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Introduction To The Practice Of Statistics 6th Edition David S. Moore, George P. McCabe, Bruce A. Craig - Solutions

14.1 Odds of drawing a heart. If you deal one card from a standard deck, the probability that the card is a heart is 0.25. Find the odds of drawing a heart.
13.50 Search the Internet. Search the Internet or your library to find a study that is interesting to you and uses a two-way ANOVA to analyze the data.First describe the question or questions of interest and then give the details of how ANOVA was used to provide answers. Be sure to include how the
13.49 Change-of-majors study: SATV. Refer to the data given for the change-of-majors study in the data set MAJORS described in the Data Appendix.Analyze the data for SATV, the SAT Verbal score.Your analysis should include a table of sample sizes, means, and standard deviations; Normal quantile
13.48 Change-of-majors study: GPA. Refer to the data given for the change-of-majors study in the data set MAJORS described in the Data Appendix. Analyze the data for GPA, the college grade point average.Your analysis should include a table of sample sizes, means, and standard deviations; Normal
13.47 Change-of-majors study: HSE. Refer to the data given for the change-of-majors study in the data set MAJORS described in the Data Appendix. Analyze the data for HSE, the high school English grades.Your analysis should include a table of sample sizes, means, and standard deviations; Normal
13.46 Change-of-majors study: HSS. Refer to the data given for the change-of-majors study in the data set MAJORS described in the Data Appendix. Analyze the data for HSS, the high school science grades.Your analysis should include a table of sample sizes, means, and standard deviations; Normal
13.45 Are insects more attracted to male plants?Some scientists wanted to determine if there are gender-related differences in the level of herbivory in the jack-in-the-pulpit, a spring-blooming perennial plant common in deciduous forests.A study was conducted in southern Maryland at forests
13.44 More on the analysis using multiple oneway ANOVAs. Perform the tasks described in Exercise 13.40 for the two response variables in the PLANTS2 data set.
13.43 Analysis using multiple one-way ANOVAs.Perform the tasks described in Exercise 13.39 for the two response variables in the PLANTS2 data set.
13.42 Examination of the residuals. Perform the tasks described in Exercise 13.38 for the two response variables in the PLANTS2 data set.
13.41 Another comparison of plant species under low water conditions. Refer to Exercise 13.37.Additional data collected by the same researchers according to a similar design are given in the PLANTS2 data set in the Data Appendix. Here, there are two response variables. They are fresh biomass and
13.40 More on the analysis using multiple one-way ANOVAs. Refer to Exercise 13.37. Run a separate one-way analysis of variance for each species and summarize the results. Since the amount of water is a quantitative factor, we can also analyze these data using regression. Run simple linear
13.39 Analysis using multiple one-way ANOVAs.Refer to Exercise 13.37. Run a separate one-way analysis of variance for each water level. If there is evidence that the species are not all the same, use a multiple-comparisons procedure to determine which pairs of species are significantly different.In
13.38 Examination of the residuals. Refer to the previous exercise. Examine the residuals. Are there any unusual patterns or outliers? If you think that there are one or more points that are somewhat extreme, rerun the two-way analysis without these observations. Does this change the results in any
13.37 A comparison of plant species under low water conditions. The PLANTS1 data set in the Data Appendix gives the percent of nitrogen in four different species of plants grown in a laboratory. The species are Leucaena leucocephala, Acacia saligna, Prosopis juliflora, and Eucalyptus citriodora.
