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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

12.46 Time levels of scale. Recall Exercise 7.42 (page 429). This experiment actually involved three groups. The last group was told the construction project would last 12 months. Here is a summary of the interval lengths (in days) between the earliest and latest completion dates.Group n x¯ s 52
12.45 Age differences across coffeehouses (continued). Recall the previous exercise. Using the estimates of the group means andσ in Figure 12.19, compare the coffeehouses using the Bonferroni method. Write a short summary of what you find.
12.44 Age differences across coffeehouses? Recall Example 12.2 (page 600) and Check-in question 12.8 (page 610). Use the data set and output shown in FIGURE 12.19 to answer the following questions.14 FIGURE 12.19 Minitab output for the coffeehouse study, Exercise 12.44.Description The output is
12.43 Innovative wine packaging. Are wine bottles outdated? A group of researchers randomly assigned 247 German consumers to one of three wine packaging styles. They were a bottle with a screw cap (SC), a wine bag-in-box (BiB), and a four-pack of single-serving StackTek glasses (ST).Each
12.42 The effect of increased sample size. Set the common standard deviation for the One-Way ANOVA applet at a middle value and set the means to roughly 5.00, 4.50, and 5.25, respectively.a. What are the F statistic, its degrees of freedom, and the P-value?b. Slide the sample size bar to the right
12.41 The effect of increased variation between groups. Set the common standard deviation for the One-Way ANOVA applet at a middle value. Set the means of the three groups so that they are approximately equal.a. What is the F statistic? Give its P-value.b. Move the mean of the second group up and
12.40 The effect of increased variation within groups. The One-Way ANOVA applet lets you see how the F statistic and the P-value depend on the variability of the data within groups, the sample size, and the differences among the means.a. The graph shows the means of the three groups. Move these up
12.39 Organic foods and friendly behavior? Refer to Exercise 12.37 for the design of the experiment. After rating the moral transgressions, the participants were told that “another professor from another department is also conducting research and really needs volunteers.” They were also told
12.38 Organic foods and morals (continued). Refer to the previous exercise.a. Analyze the scores using one-way ANOVA. Report the test statistic, degrees of freedom, and Pvalue.b. Assess the assumptions necessary for inference by examining the residuals. Summarize your findings. Do they agree with
12.37 Organic foods and morals? Organic foods are often marketed using moral terms such as“honesty” and “purity.” Is this just a marketing strategy, or is there a conceptual link between organic food and morality? In one experiment, 62 undergraduates were each randomly assigned to one of
12.36 What’s wrong? For each of the following, explain what is wrong and why.a. In rejecting the null hypothesis, one can conclude that all the means are different from one another.b. A multiple-comparisons procedure is used to compare a relationship among means that was specified prior to
12.35 Power for a different alternative. Refer to the previous exercise. Suppose we increaseμ4 to 4.2. For each of the choices of n in the previous example, would the power be larger or smaller under this new set of alternative means? Explain your answer without doing the calculations.
