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essential statistics
Understanding Statistics In The Behavioral Sciences 10th Edition Robert R Pagano - Solutions
3. The sets of numbers given below in each table cell were obtained from the table of random numbers, Table J, in Appendix D. There are 6 table cells, one at the intersection of each combination of the levels of Factor A and Factor B, e.g., the cell located at the intersection of Factor ALevel 1
2. A researcher is interested in whether the effects of marijuana vary with prior usage of the drug.An experiment is conducted in which 12 moderate users, 12 high users, and 12 nonusers (no prior use)are randomly sampled from the college population.Within each usage level, half of the subjects are
1. Use SPSS to analyze the data of the experiment presented in Chapter 16, Problem 13, p. 474, in the textbook.Using SPSS, what do you conclude regarding the main effect for Previous Use, the main effect for Drowson Concentration, and the interaction effect between Previous Use and Drowson
13. A sleep researcher conducts an experiment to determine whether a hypnotic drug called Drowson, which is advertised as a remedy for insomnia, actually does promote sleep. In addition, the researcher is interested in whether a tolerance to the drug develops with chronic use. The design of the
12. Assume you have just accepted a position as chief scientist for a leading agricultural company. Your fi rst assignment is to make a recommendation concerning the best type of grass to grow in the Pacifi c Northwest and the best fertilizer for it. To provide the database for your recommendation,
11. It is theorized that repetition aids recall and that the learning of new material can interfere with the recall of previously learned material. A professor interested in human learning and memory conducts a 2 3 factorial experiment to investigate the effects of these two variables on recall.
10. What are the assumptions underlying the two-way ANOVA, independent groups design?
9. If the B variable’s effect increased, what would happen to the differences among the column means?What would happen to MScolumns? Explain. Assuming there is no interaction, what would happen to the differences among the row means?
8. If the A variable’s effect increased, what do you expect would happen to the differences among the row means? What would happen to MSrows? Explain.Assuming there is no interaction, what would happen to the differences among the column means?
7. The four variance estimates (MSrows, MScolumns, MSinteraction, and MSwithin-cells) are also referred to as mean squares. Can you explain why?
6. Why is the within-cells variance estimate used as the yardstick against which the other variance estimates are compared?
5. In the two-way ANOVA, the total sum of squares is partitioned into four components. What are the four components?
4. In the two-way ANOVA, what is a main effect?What is an interaction? Is it possible to have a main effect without an interaction? An interaction without a main effect? Explain.
3. What is a factorial experiment?
2. What are the advantages of the two-way ANOVA compared with the one-way ANOVA?
1. Defi ne or identify each of the terms in the Important New Terms section.
11. It is theorized that repetition aids recall and that the learning of new material can interfere with the recall of previously learned material. A professor interested in human learning and memory conducts a 2 3 factorial experiment to investigate the effects of these two variables on recall.
10. What are the assumptions underlying the two-way ANOVA, independent groups design?
9. If the B variable’s effect increased, what would happen to the differences among the column means?What would happen to MScolumns? Explain. Assuming there is no interaction, what would happen to the differences among the row means?
8. If the A variable’s effect increased, what do you expect would happen to the differences among the row means? What would happen to MSrows? Explain.Assuming there is no interaction, what would happen to the differences among the column means?
7. The four variance estimates (MSrows, MScolumns, MSinteraction, and MSwithin-cells) are also referred to as mean squares. Can you explain why?
6. Why is the within-cells variance estimate used as the yardstick against which the other variance estimates are compared?
5. In the two-way ANOVA, the total sum of squares is partitioned into four components. What are the four components?
4. In the two-way ANOVA, what is a main effect?What is an interaction? Is it possible to have a main effect without an interaction? An interaction without a main effect? Explain.
3. What is a factorial experiment?
2. What are the advantages of the two-way ANOVA compared with the one-way ANOVA?
1. Defi ne or identify each of the terms in the Important New Terms section.
1. Much Ado About Almost Nothinga. The golf company reports mean data, but no signifi cance analysis. Do you think it important to do a signifi cance test on these data? Explain why or why not. In general, do you believe advertisements should include sample data and signifi cance testing?Explain.b.
