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essentials of statistics

Essentials Of Statistics For The Behavioral Sciences 5th Edition Frederick J Gravetter, Larry B. Wallnau - Solutions

7. In the previous problem the treatments were significantly different primarily because the mean for sample III is noticeably different from the other two samples(M, = 3, M2 = 4, and M3 = 8). For the following data, we have taken the scores from Problem 6 and reduced the differences between
6. The following data represent the results from an independent-measures experiment comparing three treatment conditions. Use an analysis of variance with a = .05 to determine whether these data are sufficient to conclude that there are significant differences between the treatments.Treatment I II
5. Posttests are done after an analysis of variance.a. What is the purpose for posttests?b. Explain why you would not do posttests if the analysis is comparing only two treatments.c. Explain why you would not do posttests if the decision from the ANOVA was to fail to reject the null hypothesis.
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 equal to 1.00 when there is no treatment effect.
27. Problem 21 in Chapter 1 1 reported the results of a study examining the effects of oatmeal on cholesterol.Cholesterol levels were tested for a sample of n = 9 participants before and after a 30-day period in which they ate oatmeal every day. The change in cholesterol level was recorded for each
26. Although people with schizophrenia often show evidence of brain abnormalities, there is evidence to suggest that the disease is not associated with progressive brain damage (Heaton et al.. 2001). To examine this phenomenon, a researcher administered a test designed to measure brain damage to a
25. Problem 25 in Chapter 1 1 presented data showing that Olympic marksmen score significantly higher for shots fired between heartbeats than they do for shots fired during heartbeats. The scores for the two conditions are as follows:Participant During heartbeats Between heartbeats A 93 98 B 90 94
24. A researcher would like to estimate how much reaction time is affected by a common over-the-counter cold medication. The researcher measures reaction time for a sample of n = 36 participants. Each is then given a dose of the cold medication and reaction time is measured again. For this sample,
23. The counseling center at the college offers a short course in study skills for students who are having academic difficulty. To evaluate the effectiveness of this course, a sample of n = 25 students is selected, and each student's grade point average is recorded for the semester before the
22. It is well known that the ability to maintain focused attention declines over time. For this reason, people who must maintain a high level of attention (such as air traffic controllers) require frequent rest breaks. To determine how much decline occurs during the first 30 minutes of focused
21. Seasonal affective disorder (SAD) is a condition in which people become more depressed during the cold, dark days of winter. To evaluate this condition, a psychologist selects a random sample of n = 36 college students and gives each student a mood questionnaire in early September. The same
20. Problem 22 in Chapter 10 presented hypothetical data showing that elderly people who own dogs are significantly less likely to pay visits to their doctors than those who do not own pets. The data are presented again here.Doctor .isits diuring past year Control group Dog owners 12 8 10 5 6 9 9 4
19. In a classic study of problem solving, Katona (1940)demonstrated that people who are required to figure out a problem on their own will learn more than people who are given the solution. One group of participants is presented with a series of problems that they must figure out. A second group
18. Most adolescents experience a growth spurt when they are between 12 and 15 years old. This period of dramatic growth generally occurs around age 12 for girls and around age 14 for boys. A researcher studying physical development selected a random sample of n = 9 girls and a second sample of n =
17. An educational psychologist has observed that children seem to lose interest and enthusiasm for school as they progress through the elementary grades. To measure the extent of this phenomenon, the psychologist selects a sample of n = 15 second-grade children and a sample of n = 15
16. A developmental psychologist would like to deter-#• mine how much fine motor skill improves for children from age 3 to age 4. A random sample of n = 15 three-year-old children and a second sample of n = 15 four-year-olds are obtained. Each child is given a manual dexterity test that measures
15. The manufacturers of a popular medicinal herb claim that their product increases the speed and accuracy of mental processing. To test this claim, a researcher obtains a random sample of n = 20 adults. Half of the adults are given the herb for 30 days and the other half take a placebo. Then, all
14. 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
^€3. In an extension of the highway speed study in Problem 1 2, the researchers also wanted to determine how much people adjust speed in response to weather conditions.In addition to the sample of speeds obtained in Problem 12, they also recorded speeds for n =100 cars during daylight hours when
12. To determine how well people are complying with posted speed limits, the State Highway Patrol measured automobile speeds on a section of highway where the posted limit is 55 mph. For a sample of n = 100 cars during daylight hours and good weather conditions, they obtained an average speed of M
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. A psychologist has developed a new personality questionnaire for measuring self-esteem and would like to estimate the population parameters for the test scores.The questionnaire is administered to a sample of n = 25 participants. This sample has an average score of M = 43 with 55 = 2400.a.