12.34 Power calculations for planning a study. You are planning a new eye gaze study for a different university than that studied in Example 12.16 (page 618). From Figure 12.9 (page 618), the pooled standard error is 1.68. To be a little conservative, useσ=2.0 for the calculations in this
12.33 Contrasts for multitasking. Refer to the previous exercise. Letμ1, μ2 ,..., μ7 represent the mean scores for the seven conditions. The first four conditions refer to off-task behaviors, and the last three conditions represent different sorts of controls.a. The researchers hypothesized that
12.32 Multitasking with technology in the classroom. Laptops and other digital technologies with wireless access to the Internet are becoming more and more common in the classroom. While numerous studies have shown that these technologies can be used effectively as part of teaching, there is
12.31 Use of a multiple-comparisons procedure. A friend performed a one-way ANOVA at theα=0.05 level to compare the nitrogen levels of I=50 different crop fields from around the state. Among the 1225 mean comparisons, he found 63 significant differences when using the least-significant differences
12.30 The Bonferroni method. For each of the following settings, state the α level to be used for each test.a. There are 21 pairs of means(I=7) , and the overall significance level is 5%.b. There are 36 pairs of means(I=9) , and the overall significance level is 1%.c. There are I=6 groups, and the
12.29 Two contrasts of interest for the stimulant study. Refer to Exercise 12.15 (page 623). There are two comparisons of interest to the experimenter. They are (1) placebo versus the average of the two lowdose treatments and (2) the difference between High A and Low A versus the difference between
12.28 Analyzing contrasts. Answer the following questions for the two contrasts that you defined in the previous exercise.a. For each contrast, give H0 and an appropriate Ha . In choosing the alternatives, you should use information given in the description of the problem, but you may not consider
12.27 Writing contrasts (continued). Return to the eye study described in Example 12.16 (page 618).Let μ1, μ2, μ3, and μ4 represent the mean scores for blue, brown, gaze down, and green eyes, respectively.a. Because a majority of the population in this study are Hispanic (eye color
12.26 Writing contrasts. You’ve been asked to help some administrators analyze survey data on textbook expenditures collected at a large public university. Let 11μ1, μ2, μ3, and μ4 represent the population mean expenditures on textbooks for the first-year, second-year, third-year, and
12.25 College dining facilities. University and college food service operations have been trying to keep up with the growing expectations of consumers with regard to the overall campus dining experience.Because customer satisfaction has been shown to be associated with repeat patronage and new
12.24 Background music contrast. Refer to Example 12.3 (page 603). The researchers hypothesize that listening to any background music (with or without lyrics) will, on average, result in fewer completed math problems than working in silence. Test this hypothesis with a contrast. Make sure to
12.23 Give the confidence interval. Refer to the previous exercise. Give a 95% confidence interval for the difference between the average of the means of the first four groups and the average mean of the last two groups.
12.22 Is the contrast significant? Refer to the previous exercise. Suppose that the average of the first four groups minus the average of the last two groups is 2.6. State an appropriate null hypothesis for this comparison and find the test statistic with its degrees of freedom. Can you draw a
12.21 Find the standard error. Refer to the previous exercise. Suppose that there are 10 observations in each group and that sp=5 .Find the standard error for the contrast.
12.20 Define a contrast. An ANOVA was run with six groups. Give the coefficients for the contrast that compares the average of the means of the first four groups with the mean of the last two groups.
12.19 The effect of extremely low-frequency electromagnetic fields. The use of electronic devices, such as smartphones, is now part of everyday life. These devices increase our exposure to extremely low-frequency electromagnetic fields (ELF-EMF). A study involving rats was run to study long-term
12.18 Constructing an ANOVA table. Refer to Check-in question 12.5 (page 608). Using the table of group means and standard deviations, construct an ANOVA table similar to that on page 543.Based on the F statistic and degrees of freedom, compute the P-value. What do you conclude?
12.17 Pain tolerance among sports teams. Many have argued that sports such as football require the ability to withstand pain from injury for extended periods of time. To see if there is greater pain tolerance among certain sports teams, a group of researchers assessed 183 male Division II athletes
12.16 Perceptions of social media. It is estimated that more than 90% of North American students use social media. This has prompted much research on the mental health impacts of these technologies. In one study, researchers investigated how mental health workers perceive the association between
12.15 The effects of two stimulant drugs. An experimenter was interested in investigating the effects of two stimulant drugs (labeled A and B). She divided 25 rats equally into five groups (placebo, Drug A low, Drug A high, Drug B low, and Drug B high) and, 20 minutes after injection of the drug,
12.14 Effects of music on imagery training (continued). Refer to the previous exercise.a. What are the numerator and denominator degrees of freedom for this study’s ANOVA F test?b. For this study, SSG=328.17 . Use this and your estimated common standard deviation to compute the F statistic.c.