27. An instructor is teaching three sections of Introductory Psychology, each section covering the same material. She has made up a different fi nal exam for each section, but she suspects that one of the versions is more diffi cult than the other two. She decides to conduct an experiment to
26. A university researcher knowledgeable in Chinese medicine conducted a study to determine whether acupuncture can help reduce cocaine addiction. In this experiment, 18 cocaine addicts were randomly assigned to one of three groups of 6 addicts per group. One group received 10 weeks of acupuncture
25. A clinical psychologist is interested in evaluating the effectiveness of the following three techniques for treating mild depression: cognitive restructuring, assertiveness training, and an exercise/nutrition program. Forty undergraduate students suffering from mild depression are randomly
24. In Chapter 14, an illustrative experiment involved investigating the effect of hormone X on sexual behavior.Although we presented only two concentrations in that problem, let’s assume the experiment actually involved four different concentrations of the hormone. The full data are shown here,
23. Assume you are employed by a consumer-products rating service and your assignment is to assess car batteries. For this part of your investigation, you want to determine whether there is a difference in useful life among the top-of-the-line car batteries produced by three manufacturers (A, B,
22. To test whether memory changes with age, a researcher conducts an experiment in which there are four groups of six subjects each. The groups differ according to the age of subjects. In group 1, the subjects are each 30 years old; group 2, 40 years old; group 3, 50 years old; and group 4, 60
21. A sleep researcher conducts an experiment to determine whether sleep loss affects the ability to maintain sustained attention. Fifteen individuals are randomly divided into the following three groups of fi ve subjects each: group 1, which gets the normal amount of sleep (7–8 hours); group 2,
20. Assume you are a nutritionist who has been asked to determine whether there is a difference in sugar content among the three leading brands of breakfast cereal (brands A, B, and C). To assess the amount of sugar in the cereals, you randomly sample six packages of each brand and chemically
19. The accompanying table is a one-way, independent groups ANOVA summary table with part of the material missing.Source SS df MS Fobt Between groups 1253.68 3 Within groups Total 5016.40 39a. Fill in the missing values.b. How many groups are there in the experiment?c. Assuming an equal number of
18. What three factors does the Scheffé test use to make it more diffi cult to reject H0?
17. In doing planned comparisons, it is better to use MSwithin from the ANOVA rather than the weighted variance estimate from the two groups being compared.Is this statement correct? Why?
16. What are the Q or Studentized range distributions?How do they avoid the problem of infl ated Type I errors that result from doing multiple comparisons with the t distribution?
15. How do planned comparisons, post hoc comparisons using the Tukey HSD test, and post hoc comparisons using the Scheffé test differ with regard toa. Power? Explain.b. The probability of making a Type I error? Explain.
14. Explain why we must correct for doing multiple comparisons when doing post hoc comparisons.
13. For each of the variables identifi ed in Question 12, state how power is affected if the variable is increased.Use the equation for Fobt on p. 421 to justify your answer.
12. What are the variables that affect the power of the one-way analysis of variance technique?
11. In Chapter 14, Practice Problem 14.2, an independent groups experiment was conducted to investigate whether lesions of the thalamus decrease pain perception. 0.051 tail was used in the analysis. The data are again presented here.Scores are pain threshold (milliamps) to electric shock.
10. Find Fcrit for the following situations:a. df(numerator) 2, df(denominator) 16, 0.05b. df(numerator) 3, df(denominator) 36, 0.05c. df(numerator) 3, df(denominator) 36, 0.01 What happens to Fcrit as the degrees of freedom increase and alpha is held constant? What happens
9. The analysis of variance is a nondirectional technique, yet it uses a one-tailed evaluation. Is this statement correct? Explain.
8. What are the assumptions underlying the analysis of variance?
7. In the analysis of variance, if Fobt is less than 1, we don’t even need to compare it with Fcrit. It is obvious that the independent variable has not had a signifi cant effect. Why is this so?
6. What are the steps in forming an F ratio in using the one-way analysis of variance technique?
5. The analysis of variance technique analyzes the variability of the data. Yet a signifi cant F value indicates that there is at least one signifi cant mean difference between the conditions. How does analyzing the variability of the data allow conclusions about the means of the conditions?
4. When doing an experiment with many groups, what is the problem with doing t tests between all possible groups without any correction? Why does use of the analysis of variance avoid that problem?
