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introduction to operations research

Introduction To The Practice Of Statistics 10th Edition David S. Moore, George P. McCabe, Bruce A. Craig - Solutions

13.65 Analysis using multiple one-way ANOVAs. Perform the tasks described in Exercise 13.61 for the two response variables in the PLANTS2 data set.
13.64 Examination of the residuals. Perform the tasks described in Exercise 13.60 for the two response variables in the PLANTS2 data set.
13.63 Another comparison of plant species under low water conditions. Refer to Exercise 13.59. Additional data collected by the same researchers according to a similar design are given in the PLANTS2 data file. Here, there are two response variables: fresh biomass and dry biomass.High values for
13.62 More on the analysis using multiple one-way ANOVAs. Refer to Exercise 13.59. Run a separate one-way analysis of variance for each species and summarize the results. Because the amount of water is a quantitative factor, we can also analyze these data using regression. Run simple linear
13.61 Analysis using multiple one-way ANOVAs. Refer to Exercise 13.59. Run a separate oneway 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.
13.60 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
13.59 A comparison of plant species under low water conditions. The PLANTS1 data file 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. The researchers who
13.58 Complete the ANOVA table. Based on the following partial ANOVA table results, complete the ANOVA table and draw conclusions at the 5% significance level.Effect df SS MS F A 2 90 B 4 165 AB 8 204 Error 60 900
13.57 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. Note that there are many possible definitions of “left-handed.” The researchers examined the effects of
13.56 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
13.55 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
13.54 Analysis using a one-way ANOVA. Refer to Exercise 13.52. Rerun the analysis as a oneway ANOVA with nine groups and four observations per group. Report the results of the F test.Examine differences in means using a multiple-comparisons procedure. Summarize your results and compare them with
13.53 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.27
13.52 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
13.51 Trust of individuals and groups. Trust is an essential element in any exchange of goods or services. The following trust game is often used to study trust experimentally:A sender starts with $X and can transfer any amount x≤X to a responder.The responder then gets $3x and can transfer any
13.50 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. They hypothesized that in countries where high achievement is not valued highly, considerable
13.49 Conspicuous consumption and men’s testosterone levels. It is argued that conspicuous consumption is a means by which men communicate their social status to prospective mates. One study looked at changes in a male’s testosterone level in response to fluctuations in his status created by
13.48 Interpreting the results. The goal of the study in the previous exercise was to understand cultural and sex differences in functional food attitudes and behaviors among young adults, the next generation of food consumers. The researchers used a sample of undergraduate students and had each
13.47 More on acceptance of functional foods. Refer to Exercise 13.44. The means for four of the response variables associated with functional foods are as follows:Sex General attitude Product benefits Culture Culture Canada United States France Canada United States France Female 4.93 4.69 4.10
13.46 Comparing the groups. Refer to Exercises 13.44 and 13.45. The researchers presented a table of means with different superscripts indicating pairs of means that differed at the 0.05 significance level, using the Bonferroni method.a. What denominator degrees of freedom would be used here?b. How
13.45 Estimating the within-group variance. Refer to the previous exercise. Here are the cell standard deviations and sample sizes for cooking enjoyment:Sex Culture Canada United States France s n s n s n Female 1.668 238 1.736 178 2.024 82 Male 1.909 125 1.601 101 1.875 87 Find the pooled estimate
13.44 Acceptance of functional foods. Functional foods are foods that are fortified with healthpromoting supplements, like calcium-enriched orange juice or vitamin-enriched cereal. Although the number of functional foods is growing in the marketplace, very little is known about how the next
13.43 Describing the effects. Refer to Exercise 13.41. The P-values for all main effects and twofactor interactions are significant at the 0.05 level. Using the table, find the marginal means (that is, the mean for the no humor treatment, the mean for the no humor and unfavorable process treatment
13.42 Pooling the standard deviations. Refer to the previous exercise. Find the pooled estimate of the standard deviation for these data. What are its degrees of freedom? Using the rule from Chapter 12 (page 608), is it reasonable to use a pooled standard deviation for the analysis?Explain your
13.41 The effect of humor. In advertising, humor is often used to overcome sales resistance and stimulate customer purchase behavior. One experiment looked at the use of humor to offset the negative feelings often associated with website encounters. The setting of the experiment was an online
13.40 Use of animated agents in a multimedia environment. Multimedia learning environments are designed to enhance learning by providing more hands-on and exploratory investigation of a topic. Often, animated agents (human-like characters) are used in the hope of enhancing social interaction with
13.39 Bilingualism (continued). Refer to the previous exercise.a. If bilingualism helps with brain functioning as we age, explain why we’d expect to find an interaction between age and lingualism. Also create an interaction plot of what sort of pattern we’d expect.20b. Analyze the reaction
13.38 Bilingualism. Not only does speaking two languages have many practical benefits in this globalized world, but there is also growing evidence that it appears to help with brain functioning as we age. In one study, 80 participants were divided equally among four groups: younger adult
13.37 The effects of proximity and visibility on food intake. A study investigated the influence that proximity and visibility of food have on food intake. A total of 40 secretaries from the University of Illinois participated in the study. A candy dish full of individually wrapped chocolates was
13.36 Transaction history and a thank-you statement (continued). Refer to the previous exercise. The numbers of subjects in the cells were not equal, so the researchers used linear regression to analyze the data. This was done by creating an indicator variable for each factor and the interaction.