13.36 A radon exposure study. Scientists believe that exposure to the radioactive gas radon is associated with some types of cancers in the respiratory system. Radon from natural sources is present in many homes in the United States. A group of researchers decided to study the problem in dogs
22.36 (handedness), 37.44 (gender), and 2.10(interaction). The following marginal mean ages at death (in years) were reported: 77.39 (females), 71.32 (males), 75.00 (right-handed), and 66.03(left-handed).(a) For each of the F statistics given above find the degrees of freedom and an approximate
13.35 Do left-handed people live shorter lives than right-handed people? A study of this question examined a sample of 949 death records and contacted next of kin to determine handedness.20 Note that there are many possible definitions of “left-handed.” The researchers examined the effects of
13.34 Analysis using a one-way ANOVA. Refer to the previous exercise. Rerun the analysis as a one-way ANOVA with 4 × 4 = 16 treatments.Summarize the results of this analysis. Use a multiple-comparisons procedure to describe combinations of number of promotions and percent discounts that are
13.33 A price promotion study. How does the frequency that a supermarket product is promoted at a discount affect the price that customers expect to pay for the product? Does the percent reduction also affect this expectation? These questions were examined by researchers in a study conducted on
13.32 Examination of a drilling process, continued.Refer to the previous exercise. Multiply each measurement by 0.04 to convert from millimeters to inches. Redo the plots and rerun the ANOVA using the transformed measurements. Summarize what parts of the analysis have changed and what parts have
13.31 Examination of a drilling process. One step in the manufacture of large engines requires that holes of very precise dimensions be drilled. The tools that do the drilling are regularly examined and are adjusted to ensure that the holes meet the required specifications. Part of the examination
13.30 Analysis using a one-way ANOVA. Refer to Exercise 13.28. Rerun the analysis as a oneway ANOVA with 9 groups and 4 observations per group. Report the results of the F test.Examine differences in means using a multiplecomparisons procedure. Summarize your results and compare them with those you
13.29 Interpreting the results. Refer to the previous exercise. Although there is a statistically significant interaction, do you think that these data support the conclusion that foods cooked in iron pots contain more iron than foods cooked in aluminum or clay pots? Discuss.
13.28 CH ALLENGE Does the type of cooking pot affect iron content? Iron-deficiency anemia is the most common form of malnutrition in developing countries, affecting about 50% of children and women and 25% of men. Iron pots for cooking foods had traditionally been used in many of these countries,
13.27 Analysis using multiple one-way ANOVAs. Refer to the previous exercise. Analyze the data for each time period separately using a one-way ANOVA.Use a multiple-comparisons procedure where needed. Summarize the results.
13.26 CHALLENGE A comparison of different types of scaffold material, continued. Refer to the previous exercise. Here are the data that were collected at 2 weeks, 4 weeks, and 8 weeks:Gpi (%)Material 2 weeks 4 weeks 8 weeks ECM1 70 75 65 55 70 70 60 65 65 ECM2 60 65 70 60 65 65 60 70 60 ECM3 80 60
13.25 A comparison of different types of scaffold material. One way to repair serious wounds is to insert some material as a scaffold for the body’s repair cells to use as a template for new tissue. Scaffolds made from extracellular material(ECM) are particularly promising for this
13.24 Designing a study. The students studied in the previous two exercises were enrolled at a large midwestern university more than two decades ago. Discuss how you would conduct a similar study at a college or university of your choice today. Include a description of all variables that you would
13.23 More on changing your major. The mean SAT Mathematics scores for the students in the previous exercise are summarized in the following table:Major Gender CS EO O Males 628 618 589 Females 582 631 543 Summarize the results of this study using appropriate plots and calculations to describe the
13.22 Changing your major. A study of undergraduate computer science students examined changes in major after the first year.15 The study examined the fates of 256 students who enrolled as firstyear computer science students in the same fall semester. The students were classified according to
13.21 The effect of chromium on insulin metabolism.The amount of chromium in the diet has an effect on the way the body processes insulin. In an experiment designed to study this phenomenon, four diets were fed to male rats. There were two factors. Chromium had two levels: low (L) and normal (N).