3. What advantages are there in doing experiments with more than two groups or conditions?
2. What are the characteristics of the F distribution?
1. Identify or defi ne the terms in the Important New Terms section.
28. A physics instructor believes that natural lighting in classrooms improves student learning. He conducts an experiment in which he teaches the same physics unit to two groups of seven randomly assigned students in each group. Everything is similar for the groups, except that one of the groups
27. Since the results of the experiment in Problem 26 were very close to being signifi cant, the researcher decides to replicate that experiment, only this time increasing the power by increasing N. This study included 10 men and 10 women. The following results were obtained.Men Women 74 87 87 90
26. Noting that women seem more interested in emotions than men, a researcher in the fi eld of women’s studies wondered if women recall emotional events better than men. She decides to gather some data on the matter. An experiment is conducted in which eight randomly selected men and women are
25. Developmental psychologists at a prominent California university conducted a longitudinal study investigating the effect of high levels of curiosity in early childhood on intelligence. The local population of 3-year-olds was screened via a test battery assessing curiosity. Twelve of the
24. Researchers at a leading university were interested in the effect of sleep on memory consolidation.Twenty-four student volunteers from an introductory psychology course were randomly assigned to either a “Sleep” or “No-Sleep” group, such that there were 12 students in each group. On the
23. An educator wants to determine whether early exposure to school will affect IQ. He enlists the aid of the parents of 12 pairs of preschool-age identical twins who agree to let their twins participate in this experiment.One member of each twin pair is enrolled in preschool for 2 years while the
22. On the basis of her experience with clients, a clinical psychologist thinks that depression may affect sleep. She decides to test this idea. The sleep of nine depressed patients and eight normal controls is monitored for three successive nights. The average number of hours slept by each subject
21. The director of human resources at a large company is considering hiring part-time employees to fi ll jobs previously staffed with full-time workers. However, he wonders if doing so will affect productivity. Therefore, he conducts an experiment to evaluate the idea before implementing it
20. Since the control group in Problem 19 also showed signifi cant reductions in headaches, the interpretation of the results in Problem 18 is in doubt. Did relaxation training contribute to the headache decrease, or was the decrease due solely to other factors, such as attention? To answer this
19. There is an interpretation diffi culty with Pro blem 18. It is clear that the headaches decreased signifi cantly. However, it is possible that the decrease was not due to the biofeedback training but rather to some other aspect of the situation, such as the attention shown to the subjects. What
18. Since muscle tension in the head region has been associated with tension headaches, you reason that if the muscle tension could be reduced, perhaps the headaches would decrease or go away altogether. You design an experiment in which nine subjects with tension headaches participate.The subjects
17. The manager of the cosmetics section of a large department store wants to determine whether newspaper advertising really does affect sales. For her experiment, she randomly selects 15 items currently in stock and proceeds to establish a baseline.The 15 items are priced at their usual
16. A nurse was hired by a governmental ecology agency to investigate the impact of a lead smelter on the level of lead in the blood of children living near the smelter. Ten children were chosen at random from those living near the smelter. A comparison group of seven children was randomly selected
15. On the basis of previous research and sound theoretical considerations, a cognitive psychologist believes that memory for pictures is superior to memory for words. To test this hypothesis, the psychologist performs an experiment in which students from an introductory psychology class are used
14. You are interested in determining whether an experimental birth control pill has the side effect of changing blood pressure. You randomly sample ten women from the city in which you live. You give fi ve of them a placebo for a month and then measure their diastolic blood pressure. Then you
13. If the effect of the independent variable is signifi cant, does that necessarily mean the effect is a large one?Explain.For each of the following problems, unless otherwise told, assume normality in the population.
12. Is the size of effect of the independent variable important? Explain.
11. Having just made what you believe to be a Type II error, using an independent groups design and a t test analysis, name all the things you might do in the next experiment to reduce the probability of a Type II error.
10. What are the assumptions underlying the t test for independent groups?
9. What are the advantages and disadvantages of using a correlated groups design as compared with using an independent groups design?
8. It is said that the variance of the sample data has an important bearing on the power of the t test. Is this statement true? Explain.
7. What is estimated in the t test for independent groups? How is the estimate obtained?
6. Why is the z test for independent groups never used?
5. What are the characteristics of the sampling distribution of the difference between sample means?
4. What is the main advantage of using the t test for correlated groups over using the sign test to analyze data from a correlated groups experiment?