12.13 Effects of music on imagery training. Music that matches a sports activity’s requirements has been shown to enhance sports performance. Very little, however, is known about the effects of music on imagery in the context of sports performance. In one study, 63 novice dart throwers were
12.12 Data collection (continued). Refer to Exercise 12.8. For each situation, discuss the method of obtaining the data and how it will affect the extent to which the results can be generalized.
12.11 Data collection and the interpretation of results. Refer to Exercise 12.7. For each situation, discuss the method of obtaining the data and how it will affect the extent to which the results can be generalized.
12.10 Determining the degrees of freedom (continued). Refer to Exercise 12.8. For each situation, give the following:a. Degrees of freedom for groups, error and total sums of squares.b. Null and alternative hypotheses.c. Numerator and denominator degrees of freedom for the F statistic.
12.9 Determining the degrees of freedom. Refer to Exercise 12.7. For each situation, give the following:a. Degrees of freedom for groups, error and total sums of squares.b. Null and alternative hypotheses.c. Numerator and denominator degrees of freedom for the F statistic.
12.8 Describing the ANOVA model (continued). For each of the following situations, identify the response variable and the populations to be compared and give I, ni , and N.a. A developer of a virtual-reality (VR) teaching tool for the deaf wanted to compare the effectiveness of different navigation
12.7 Describing the ANOVA model. For each of the following situations, identify the response variable and the populations to be compared and give I, ni , and N.a. A poultry farmer is interested in reducing the cholesterol level in his marketable eggs. He wants to compare two different
12.6 Calculating the pooled standard deviation. An experiment was run to compare three groups. The sample sizes were 32, 27, and 98, and the corresponding estimated standard deviations were 2.2, 2.4, and 4.3.a. Is it reasonable to use the assumption of equal standard deviations when we analyze
12.5 Calculating the ANOVA F test P-value (continued). For each of the following situations, find the F statistic and the degrees of freedom. Then draw a sketch of the distribution under the null hypothesis and shade in the portion corresponding to the P-value. State how you would report the
12.4 Calculating the ANOVA F test P-value. For each of the following situations, find the degrees of freedom for the F statistic and then use Table E (or software) to approximate (obtain) the P-value.a. Five groups are being compared, with 5 observations per group. The value of the F statistic is
12.3 Visualizing the ANOVA model (continued). Refer to the previous exercise. If SRSs of size n=5 were obtained from each of the three populations, under which setting would you most likely obtain a significant ANOVA F test? Explain your answer.
12.2 Visualizing the ANOVA model. For each of the following settings, draw a picture of the ANOVA model similar to Figure 12.5 (page 607). To sketch the Normal curves, you may want to review the 68–95–99.7 rule on page 51.a. μ1=17, μ2=13, μ3=12, and σ=2.b. μ1=17, μ2=13, μ3=12, and
12.1 A one-way ANOVA example. A study compared four groups with five observations per group. An F statistic of 3.78 was reported.a. Give the degrees of freedom for this statistic and the entries from Table E that correspond to the F distribution under the null hypothesis.b. Sketch a picture of this
11.74 CEO pay and gross profits. In Exercise 10.50 (page 559), you assessed the relationship between the logarithm of a CEO’s pay ratio and the logarithm of the company’s gross profit per employee. These companies, however, are divided up into different industries. Is the relationship the same
11.73 Brain injuries in Canadian football players. Multiple concussions have been shown to be associated with neurodegenerative diseases. In one study, the brain volumes of the left hippocampus of 53 retired Canadian football players, 25 age- and education-matched controls, and controls from the
11.72 Is there a difference? In Exercises 10.31 and 10.32 (page 556), we studied the relationship between room temperature and academic performance for each of the sexes. Use what was learned in Exercise 11.18 (page 575) to compare these two regression lines using one multiple regression
11.71 The final multiple regression model of Taste. Use the three explanatory variables Acetic, H2S, and Lactic in a multiple regression to predict Taste. Write a short summary of your results, including an examination of the residuals. Based on all the regression analyses you have carried out on
11.70 Another multiple regression model of Taste. Carry out a multiple regression using H2S and Lactic to predict Taste. When we compare the results of this analysis with the simple linear regressions using each of these explanatory variables alone, it is evident that a better result is obtained by
11.69 Multiple regression model of Taste. Carry out a multiple regression using Acetic and H2S to predict Taste. Summarize the results of your analysis. Compare the statistical significance of Acetic in this model with its significance in the model with Acetic alone as a predictor (Exercise 11.65).