13.20 Assessing the Normality assumption. Refer to Exercises 13.15 and 13.16. The ratings for this study were each measured on a seven-point scale, anchored by bad–good, low quality–high quality, unappealing–appealing, and unpleasant–pleasant.The results presented were averaged over three
13.19 Interpreting the results. Refer to Exercises 13.15 and 13.16. The subjects were 94 adult staff members at aWest Coast university. They watched a half-hour local news show from a different state that included the ads. The selected ads were judged to be “good” by some experts and had been
13.18 More on estimating the within-group variance.Refer to Exercise 13.16. Here are the standard deviations for total thoughts:Repetition Familiarity 1 2 3 Familiar 1.63 1.42 1.52 Unfamiliar 1.64 2.16 1.59 Find the pooled estimate of the standard deviation for these data. Use the rule for
13.17 Estimating the within-group variance. Refer to the previous exercise. Here are the standard deviations for attitude toward brand:Repetition Familiarity 1 2 3 Familiar 1.16 1.46 1.16 Unfamiliar 1.39 1.22 1.42 Find the pooled estimate of the standard deviation for these data. Use the rule for
13.16 CHALLENGE More on brand familiarity and repetitive advertising. Refer to the previous exercise.In settings such as this, researchers collect data for several response variables. For this study, they also constructed variables that were called attitude toward the brand, total thoughts, support
13.15 Brand familiarity and repetitive advertising.Does repetition of an advertising message increase its effectiveness? One theory suggests that there are two phases in the process. In the first phase, called “wearin,” negative or unfamiliar views are transformed into positive views. In the
13.14 What can you conclude? A study reported the following results for data analyzed using the methods that we studied in this chapter:Effect F P-value A 7.50 0.006 B 18.66 0.001 AB 6.14 0.011(a) What can you conclude from the information given?(b) What additional information would you need to
13.13 What can you conclude? Analysis of data for a 3 × 2 ANOVA with 5 observations per cell gave the F statistics in the following table:Effect F A 1.53 B 3.87 AB 2.94 What can you conclude from the information given?
13.12 CHALL ENGE The effects of peer pressure on mathematics achievement. Researchers were interested in comparing the relationship between high achievement in mathematics and peer pressure across several countries.12 They hypothesized that in countries where high achievement is not valued highly,
13.11 The acceptability of lying. Lying is a common component of all human relationships. To investigate the acceptability of lying under various scenarios, researchers questioned 229 high school students from a West Coast public high school and 261 college students from a state university in the
13.10 CH ALLENGE More on the assessment of an intervention program. Refer to the previous exercise. Table 13.1 gives the percents of women who responded that they performed each of the 15 safety behaviors studied.(a) Summarize these data graphically. Do you think that your graphical display is more
13.9 Evaluation of an intervention program. The National Crime Victimization Survey estimates that there were over 400,000 violent crimes committed against women by their intimate partner that resulted in physical injury. An intervention study designed to increase safety behaviors of abused women
13.8 Hypotension and endurance exercise. In sedentary individuals, low blood pressure(hypotension) often occurs after a single bout of aerobic exercise and lasts nearly two hours.This can cause dizziness, light-headedness, and possibly fainting upon standing. It is thought that endurance exercise
13.7 The effects of proximity and visibility on food intake. A recent study investigated the influence that proximity and visibility of food have on food intake.8 A total of 40 secretaries from the University of Illinois participated in the study. A candy dish full of individually wrapped
13.6 Determining the degrees of freedom. For each part in Exercise 13.5, outline the ANOVA table, giving the sources of variation and the degrees of freedom.
