mean of MD 5 with a variance of s 2 64.a. If n 4, is this sample sufficient to reject the null hypothesis using a two-tailed test with .05?b. Would you reject H0 if n 16? Again, assume a two-tailed test with .05.c. Explain
7.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 .05 to determine
6.a. A repeated-measures study with a sample of n 9 participants produces a mean difference of MD 4 with a standard deviation of s 12. 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 .05 to determine
5. A sample of n 16 individuals participates in a repeated-measures study that produces a sample mean difference of MD 9 with SS 960 for the difference scores.a. Calculate the standard deviation for the sample of difference scores. Briefly explain what is measured by the standard deviation.b.
4. 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
3. Explain the difference between a matched-subjects design and a repeated-measures design.
2. 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
1. 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 females.b. A researcher is comparing two new designs for cell
23. Siegel (1990) found that elderly people who owned dogs were less likely to pay visits to their doctors after upsetting events than were those who did not own pets. Similarly, consider the following hypothetical data. A sample of elderly dog owners is compared to a similar group (in terms of age
22. 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 nonhumorous sentences and significantly more humorous sentences were recalled.However, Schmidt argued that the humorous sentences were
21. 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
20. 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
19. Research indicates that adolescent boys report higher levels of self-esteem than is reported by adolescent girls (Kling, Hyde, Showers, & Buswell, 1999). To examine this phenomenon a researcher obtains a sample of 40 adolescents, 20 boys and 20 girls, and administers a standardized measure of
18. 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
17. 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
16. 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
15. 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.
14. 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 .05, is there a significant difference between the two treatments?c. Compute r 2
13. Suppose the research study in the previous problem produced larger variances of s 2 27 and s 2 21 for the two samples. Assuming that the means and sample sizes are the same as in problem 12, are the data sufficient to conclude that there is a significant difference between the two
12. An independent-measures research study was used to compare two treatment conditions with n 12 participants in each treatment. The first treatment had a mean of M 55 with a variance of s 2 8, and the second treatment had M 52 and s 2 4. Do these data indicate a significant difference
11. 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 s 2 38 for the first sample and s 2 42 for the second.
10. 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
9. 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
8. As noted on page 281, 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
7. 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
6. 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
5. Describe the homogeneity of variance assumption and explain why it is important for the independentmeasures t test.
4. If other factors are held constant, how does increasing the sample variance affect the value of the independent-measures t statistic and the likelihood of rejecting the null hypothesis?
3. If other factors are held constant, how does increasing the number of scores in each sample affect the value of the independent-measures t statistic and the likelihood of rejecting the null hypothesis?
2. Describe what is measured by the estimated standard error in the bottom of the independent-measures t statistic.
1. Describe the basic characteristics of an independentmeasures, or a between-subjects, research study.
3. 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
2. A survey of female high school seniors shows that the average amount of time spent on clothes, hair, and makeup each morning before school is 35 minutes.Assume that the distribution of preparation times is approximately normal with a standard deviation of 14 minutes, and find each of the
1. Find each of the requested values for a population with a mean of 40 and a standard deviation of 8.a. What is the z-score corresponding to X 52?b. What is the X value corresponding to z –0.50.c. If all the scores in the population are transformed into z-scores, what will be the values for
23. A researcher expects a treatment to increase scores by 5 points. The regular population, without treatment, averages 40 with a standard deviation of 8, and the scores form a normal distribution. If the researcher uses a one-tailed test with .01,a. What is the power of the test for a sample
22. A researcher is evaluating the influence of a treatment using a sample selected from a normally distributed population with a mean of 80 and a standard deviation of 20. The researcher expects a 12-point treatment effect and plans to use a two-tailed hypothesis test with .05.a. Compute the
21. 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 160 with a standard deviation of 20, and the scores form a normal-shaped distribution. The
20. Explain how the power of a hypothesis test is influenced by each of the following. Assume that all other factors are held constant.a. Increasing the alpha level from .01 to .05.b. Changing from a one-tailed test to a two-tailed test.
19. 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.
18. Researchers have often noted increases in violent crimes when it is very hot. In fact, Reifman, Larrick, and Fein (1991) noted that this relationship even extends to baseball. That is, there is a much greater chance of a batter being hit by a pitch when the temperature increases. Consider the
17. Montarello and Martins (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
16. A researcher is testing the hypothesis that consuming a sports drink during exercise improves endurance. A sample of n 50 male college students is obtained and each student is given a series of three endurance tasks and asked to consume 4 ounces of the drink during each break between tasks. The
15. A psychologist is investigating the hypothesis that children who grow up as the only child in the household develop different personality characteristics than those who grow up in larger families. A sample of n 30 only children is obtained and each child is given a standardized personality
14. There is some evidence indicating that people with visible tattoos are viewed more negatively than people without visible tattoos (Resenhoeft, Villa, & Wiseman, 2008). In a similar study, a researcher first obtained overall ratings of attractiveness for a woman with no tattoos shown in a color
13. There is some evidence that REM sleep, associated with dreaming, may also play a role in learning and memory processing. For example, Smith and Lapp (1991) found increased REM activity for college students during exam periods. Suppose that REM activity for a sample of n 16 students during the
12. A random sample is selected from a normal population with a mean of 40 and a standard deviation of 10.After a treatment is administered to the individuals in the sample, the sample mean is found to be M 42.a. How large a sample is necessary for this sample mean to be statistically
11. Miller (2008) examined the energy drink consumption of college undergraduates and found that males use energy drinks significantly more often than females.To further investigate this phenomenon, suppose a researcher selects a random sample of n 36 male undergraduates and a sample of n 25
10. A random sample of n 36 scores is selected from a normal population with a mean of 60. After a treatment is administered to the individuals in the sample, the sample mean is found to be M 52.a. If the population standard deviation is 18, is the sample mean sufficient to conclude that the
9. A random sample is selected from a normal population with a mean of 50 and a standard deviation of ?
8. State College is evaluating a new English composition course for freshmen. A random sample of n 25 freshmen is obtained and the students are placed in the course during their first semester. One year later, a writing sample is obtained for each student and the writing samples are graded using a
7. 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
6. A researcher is investigating the effectiveness of a new study-skills training program for elementary school children. A sample of n 25 third-grade children is selected to participate in the program and each child is given a standardized achievement test at the end of the year. For the regular
5. 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
4. If the alpha level is changed from .05 to .01,a. What happens to the boundaries for the critical region?b. What happens to the probability of a Type I error?
3. In words, define the alpha level and the critical region for a hypothesis test.
2. The value of the z-score in a hypothesis test is influenced by a variety of factors. Assuming that all other variables are held constant, explain how the value of z is influenced by each of the following:a. Increasing the difference between the sample mean and the original population mean.b.
1. In the z-score formula as it is used in a hypothesis test,a. Explain what is measured by M in the numerator.b. Explain what is measured by the standard error in the denominator.
22. Welsh, Davis, Burke, and Williams (2002)conducted a study to evaluate the effectiveness of a carbohydrate-electrolyte drink on sports performance and endurance. Experienced athletes were given either a carbohydrate-electrolyte drink or a placebo while they were tested on a series of
21. People are selected to serve on juries by randomly picking names from the list of registered voters. The average age for registered voters in the county is 44.3 years with a standard deviation of 12.4.A statistician computes the average age for a group of n 12 people currently serving on a
20. The average age for licensed drivers in the county is 40.3 years with a standard deviation of 13.2 years.a. A researcher obtained a random sample of n 16 parking tickets and computed an average age of M 38.9 years for the drivers. Compute the z-score for the sample mean and find the

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