11.68 Comparing the simple linear regression models. Compare the results of the regressions performed in the three previous exercises. Construct a table with values of the F statistic, its P-value, R2 , and the estimate s of the standard deviation for each model. Report the three regression
11.67 The final simple linear regression model of Taste. Repeat the analysis of Exercise 11.65 using Taste as the response variable and Lactic as the explanatory variable.12
11.66 Another simple linear regression model of Taste. Repeat the analysis of Exercise 11.65 using Taste as the response variable and H2S as the explanatory variable.
11.65 Simple linear regression model of Taste. Perform a simple linear regression analysis using Taste as the response variable and Acetic as the explanatory variable. Be sure to examine the residuals carefully. Summarize your results. Include a plot of the data with the least-squares regression
11.64 Pairwise scatterplots of the explanatory variables. Make a scatterplot for each pair of variables in the CHEESE data file (you will have six plots). Describe the relationships. Calculate the correlation for each pair of variables and report the P-value for the test of zero population
11.63 Describing the explanatory variables. For each of the four variables in the CHEESE data file, find the mean, median, standard deviation, and interquartile range. Display each distribution by means of a stemplot and use a Normal quantile plot to assess Normality of the data. Summarize your
11.62 Interpretation of coefficients in log PCB regressions. Use the results of your analysis of the log PCB data in Exercise 11.60 to write an explanation of how regression coefficients, standard errors of regression coefficients, and tests of significance for explanatory variables can change
11.61 Predicting total TEQ using transformed variables. Use the log data set that you created in Exercise 11.58 to find a good multiple regression model for predicting the log of TEQ. Use only log PCB variables for this analysis. Write a report summarizing your results and comparing them with the
11.60 Even more on predicting total amount of PCB using transformed variables. Use the log data set that you created in Exercise 11.58 to find a good multiple regression model for predicting the log of PCB. Use only log PCB variables for this analysis. Write a report summarizing your results.
11.59 Predicting total amount of PCB using transformed variables (continued). Refer to the previous exercise.a. Use numerical and graphical summaries to describe the relationship between each pair of log variables.b. Compare these summaries with the summaries that you produced in Exercise 11.53 for
11.58 Predicting total amount of PCB using transformed variables. Because distributions of variables such as PCB, the PCB congeners, and TEQ tend to be skewed, researchers frequently analyze the logarithms of the measured variables. Create a data set that has the logs of each of the variables in
11.57 Multiple regression model for total TEQ (continued). The information summarized in TEQ is used to assess and manage risks from these chemicals. For example, the World Health Organization (WHO) has established the tolerable daily intake (TDI) as one to four TEQs per kilogram of body weight per
11.56 Multiple regression model for total TEQ. Dioxins and furans are other classes of chemicals that can cause undesirable health effects similar to those caused by PCB. The three types of chemicals are combined using toxic equivalent scores (TEQs), which attempt to measure the health effects on a
11.55 More on predicting the total amount of PCB. Run a regression to predict PCB using the variables PCB52, PCB118, and PCB138. Note that this is similar to the analysis that you did in Exercise 11.53, with the change that PCB180 is not included as an explanatory variable.a. Summarize the
11.54 Adjusting the analysis for potential outliers. The examination of the residuals in part (c) of the previous exercise suggests that there may be two outliers: one with a high residual and one with a low residual.11a. Because of safety issues, we are more concerned about underestimating PCB in
11.53 Predicting the total amount of PCB. Use the four congeners PCB52, PCB118, PCB138, and PCB180 in a multiple regression to predict PCB.a. Write the statistical model for this analysis. Include all assumptions.b. Run the regression and summarize the results.c. Examine the residuals. Do they
11.52 Relationships among PCB congeners. Consider the following variables: PCB (the total amount of PCB) and four congeners: PCB52, PCB118, PCB138, and PCB180.a. Using numerical and graphical summaries, describe the distribution of each of these variables.b. Using numerical and graphical summaries,
11.51 Predicting bone resorption using transformed variables. Refer to the previous exercise. Rerun using logs.The following 11 exercises use the PCB data file. Polychlorinated biphenyls (PCBs) are a collection of synthetic compounds, called congeners, that are particularly toxic to fetuses and
11.50 Predicting bone resorption. Refer to Exercises 11.46, 11.47, and 11.48. Answer these questions with the roles of VO+ and VO− reversed; that is, run models to predict VO− , with VO+ as an explanatory variable.