13.5 Identifying the factors of a two-way ANOVA model. For each of the following situations, identify both factors and the response variable.Also, state the number of levels for each factor (I and J) and the total number of observations (N).(a) A child psychologist is interested in studying how a
13.4 Determining the critical value of F. For each of the following situations, state how large the F statistic needs to be for rejection of the null hypothesis at the 5% level. Sketch each distribution and indicate the region where you would reject.(a) The main effect for the first factor in a 3
13.3 Describing a two-way ANOVA model. A 2 × 3 ANOVA was run with 6 observations per cell.(a) Give the degrees of freedom for the F statistic that is used to test for interaction in this analysis and the entries from Table E that correspond to this distribution.(b) Sketch a picture of this
13.2 What’s wrong? For each of the following, explain what is wrong and why.(a) You can perform a two-way ANOVA only when the sample sizes are the same in all cells.(b) The estimate s2p is obtained by pooling the marginal sample variances.(c) When interaction is present, the main effects are
13.1 What’s wrong? For each of the following, explain what is wrong and why.(a) A two-way ANOVA is used when there are two outcome variables.(b) In a 3 × 3 ANOVA each level of Factor A appears with only two levels of Factor B.(c) The FIT part of the model in a two-way ANOVA represents the
12.69 CHALLENGE Planning another restaurant ambience study. Exercise 12.24 (page 672) gave data for a study that examined the effect of background music on total food spending at a high-end restaurant. You are planning a similar study but intend to look at total food spending at a more casual
12.68 CHALLENGE Planning another isoflavone study.Exercise 12.39 (page 676) gave data for a bone health study that examined the effect of isoflavones on rat bone mineral density. In this study there were three groups. Controls received a placebo, and the other two groups received either a low or a
12.67 Planning another emotions study. Scores on an emotional scale were compared for five different cultures in Exercise 12.27 (page 674).Suppose that you are planning a new study using the same outcome variable. Your study will use European American, Asian American, and Hispanic American students
12.66 A power calculation exercise (optional). In Example 12.27 (page 674) the power calculation indicated that there was a fairly small chance of detecting the alternative given. Redo the calculations for the alternative μ1 = 40, μ2 = 47, and μ3 = 43. Do you think that the choice of 10 students
12.65 CHALL ENGE Search the Internet. Search the Internet or your library to find a study that is interesting to you and that used one-way ANOVA to analyze the data. First describe the question or questions of interest and then give the details of how ANOVA was used to provide answers. Be sure to
12.64 Overall standard deviation versus the pooled standard deviation. The last line of the summary table given in Exercise 12.26 (page 673) gives the mean and the standard deviation for all of the data combined. Compare this standard deviation with the pooled standard deviation that you would use
12.63 CH ALLENGE More on the price promotion study.Refer to the price promotion study that we examined in Exercise 12.40 (page 677). The explanatory variable in this study is the number of price promotions in a 10-week period, with possible values of 1, 3, 5, and 7. When using analysis of variance,
12.62 CH ALLENGE More on the reading comprehension study. In the study described in the previous exercise, Basal is the traditional method of teaching, while DRTA and Strategies are two innovative methods based on similar theoretical considerations. The READING data set includes three response
12.61 CH ALLENGE Comparing three levels of reading comprehension instruction. A study of reading comprehension in children compared three methods of instruction.20 The three methods of instruction are called Basal, DRTA, and Strategies. As is common in such studies, several pretest variables were
12.60 CHALLENGE Linear transformation of the response variable. Refer to the previous exercise.Can you suggest a general conclusion regarding what happens to the test statistic, degrees of freedom, P-value, and conclusion when you perform analysis of variance on data that have been transformed by
12.59 More on changing the response variable of the storage time study. Refer to the previous exercise and Exercise 12.31 (page 675). The flour used to make the loaves contained 5 mg of vitamin A per 100 g of flour and 100 mg of vitamin E per 100 g of flour. Summarize the effects of transforming
12.58 CHALLENGE Changing the response variable of the storage time study. Refer to Exercise 12.29(page 675), where we studied the effects of storage on the vitamin C content of bread. In this experiment 64 mg of vitamin C per 100 g of flour was added to the flour that was used to make each loaf.(a)
12.57 Testing several contrasts from the dandruff study. Refer to Exercise 12.54. There are several natural contrasts in this experiment that describe comparisons of interest to the experimenters.They are (1) Placebo versus the average of the three treatments; (2) Keto versus the average of the two
12.56 Comparing each pair of dandruff treatments.Refer to Exercise 12.54. Use the Bonferroni or another multiple-comparisons procedure that your software provides to compare the individual group means in the dandruff study. Write a short summary of your conclusions.