9. Standardized measures seem to indicate that the average level of anxiety has increased gradually over the past 50 years (Twinge, 2000). In the 1950s, the average score on the Child Manifest Anxiety Scale was p= 15.1. A sample of a; = 16 of today's children produces a mean score of M = 23.3 with
8. A researcher is evaluating the effectiveness of a special summer reading program for grade-school children. Over the past several years, it has been determined that the average reading achievement score for children entering the second grade is p. = 81. It is reasonable to assume that the
7. A sample is obtained from an unknown population.The sample mean is M = 34 with a sample variance of s2 = 36.a. Assuming /; = 4. use the data to make a 90% confidence interval estimate of the unknown population mean.b. Assuming n = 16. use the data to make a 90%confidence interval estimate of
A sample of n = 16 scores is obtained from an unknown population. The sample has a mean of M — 46 with SS = 6000.a. Use the sample data to make an 80% confidence interval estimate of the unknown population mean.b. Make a 90% confidence interval estimate of /jl.c. Make a 95% confidence interval
A college administrator would like to determine how much time students spend on homework assignments during a typical week. A questionnaire is sent to a sample of n = 25 students and their responses indicate a mean of M = 7.4 hours per week with SS = 216.a. Use the data to make a point estimate of
4. For the following studies, state whether estimation or hypothesis testing is required. Also, is an independentor a repeated-measures t statistic appropriate?a. An educator wants to determine how much mean difference can be expected for the population in SAT scores following an intensive review
3. Explain how each of the following factors affects the width of a confidence interval:a. Increasing the sample sizeb. Increasing the sample variabilityc. Increasing the level of confidence (the percentage of confidence)
2. Explain why it would not be reasonable to use estimation after a hypothesis test where the decision was"fail to reject // ."
1. Explain how the purpose of estimation differs from the purpose of a hypothesis test.
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 month,
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
Does the treatment have a significant effect on the number of trips a person takes? Test with a = .05, two tails.
23. People with agoraphobia feel such a high level of anxiety about being in public places that they seldom leave their homes. Knowing this is a difficult disorder to treat, a researcher tries a long-term treatment. A sample of individuals report how often they have ventured out of the house in the
22. 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
Before After Participant treatment treatment A 7 3 B 6 14 C 9 11 D 5 15 The previous two problems both have the same sample mean difference of M = 4 points. However, the two samples have different variances and produce different outcomes for the hypothesis test.a. Compute Cohen's d and r to measure
21.Another researcher did the exact same study as described in Problem 18, and the data are presented here.a. Calculate the difference scores and MD. Compare the results to part (a) of the previous problem.b. Compute 55, sample variance, and estimated standard error. Compare theses results to those
18. A researcher studies the effect of cognitive psychotherapy on positive self-regard. The number of positive statements made about oneself is recorded for each participant during the first meeting. After 8 weekly therapy sessions, the measures are repeated for each person. For the following
*n. The following data are exactly the same as the scores shown in Problem 16 except that we have added'40 points to the first score in each treatment condition.The result is that each condition now contains one score that is very different from the others. In a research study, an odd score can
16. The following data are from a research study comparing two treatment conditions.a. Assume that the data are from an independentmeasures study using two separate samples. Use a two-tailed test with a = .05 to determine whether there is a significant difference between the two treatments.b. Now
15. The level of lymphocytes (white blood cells) in the blood is associated with susceptibility to disease—lower levels indicate greater susceptibility. In a study of the effects of stress on physical well-being, Schleifer and colleagues (1983) recorded the lymphocyte counts for men who were
14. A psychologist is testing a new drug for its painkilling effects. The pain threshold is measured for a sample of n = 9 participants by determining the intensity of an electric shock that causes discomfort. After the initial baseline is established, each participant receives the drug, and the
13. One of the benefits of aerobic exercise is the release of endorphins, which are natural chemicals in the brain that produce a feeling of general well-being. A sample of n — 16 participants is obtained, and each person's tolerance for pain is tested before and after a 50-minute session of
12. A recent report indicates 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 five
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 = 30 college students was given a problem-solving task at noon on one day and
9. A sample of n = 25 difference scores from a repeatedmeasures experiment has a mean difference of MD = 3.a. If the sample variance is s 2 = 25, is this sample sufficient to reject the null hypothesis for a two-tailed test with a = .05?b. If the sample variance is s 2 = 100, is this sample
8. A sample of difference scores (D values) from a repeated-measures experiment has a mean of MD = 5.00 with a variance of s 2 = 16.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 H{) if n = 16? Again, assume a two-tailed
7. A sample of n = 9 difference scores (D values) from a repeated-measures experiment has SS = 288.a. Would a sample mean difference of MD = 3 be large enough to reject the null hypothesis for a two-tailed test with a = .05?b. Would a sample mean difference of MD = 6 be large enough to reject the
6. Each of the following describes a sample of difference scores (D scores) from a repeated-measures study:Sample 1: n = 10, MD = +4.00, s = 10 Sample 2: n = 10,MD = +4.00, s = 2a. For each sample, use the mean and standard deviation to sketch the distribution (or simply describe the distribution).