13.35 The influences of transaction history and a thank-you statement. A service failure is defined as any service-related problem (real or perceived) that transpires during a customer’s experience with a firm. In the hotel industry, there is a high human component, so these sorts of failures
13.34 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
13.33 Where are your eyes? The objectifying gaze, often referred to as “ogling” or “checking out,” can have many adverse consequences. A group of researchers used eye-tracking technology to better understand the nature and causes for this gaze. They asked 29 women and 36 men to look at
13.32 Significant effects and the interaction plot. Consider a 2×2 ANOVA in which only the F tests for the main effect of A and the interaction AB are statistically significant.Create an interaction plot with factor B on the x axis that could be possible given these results.
13.31 Influence of age and sex on motor performance (continued). Refer to the previous exercise.a. In their article, the researchers state that each of their response variables was assessed for Normality prior to performing a two-way ANOVA. Is it necessary for the 246 time measurements to be
13.30 Influence of age and sex on motor performance. The slowing of motor performance as humans age is well established. Differences across the sexes, however, are less so. A recent study assessed the motor performance of 246 healthy adults. One task was to tap the thumb and forefinger of the right
13.29 Is there an interaction? Each of the following tables gives means for a two-way ANOVA.Make a plot of the means with the levels of Factor A on the x axis. State whether there is an interaction, and if there is, describe it.a.Factor B Factor A 1 2 3 1 15 21 27 2 7 10 13 b.Factor B Factor A 1 2
13.28 Outlining the ANOVA table. Refer to the previous exercise. For each situation, outline the ANOVA table, giving the sources of variation and the degrees of freedom.
13.27 Describe the two-way problem. Each of the following situations is a two-way study design. For each case, identify the response variable and both factors and state the number of levels for each factor (I and J) and the total number of observations (N).a. A suitcase producer investigates the
13.26 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
13.25 What’s wrong? For each of the following, explain what is wrong and why.a. You should reject the null hypothesis that there is no interaction in a two-way ANOVA when the AB F statistic is small.b. Sums of squares are equal to mean squares divided by degrees of freedom.c. The test statistics
13.24 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 2×3 ANOVA, there are three levels of Factor A.c. In an I×J ANOVA, DFAB=IJ−1 .d. In a 5×3 ANOVA, there are 15 marginal means.
13.23 Smart shopping carts. Smart shopping carts are shopping carts equipped with scanners that track the total price of the items in the cart (providing real-time feedback). To help understand the smart shopping cart’s influence on spending behavior, a group of researchers designed a two-factor
13.22 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
13.21 Study of resveratrol and dietary copper (continued). Refer to Exercise 13.19. The mean glucose level (mmol/L) for each group of rats is shown in the following table:Group x¯Carbonate 17.66 Carbonate + resveratrol 17.89 Nanoparticle 20.37 Nanoparticle + resveratrol 16.96a. Construct an
13.20 Ecological effects of pharmaceuticals on fish (continued). Refer to Exercise 13.18.a. Often with a count as the response, one considers taking the square root of the count and performing ANOVA on this transformed response. Explain why a transformation might be useful here.b. Using the
13.19 Study of resveratrol and dietary copper. Past studies have shown that cardiovascular alterations can be improved through long-term use of dietary copper and resveratrol. A study in rats was run to look at the interaction between resveratrol and two forms of copper. This experiment involved 36
13.18 Ecological effects of pharmaceuticals on fish. Drugs used to treat anxiety persist in wastewater effluent, resulting in relatively high concentrations of these drugs in our rivers and streams. To understand the impacts of these anxiety drugs on fish, researchers commonly expose fish to
13.17 What can you conclude, given the design and F statistics? Analysis of data for a 2×3 ANOVA with five observations per cell gave the following F statistics:Effect F A 3.28 B 4.64 AB 1.43a. What can you conclude from the information given?b. What additional information would you want in order
13.16 What can you conclude, given the P-values? A study reported the following results for data analyzed using a two-way ANOVA at the 5% significance level:Effect F P-value A 4.75 0.009 B 14.26 0.001 AB 5.14 0.007a. What can you conclude from the information given?b. What additional information
13.15 Is there interaction? A 3×3 ANOVA was run with four observations per cell.a. Outline the two-way ANOVA table for this analysis, giving the sources of variation and the degrees of freedom.b. Give the degrees of freedom for the F statistic that is used to test for interaction in this analysis
13.14 Outlining the ANOVA table. For each part in Exercise 13.3 (page 661), outline the ANOVA table, giving the sources of variation and the degrees of freedom.