12.55 The dandruff study, continued. Refer to the previous exercise.(a) Plot the residuals versus case number (the first variable in the data set). Describe the plot. Is there any pattern that would cause you to question the assumption that the data are independent?(b) Examine the standard
12.54 A dandruff study. Analysis of variance methods are often used in clinical trials where the goal is to assess the effectiveness of one or more treatments for a particular medical condition. One such study compared three treatments for dandruff and a placebo. The treatments were 1% pyrithione
12.53 Two contrasts of interest for the stimulant study. Refer to Exercise 12.25 (page 673).There are two comparisons of interest to the experimenter. They are (1) Placebo versus the average of the 2 low-dose treatments; and (2) the difference between High A and Low A versus the difference between
12.52 A comparison of different types of scaffold material, continued. Refer to the previous exercise.(a) Examine the residuals. Is the Normality assumption reasonable for these data?(b) Use the Bonferroni or another multiplecomparisons procedure to determine which pairs of means differ
12.51 A comparison of different types of scaffold material. One way to repair serious wounds is to insert some material as a scaffold for the body’s repair cells to use as a template for new tissue. Scaffolds made from extracellular material(ECM) are particularly promising for this
12.50 The cooking pot study, continued. Refer to the previous exercise.(a) Examine the residuals. Is the Normality assumption reasonable for these data?(b) Use the Bonferroni or another multiplecomparisons procedure to determine which pairs of means differ significantly. Summarize your results in a
12.49 Does the type of cooking pot affect iron content? Iron-deficiency anemia is the most common form of malnutrition in developing countries, affecting about 50% of children and women and 25% of men. Iron pots for cooking foods had traditionally been used in many of these countries, but they have
12.48 Exercise and healthy bones, continued. Refer to the previous exercise.(a) Examine the residuals. Is the Normality assumption reasonable for these data?(b) Use the Bonferroni or another multiplecomparisons procedure to determine which pairs of means differ significantly. Summarize your results
12.47 Exercise and healthy bones. Many studies have suggested that there is a link between exercise and healthy bones. Exercise stresses the bones and this causes them to get stronger. One study examined the effect of jumping on the bone density of growing rats.17 There were three treatments: a
12.46 Breast-feeding study, continued. Refer to the previous exercise.(a) Examine the residuals. Is the Normality assumption reasonable for these data?(b) Explain why you do not need to use a multiplecomparisons procedure for these data.
12.45 How long should an infant be breast-fed?Recommendations regarding how long infants in developing countries should be breast-fed are controversial. If the nutritional quality of the breast milk is inadequate because the mothers are malnourished, then there is risk of inadequate nutrition for
12.44 More on the piano lessons study. The researchers in Exercise 12.42 based their research on a biological argument for a causal link between music and spatial-temporal reasoning. Therefore, it is natural to test the contrast that compares the mean of the piano lesson group with the average of
12.43 The piano lessons study, continued. Refer to the previous exercise. Use the Bonferroni or another multiple-comparisons procedure to compare the group means. Summarize the results and support your conclusions with a graph of the means.
12.42 Do piano lessons improve the spatial-temporal reasoning of preschool children? The data in Table 12.4 contain the change in spatial-temporal reasoning (after treatment minus before treatment) of 34 children who took piano lessons, 10 who took singing lessons, 20 who had some computer
12.41 A consumer price promotion study, continued.Refer to the previous exercise. Use the Bonferroni or another multiple-comparisons procedure to compare the group means. Summarize the results and support your conclusions with a graph of the means.