5. Each of the following describes a sample of difference scores (D scores) from a repeated-measures study:Sample 1: n = 10, MD = +4.00, s = 10 Sample 2: n = 10, MD = + 12.00, s = 10a. For each sample, use the mean and standard deviation to sketch the distribution (or simply describe the
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. What is the primary advantage of a repeated-measures design over an independent-measures design?
1. For the following studies, indicate whether or not a repeated-measures t test is the appropriate analysis.Explain your answers.a. A teacher is evaluating the effectiveness of a new computer training program for third-grade mathematics.One third-grade class gets regular mathematics instruction
24. A researcher studied the effect of feedback on estimation of length. Two samples of participants are given practice estimating the lengths of lines drawn by the researcher on a chalkboard. One group receives no feedback about the accuracy of the estimates. The second group receives feedback
23. A researcher reports an independent-measures t statistic of t = 2.53 with df = 24.a. How many individuals participated in the researcher's experiment?b. Can the researcher conclude that there is a significant difference between the two samples with a = .05, two tails?c. Can the researcher
22.- 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
In a classic study of problem solving. Duncker (1945)asked participants to mount a candle on a wall in an upright position so that it would burn normally. One group was given a candle, a book of matches, and a box of tacks. A second group was given the same items, except the tacks and the box were
20. Stephen Schmidt ( 1994) conducted a series of experiments examining the effects of humor on memory. He collected a set of humorous sentences and then modified each one to produce a nonhumorous version of the same sentence. The humorous sentences were then presented to one group of participants
The following data represent results similar to those obtained by Harris and Schoen. Is there a significant difference between the two groups? Use a two-tailed test with a = .05.Number of errors recalling the Mexican story Participants from Mexico Participants from U.S.n = 20 M = 4.1 55 = 1 80//M
18. Harris and Schoen (1992) conducted a research study showing how cultural experience can influence memory.They presented participants with two different versions of stories. One version contained facts or elements that were consistent with a U.S. culture and the second version contained material
Friedman and Rosenman (1974) have classified people into two categories: Type A personalities and Type B personalities. Type As are hard-driving, competitive, and ambitious. Type Bs are more relaxed, easy-going people. One factor that differentiates these two groups is the chronically high level of
19.n = 10 M= 78 55 = 1420 nM SS 15 66 2030 17a. Are these data sufficient to indicate a significant difference between groups? Use a two-tailed test with a = .05.b. Use Cohen's d to measure the effect size for this study.
16. The animal learning course in the psychology department requires that each student train a rat to perform certain behaviors. The student's grade is partially determined by the rat's performance. The instructor for this course has noticed that some students are very comfortable working with the
15. The data in Problems 13 and 14 produce the same pooled variance (32) and the same sample mean difference (6 points). However, the two problems use different-sized samples and result in different values for t (t = 1.50 with df = 6 for Problem 13, and t = 3.00 with df = 30 for Problem 14).a. With
14. The researcher from the previous problem attempted to repeat the experiment using larger samples. The data for the second attempt are as follows:PROBLEMS Treatment 1 Treatment 2 n = 16 M = 58 55 = 420 n = 16 M = 52 SS = 540 271a. Calculate the variance for each of the two samples and then
13. A researcher using an independent-measures design to compare two treatments obtained the following data:Treatment 1 Treatment 2 nM SS 458 84 n = 4 M= 52 55 = 108a. Calculate the variance for each of the two samples and then compute the pooled variance. (You should find that the pooled variance
12. The local school district is comparing two methods for teaching mathematics to third-grade children. One class of n = 20 students is being taught by method A and another class of n = 20 is being taught by method B. At the end of the school year, all of the students take a standardized math
11. In a study examining the permanence of academic learning. Bahrick and Hall ( 1991 ) tested knowledge of high school algebra for two groups of participants 50 years after they graduated from high school. One group had received additional college math courses and the other group had no advanced
10. A researcher is evaluating the pain relief effectiveness of a new medication by comparing pain tolerance for a sample of n = 10 people who receive the medication with pain tolerance for a sample of n = 10 people who receive an inactive placebo. The scores for the placebo group produce a mean of
9. One sample has n = 6 scores with 55 = 500 and a second sample has n = 9 with 55 = 670.a. Calculate 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 10 points, is this enough to reject the null
8. One sample has n = 15 with 55 = 1660, and a second sample has n = 15 with 55 = 1700.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 difference is 8 points, is this enough to reject the null hypothesis
7. In the independent-measures hypothesis test, the difference between two sample means is used to test a hypothesis about the difference between two population means. The sample mean difference is not expected to be exactly equal to the population mean difference, and the estimated standard error
6. One sample has 55 = 32 and a second sample has 55 = 48.a. Calculate the variance for each sample and the pooled variance, assuming that n = 5 for both samples. You should find that the pooled variance is halfway between the two sample variances.b. Now assume that the first sample has n = 9
5. One sample has 55 = 63, and a second sample has 55 = 45.a. Assuming that n = 10 for both samples, find each of the sample variances, and calculate the pooled variance. You should find that the pooled variance is exactly halfway between the two sample variances.b. Now assume that n = 10 for the
Several factors influence the value obtained for the independent-measures / statistic. Some factors affect the numerator of the t statistic and others influence the size of the estimated standard error in the denominator.For each of the following, indicate whether the factor influences the
Describe the homogeneity of variance assumption, and explain why it is important for the independentmeasures hypothesis test.