13.13 What’s wrong? For each of the following, explain what is wrong and why.a. For a 3×5 ANOVA, DFAB=15 .b. You can perform a two-way ANOVA only when the sample sizes are the same in all cells.c. In a two-way ANOVA, the error variation is separated in parts for each main effect and
13.12 How large does the F statistic need to be? For each of the following situations, sketch the F distribution and indicate the region where you would reject at the 5% significance level.a. The main effect for B in a 2×4 ANOVA with three observations per cell.b. The interaction in a 4×3 ANOVA
13.11 Compare employee training programs. A company wants to compare three different training programs for its new employees. Each of these programs takes six hours to complete. The training can be given for six hours on one day or for three hours on two consecutive days. The next 100 employees
13.10 Proposing a two-factor design. A paint supplier is interested in assessing the hardness of four brands of paint, each with and without an additive that is supposed to add durability. The supplier has a total of 40 panels that can be painted. Hardness will be measured after 180 days of
13.9 Alternative interaction plot. In Figure 13.2 (page 659), the interaction plot involves two profiles because group size was used on the x axis. Construct the alternative interaction plot involving five profiles by using location on the x axis. Which of these two interaction plots do you prefer,
13.8 Using makeup. A study was performed in which 44 women participated as models. Each model was photographed after applying makeup as if she were going on a “night out.” Software was then used to create a sequence of 21 images ranging from 50% makeup to 150% makeup. Another set of observers
13.7 Writing about testing worries and exam performance. For many students, self-induced worries and pressure to perform well on exams cause them to perform below their ability. This is because these worries compete with the working memory available for performance. Expressive writing has been
13.6 Lack of interaction. Refer to Example 13.5 (page 657). Suppose that the difference between 2010 and 2016 remained fixed at 40.8 calories for all three age groups and that the 2010 means for each age group are as given in the table. Find the consumption means for 2016 for each age group and
13.5 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).
13.4 Is there an interaction? Each of the following tables gives means for a two-way ANOVA. Make a plot of the means with the levels of Factor A on the x axis. State whether or not there is an interaction, and if there is, describe it.a.Factor B Factor A 1 2 3 1 11 21 31 2 6 11 16 b.Factor B Factor
13.3 Describe the two-way problem. 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 child’s percent of
13.2 What’s wrong? For each of the following, explain what is wrong and why.a. Parallel profiles of cell means imply that a strong interaction is present.b. In a 2×3 ANOVA, each level of Factor A appears with two levels of Factor B.c. The estimate sp2 is obtained by pooling the marginal sample
13.1 A/B testing. A/B testing, or split testing, is often used to understand user behavior related to online features. It involves randomly assigning users to two levels of a single factor and comparing some outcome. Suppose a company is interested in updating its website and is considering between
12.81 Contrasts for the massage study. Refer to the previous Exercise. There are several comparisons of interest in this study. They are (1) usual care versus the average of the massage groups; (2) the average of the two 30-minute massage groups versus the average of the two 60-minute massage
12.80 Massage therapy for osteoarthritis of the knee. Various studies have shown the benefits of massage to manage pain. In one study, 125 adults suffering from osteoarthritis of the knees were randomly assigned to one of five eight-week regimens. The primary outcome was the decrease in the Western
12.79 The effect of music on risky financial decisions. Decisions regarding investments involve some degree of risk. The degree of risk someone is willing to accept is related to the individual’s mood and arousal. Because music has been shown to influence both mood and arousal, researchers were
12.78 The noncentral F distribution. The noncentral F distribution is defined by three parameters:the numerator and denominator degrees of freedom and a noncentrality parameterλ. When n is the sample size for each group, 26μ¯ is the ordinary average of the μi andλ=nΣ(μi−u¯)2σ2 Large λ
12.77 Planning another restaurant ambiance study. Exercise 12.58 (page 645) 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 restaurant. Use
12.76 Planning another isoflavone study. Exercise12.59 (page 645) 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 dose or a high
12.75 Planning another emotions study. Scores on an emotional scale were compared for five different cultures in Exercise 12.55 (page 644). Suppose that you are planning a new study using the same outcome variable. Your study will use European American, Asian American, and Hispanic American
12.74 Linear transformation of the response variable. Refer to the previous two Exercises. 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
12.73 More on changing the response variable. Refer to the previous Exercise and Exercise 12.65(page 647). A calibration error was found with the device that measured Gpi, which resulted in a shifted response. Add 5% to each response and redo the calculations. Summarize the effects of transforming
12.72 Changing the response variable. Refer to Exercise 12.65 (page 647), where we compared six types of scaffold material to repair wounds. The data are given as percents ranging from 5 to 75.a. Convert these percents into their decimal form by dividing by 100. Calculate the transformed means,
12.71 Testing several contrasts from the dandruff study. Refer to Exercise 12.68. 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 other three treatments, (2) Keto versus the average of
12.70 Comparing each pair of dandruff treatments. Refer to Exercise 12.68. Use the Bonferroni or another multiple-comparisons method that your software provides to compare the individual group means in the dandruff study. Write a short summary of your conclusions.