12.40 A consumer price promotion study. If a supermarket product is offered at a reduced price frequently, do customers expect the price of the product to be lower in the future? This question was examined by researchers in a study conducted on students enrolled in an introductory management course
12.39 Do isoflavones increase bone mineral density?Kudzu is a plant that was imported to the United States from Japan and now covers over seven million acres in the South. The plant contains chemicals called isoflavones that have been shown to have beneficial effects on bones. One study used three
12.38 CHALL ENGE Do poets die young? According toWilliam Butler Yeats, “She is the Gaelic muse, for she gives inspiration to those she persecutes. The Gaelic poets die young, for she is restless, and will not let them remain long on earth.” One study designed to investigate this issue examined
12.37 CHALL ENGE Taking the log of the response variable.The distributions of the flower lengths in Exercise 12.35 are somewhat skewed. Take logs of the lengths and reanalyze the data. Write a summary of your results and include a comparison with the results you found in Exercise 12.35.
12.36 CHALL ENGE Air quality in poultry-processing plants, continued. Refer to Exercise 12.34. There is not sufficient information to examine the distributions in detail, but it is not unreasonable to expect count data such as these to be skewed.Reanalyze the data after taking logs of the CFU
12.35 CH ALLENGE A comparison of tropical flower varieties. Different varieties of the tropical flower Heliconia are fertilized by different species of hummingbirds. Over time, the lengths of the flowers and the form of the hummingbirds’ beaks have evolved to match each other. Here are data on
12.34 Air quality in poultry-processing plants. The air in poultry-processing plants often contains fungus spores. If the ventilation is inadequate, this can affect the health of the workers. To measure the presence of spores, air samples are pumped to an agar plate, and “colony-forming units
12.29 to 12.32. Write a report summarizing what happens to vitamins A, C, and E after bread is baked. Include appropriate statistical inference results and graphs.
12.33 CH ALLENG E Summarizing the results of storage time on vitamin content. Refer to Exercises
12.32 Storage time and vitamin A and E content, continued. Refer to the previous exercise.(a) Explain why it is inappropriate to perform a multiple-comparisons analysis for the vitamin E data.(b) Perform the Bonferroni or another multiplecomparisons procedure for the vitamin A data and summarize
12.31 Storage time and vitamin A and E content. Refer to Exercise 12.29. Measurements of the amounts of vitamin A (beta-carotene) and vitamin E in each loaf are given below. Use the analysis of variance method to study the data for each of these vitamins.Vitamin A Vitamin E Condition (mg/100 g)
12.30 Storage time and vitamin C content, continued.Refer to the previous exercise. Use the Bonferroni or another multiple-comparisons procedure to compare the group means. Summarize the results.
12.29 Storage time and the vitamin C content of bread. Does bread lose its vitamins when stored?Small loaves of bread were prepared with flour that was fortified with a fixed amount of vitamins.After baking, the vitamin C content of two loaves was measured. Another two loaves were baked at the same
12.28 CHALL ENGE The emotion study, continued. Refer to the previous exercise. The experimenters also measured emotions in some different ways.For a period of a week, each participant carried a device that sounded an alarm at random times during a 3-hour interval 5 times a day. When the alarm
12.27 Do we experience emotions differently?Do people from different cultures experience emotions differently? One study designed to examine this question collected data from 416 college students from five different cultures.9 The participants were asked to record, on a 1 (never)to 7 (always)
12.26 CHALLENGE Exam accommodations and end-ofterm grades. The Americans with Disabilities Act (ADA) requires that students with learning disabilities (LD) and/or attention deficit disorder (ADD) be given certain accommodations when taking examinations. One study designed to assess the effects of
12.25 The effects of two stimulant drugs. An experimenter was interested in investigating the effects of two stimulant drugs (labeled A and B). She divided 20 rats equally into 5 groups(placebo, Drug A low, Drug A high, Drug B low, and Drug B high) and, 20 minutes after injection of the drug,
12.24 Restaurant ambience and consumer behavior.There have been numerous studies investigating the effects of restaurant ambience on consumer behavior. A recent study investigated the effects of musical genre on consumer spending.7 At a single high-end restaurant in England over a 3-week period,
12.23 The importance of recreational sports to college satisfaction. The National Intramural-Recreational Sports Association (NIRSA)performed a survey to look at the value of recreational sports on college campuses.6 One of the questions asked each student to rate the importance of recreational

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