3. The t test for correlated groups can be thought of as a special case of the t test for single samples, discussed in the previous chapter. Explain.
2. Discuss the advantages of the two-condition experiment compared with the advantages of the single sample experiment.
1. Identify or defi ne the terms in the Important New Terms section.
2. A physician employed by a large corporation believes that due to an increase in sedentary life in the past decade, middle-age men have become fatter. In 1995, the corporation measures the percentage of fat in its employees. For the middle-age men, the scores were normally distributed, with a
1. Use SPSS to do Practice Problem 13.1, p. 335 of the textbook. Compare your answer with that given in the textbook. Name the variable Height.
26. A developmental psychologist is interested in whether tense parents tend to have tense children.A study is done involving one parent for each of 15 families and the oldest child in each family, measuring tension in each pair. Pearson r 0.582.Using 0.052 tail, is the relationship signifi
25. In Chapter 6, Problem 15, a sociology professor gave two exams to 8 students. The results are again shown here.a. Calculate the value of Pearson r for the two exams.b. Using 0.052 tail, determine whether the correlation is signifi cant. If not, does this mean that 0? Explain.c. Assume you
24. In Chapter 6, Problem 18, an educator evaluated the reliability of a test for mechanical aptitude that she had constructed. Two administrations of the test, spaced 1 month apart, were given to 10 students. The data are again shown here.a. Calculate the value of Pearson r for the two
23. In Chapter 6, Problem 17, data were presented from a study conducted to investigate the relationship between cigarette smoking and illness. The number of cigarettes smoked daily and the number of days absent from work in the last year due to illness was determined for 12 individuals employed at
22. You wanted to estimate the mean number of vehicles crossing a busy bridge in your neighborhood each morning during rush hour for the past year. To accomplish this, you stationed yourself and a few assistants at one end of the bridge on 18 randomly selected mornings during the year and counted
21. A local business school claims that its graduating seniors get higher-paying jobs than the national average for business school graduates. Last year’s fi gures for salaries paid to all business school graduates on their fi rst job showed a mean of $10.20 per hour. A random sample of 10
20. A physician employed by a large corporation believes that due to an increase in sedentary life in the past decade, middle-age men have become fatter. In 1995, the corporation measured the percentage of fat in their employees. For the middle-age men, the scores were normally distributed, with a
19. A cognitive psychologist believes that a particular drug improves short-term memory. The drug is safe, with no side effects. An experiment is conducted in which 8 randomly selected subjects are given the drug and then given a short time to memorize a list of 10 words. The subjects are then
18. A professor in the women’s studies program believes that the amount of smoking by women has increased in recent years. A complete census taken 2 years ago of women living in a neighboring city showed that the mean number of cigarettes smoked daily by the women was 5.4 with a standard
17. A college counselor wants to determine the average amount of time fi rst-year students spend studying.He randomly samples 61 students from the freshman class and asks them how many hours a week they study. The mean of the resulting scores is 20 hours, and the standard deviation is 6.5 hours.a.
16. As the principal of a private high school, you are interested in fi nding out how the training in mathematics at your school compares with that of the public schools in your area. For the last 5 years, the public schools have given all graduating seniors a mathematics profi ciency test. The
15. In Problem 21 of Chapter 12, a student conducted an experiment on 25 schizophrenic patients to test the effect of a new technique on the amount of time schizophrenics need to stay institutionalized. The results showed that under the new treatment, the 25 schizophrenic patients stayed a mean
14. Using each of the following random samples, determine the 95% and 99% confi dence intervals for the population mean:a. Xobt 25, s 6, N 15b. Xobt 120, s 8, N 30c. Xobt 30.6, s 5.5, N 24d. Redo part a with N 30. What happens to the confi dence interval as N increases? other
13. Is it reasonable to consider a sample with N 22, Xobt 42, and s 9 to be a random sample from a normal population with 38? Use 0.051 tail in making your decision. Assume Xobt is in the right direction. other
12. A sample set of 29 scores has a mean of 76 and a standard deviation of 7. Can we accept the hypothesis that the sample is a random sample from a population with a mean greater than 72? Use 0.011 tail in making your decision. other
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