2. What is measured by the estimated standard error that is used for the independent-measures t statistic?
1. Describe the general characteristics of a research study for which an independent-measures t would be the appropriate test statistic.
25. On a standardized spatial skills task, normative data reveal that people typically get u. = 15 correct solutions.A psychologist tests n - 1 individuals who have brain injuries in the right cerebral hemisphere. For the following data, determine whether or not righthemisphere damage results in
24. A psychologist would like to determine whether there is a relation between depression and aging. It is known that the general population averages p. = 40 on a standardized depression test. The psychologist obtains a sample of n = 36 individuals who are all over the age of 70. The average
23. A researcher would like to examine the effects of humidity on eating behavior. It is known that laboratory rats normally eat an average of u. = 2 1 grams of food each day. The researcher selects a random sample of n = 100 rats and places them in a controlled atmosphere room where the relative
22. A random sample of n — 16 scores has a mean of M = 48. Use this sample to test the null hypothesis PROBLEMS 245 that the population mean is |x= 45 for each of the following situations:a. Assume that the sample has a variance of s~ = 4 and use a two-tailed test with a = .05.b. Assume the
21. A random sample has a mean of M = 81 with s = 10.Use this sample to test the null hypothesis that u, = 85 for each of the following situations.a. Assume that the sample size is n = 25. and use a = .05 for the two-tailed hypothesis test.b. Assume that the sample size is n = 400. and use a = .05
20. A major corporation in the Northeast noted that last'year its employees averaged u, = 5.8 absences during the winter season (December to February). In an attempt to reduce absences, the company offered free flu shots to all employees this year. For a sample of n = 100 people who took the shots,
19. A researcher suspects that there is a direct relationship between hand-eye coordination and academic success in mathematics. A sample of n = 16 students who have demonstrated above average performance on a second-grade mathematics achievement test is selected. These students are given a
18.An example of the verticalhorizontal illusion When adults are given a set of items to hold in memory, they automatically rehearse the items to prevent forgetting. Young children, however, do not spontaneously use rehearsal. As a result, when given a small set of items to remember, 2-year-old
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
17.c. Comparing your answers from parts (a) and (b), how does sample variance influence measures of effect size?
16. A random sample of h = 16 scores is obtained from a population with a mean of p = 80. and a treatment is administered to the sample. After treatment, the sample mean is found to be M = 82.a. Assuming the sample variance is s 2 = 64, compute Cohen's d and r to measure the si/c of the treatment
15. A random sample is obtained from a population with a mean of p. = 100, and a treatment is administered to the sample. After treatment, the sample mean is found to be M = 104 and the sample variance is s 2 = 400.a. Assuming the sample contained n = \6 individuals, measure the size of the
14. The herbal supplement ginkgo biloba is advertised as producing an increase in physical strength and stamina.To test this claim, a sample of n = 36 adults is obtained and each person is instructed to take the regular daily dose of the herb for a period of 30 days.At the end of the 30-day period,
13. Numerous studies have shown that IQ scores have been increasing, generation by generation, for years(Flynn. 1984. 1999). The increase is called the Flynn Effect, and the data indicate that the increase appears to be about 7 points per decade. To demonstrate this phenomenon, a researcher obtains
Last fall, a sample of n = 25 freshmen was selected to participate in a new 4-hour training program designed to improve study skills. To evaluate the effectiveness of the new program, the sample was compared with the rest of the freshman class. All freshmen must take the same English Language
A random sample of n = 9 individuals is obtained from a population with a mean of u, = 80. A treatment is administered to each individual in the sample and, after treatment, each individual is measured. The average score for the treated sample is M = 86 with SS = 288.a. How much difference is there

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