11.49 Predicting bone formation using transformed variables. Because the distributions of VO+ , VO− , OC, and TRAP tend to be skewed, it is common to work with logarithms rather than the measured values. Using the questions in the previous three exercises as a guide, analyze the log data.
11.48 More on predicting bone formation. Now consider a regression model for predicting VO+ using OC, TRAP, and VO− .a. Write out the statistical model for this analysis, including all assumptions.b. Run the multiple regression to predict VO+ using OC, TRAP, and VO− .Summarize the results.c.
11.47 Predicting bone formation. Let’s use regression methods to predict VO+, the measure of bone formation.10a. Because OC is a biomarker of bone formation, we start with a simple linear regression, using OC as the explanatory variable. Run the regression and summarize the results. Be sure to
11.46 Bone formation and resorption. Consider the following four variables:VO+ , a measure of bone formation; VO− , a measure of bone resorption; OC, a biomarker of bone formation; and TRAP, a biomarker of bone resorption.a. Using numerical and graphical summaries, describe the distribution of
11.45 Selecting from among several models. Refer to the results from the previous exercise.a. Make a table showing the estimated regression coefficients, standard errors, t statistics, and Pvalues.b. Describe how the coefficients and P-values change for the four models.c. Based on the table of
11.44 Building a multiple linear regression model. Let’s now build a model to predict the lifesatisfaction score, LSI.a. Consider a simple linear regression using GINI as the explanatory variable. Run the regression and summarize the results. Be sure to check assumptions.b. Now consider a model
11.43 Predicting a nation’s “average happiness” score. Consider the five statistics for each nation:LSI, the average life-satisfaction score; GINI, the GINI index; Corrupt, the degree of government corruption; Life, the average life expectancy; and Democracy, a measure of civil and political
11.42 Considering the log transformation. Refer to Exercise 11.39. Variables like income often have very skewed distributions. This can result in certain cases strongly influencing the fit of the model. A common remedy is to take the log before analysis. Create a new response variable by taking the
11.41 Predicting U.S. movie revenue. The movie Kick-Ass was released during this same time period. It had a budget of $30.0 million and was shown in 3065 theaters, grossing $19.83 million during the first weekend.a. Use software to construct a 95% prediction interval based on the model with all
11.40 A simpler model. In the multiple regression analysis using all four explanatory variables, Theaters and Budget appear to be the least helpful (given that the other two explanatory variables are in the model).a. Perform a new analysis using only the movie’s opening-weekend revenue and IMDb
11.39 Predicting movie revenue: Multiple linear regression. Now consider fitting a model using all the explanatory variables.a. Write out the statistical model for this analysis, making sure to specify all assumptions.b. Run the multiple regression model and specify the fitted regression
11.38 Predicting movie revenue: Simple linear regressions. Now let’s look at the response variable and its relationship with each explanatory variable.a. Using numerical and graphical summaries, describe the distribution of the response variable USRevenue.b. This variable is not Normally
11.37 Predicting movie revenue: Preliminary analysis. The response variable is a movie’s total U.S.revenue (USRevenue). Let’s consider as explanatory variables the movie’s budget (Budget); openingweekend revenue (Opening); the number of theaters (Theaters) the movie was in for the opening
11.36 Architectural firm billings. A summary of firms engaged in commercial architecture in the Indianapolis, Indiana, area provides firm characteristics, including total annual billing in the current year, total annual billing in the previous year, the number of architects, the number of
11.35 Checking for a polynomial relationship. When looking at the residuals from the simple linear model of BMI versus physical activity (PA), Figure 10.5 (page 524) suggested a possible curvilinear relationship. Let’s investigate fitting a quadratic(q=2) polynomial (see Exercise 11.15, page 574)