12.69 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
12.68 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
12.67 The two-sample t test and one-way ANOVA. Refer to the diet and mood study in Exercise 7.48 (page 430). Find the two-sample pooled t statistic for comparing the two energy-restricted diets.Then formulate the problem as an ANOVA and report the results of this analysis. Verify that F=t2 .
12.66 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 multiple-comparisons method to determine which pairs of means differ significantly.
12.65 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
12.64 Public transit use and physical activity. In one study on physical activity, participants used accelerometers and a seven-day travel log to monitor their physical activity. Researchers used the data from each participant to quantify the amount of daily physical activity and to classify each
12.63 Contrasts of interest. Refer to Exercise 12.57 (page 645). Given the group means and F statistic, we can determine that MSE=2.421 . Use this value and the other information in Exercise 12.57 to do the following.a. Test if there is a difference between the sexes.b. Test if there is a
12.62 Exercise and healthy bones (continued). Refer to the previous exercise.23a. Examine the residuals. Is the Normality assumption reasonable for these data?b. Use the Bonferroni method to determine which pairs of means differ significantly. Summarize your results in a short report. Be sure to
12.61 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. There were three treatments: a
12.60 Do poets die young? According to William 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 the age at
12.59 Do isoflavones increase bone mineral density? Kudzu is a plant that was imported to the United States from Japan and now covers over 7 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
12.58 Restaurant ambiance and consumer behavior. Numerous studies have investigated the effects of restaurant ambiance on consumer behavior. One study investigated the effects of musical genre on consumer spending. At a single high-end restaurant in England over a three-week period, there were a
12.57 Shopping and bargaining in Mexico. Price haggling and other bargaining behaviors among consumers have been observed for a long time. However, research addressing these behaviors, especially in a real-life setting, remains relatively sparse. A group of researchers performed a small study to
12.56 The emotions 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 three-hour interval five times a day. When the alarm
12.55 Do we experience emotions differently? Do people from different cultures experience emotions differently? One study designed to examine this question collected data from 410 college students from five different cultures. The participants were asked to record, on a 1 (never) to 7(always)
12.54 Do labels matter? A study was performed to examine the self-identification of college students of Asian descent with various identity categories and assess whether there are attitudinal differences across these categories. Undergraduates at a large midwestern university who had identified
12.53 Changing the response variable. Refer to the previous two exercises, where we compared three weight-loss programs using change in weight measured in pounds. Suppose that you decide to instead make the comparison using change in weight measured in kilograms.a. Convert the weight loss from
12.52 Financial incentives for weight loss (continued). Refer to the previous exercise.a. Analyze the change in weight using analysis of variance. Report the test statistic, degrees of freedom, P-value, and your conclusions.b. Even though you assessed the model assumptions in the previous exercise,
12.51 Financial incentives for weight loss. The use of financial incentives has shown promise in promoting weight loss and healthy behaviors. In one study, 104 employees of the Children’s Hospital of Philadelphia, with BMIs of 30 to 40 kilograms per square meter(kg/m2) , were each randomly
12.50 Which means differ significantly? Here is a table of means for a one-way ANOVA with four groups ordered from smallest to largest:15 Group x¯ s n 1 128.2 7.7 20 4 135.0 8.6 20 2 142.1 8.7 20 3 148.6 10.8 20 Let’s compare the results using the two multiple-comparisons methods described in
12.49 Winery websites. As part of a study of British Columbia wineries, each of the 193 wineries was classified into one of three categories, based on its website features. The Presence stage just had information about the winery. The Portals stage included order placement and online feedback. The
12.48 Facebook recruitment of young adult smokers. Studies about tobacco use have had difficulties recruiting young adults. Because Facebook is visited daily by a very large percent of young adults, researchers decided to investigate the effectiveness of using Facebook to recruit young adults for a
12.47 Time levels of scale (continued). Refer to the previous exercise.a. Run the ANOVA and report the results.b. Use a multiple-comparisons method to compare the three groups. State your conclusions.c. The researchers hypothesized that the more fine-grained the time unit presented to a

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