11.34 Is the number of tornadoes increasing? In Exercise 10.15, data on the number of tornadoes in the United States between 1953 and 2019 were analyzed to see if there was a linear trend over time.Some argue that it’s not the number of tornadoes increasing over time but rather the probability of
11.33 Predicting energy-drink consumption. Energy-drink advertising consistently emphasizes a physically active lifestyle and often features extreme sports and risk taking. Are these typical characteristics of an energy-drink consumer? A researcher decided to examine the links between energydrink
11.32 Consider the sex of the students. Refer to Example 11.11 (page 586). The seventh explanatory variable provided in the GPA data set is a sex indicator variable. This variable (Sex) takes the value 0 for males and 1 for females. If we include it in our model involving the other six variables,
11.31 A mechanistic explanation of popularity. In Exercise 10.61 (page 561), correlations between an adolescent’s “popularity,” expression of a serotonin receptor gene, and rule-breaking behaviors were assessed. An additional portion of the analysis looked at the relationship between the gene
11.30 Testing a collection of variables. Refer to the previous exercise. Although the F test was highly significant, only Admit is found to be significant using the individual parameter t tests. This raises the question whether the other three variables further contribute to the prediction of
11.29 Predicting college debt: Inference. Refer to the previous exercise. Let’s proceed using the entire data set.a. Report the F statistic, its degrees of freedom, and the P-value. What do you conclude based on this test result?b. What percent of the variability in average debt is explained by
11.28 Predicting college debt: Multiple regression. Refer to Exercises 10.6 (page 536) and 10.11 (page 537) for a description of the problem and data set. Let’s now consider fitting a model to predict average debt (AveDebt) using all four explanatory variables: Admit, Grad4Rate, InCost, and
11.27 Refining the GPA model: Inference. Refer to Exercise 11.25. For each of the four models under consideration, report the least-squares equation, estimated model standard deviation s, and P-values for each of the individual coefficients. Based on these results and the residuals checks of the
11.26 Considering a transformation. When we regressed GPA versus the high school scores, the residuals were skewed to the left (Figure 11.7, page 583). Refit the model but now use GPA2 as the response variable. Does this transformed response improve the distribution of the residuals? Does the
11.25 Refining the GPA model: Residual checks. Figure 11.11 (page 574) provides a list of the top models based on R2 . Let’s look more closely at the four models listed with p=3 and p=4 . Fit each of these models to the data and obtain the residuals. Do the data fit to each of these models, at
11.24 Explaining the results. Refer to the previous exercise. A friend, knowing that these three categories were all weighted the same by Times Higher Education, does not understand why your model fit seems to suggest different weights for these three scores. Explain to your friend why this can
11.23 Multiple linear regression model. Refer to the previous two exercises. Let’s now consider a linear regression using all three explanatory variables.a. Write out the statistical model for this analysis, making sure to specify all assumptions.b. Run the multiple regression model and specify
11.22 Looking at the simple linear regressions. Refer to the previous exercise. Now look at the relationship between each explanatory variable and the total score.a. Generate scatterplots for each explanatory variable and the total score. Do these relationships all look linear?b. Compute the
11.21 Annual ranking of world universities. Since 2004, Times Higher Education has provided an annual ranking of the world universities. A total score for each university is calculated based on weighting the scores for the following five categories: Teaching (30%), Research (30%), Citations(30%),

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