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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

3.11 A different design for online sales of running shoes. Refer to Exercise 3.9. Here is another way in which the experiment could be designed. Suppose that you randomly select a strategy each time a customer visits the website. Discuss this experiment in terms of the principles of experimental
3.10 A different randomization for online sales of running shoes. Refer to the previous exercise.Suppose that for each day, you randomized the web pages, showing each of the strategies on 5 days. Do you prefer this experiment or the one in the previous exercise? Give reasons for your answer.
3.9 Online sales of running shoes. A company that sells running shoes online wants to compare three new marketing strategies. It will test the strategies on 15 weekdays. For the first 5 weekdays, a web page describing the comfort of the running shoes will be displayed. For the next 5 weekdays days,
3.8 Does acupuncture reduce pain? Some claim that acupuncture (insertion of very small needles under the skin) can be used to reduce pain. Design an experiment to test this claim. Write a proposal requesting funding for your study, giving all the important details, including the number of subjects,
3.7 Blueberries and bones. A study of the effects of blueberries on the bones of mice compared diets containing no blueberries, blueberries as 4% of the diet, and blueberries as 8% of the diet. Twelve mice were randomly assigned to each diet. The mice were fed the diets for 30 days, and the total
3.6 Online homework. Thirty students participated in a study designed to evaluate a new online homework system. None of the students had used an online homework system in the past. After using the system for a month, they were asked to rate their satisfaction with the system using a five-point
3.5 Does echinacea reduce the severity of the common cold? In a study designed to evaluate the benefits of taking echinacea when you have a cold, 719 patients were randomly divided into four groups. The groups were (1) no pills, (2) pills that had no echinacea, (3) pills that had echinacea but the
3.4 What’s wrong? Explain what is wrong in each of the following statements.a. Anecdotal data always come from an experiment.b. A sample survey collects information on all subjects in the population of interest.c. A treatment is imposed in a sample survey.
3.3 Satisfaction with allocation of concert tickets. Your college sponsored a concert that sold out.a. After the concert, an article in the student newspaper reported interviews with three students who were unable to get tickets and were very upset. What kind of data does this represent? What kinds
3.2 More about tuna. According to a story in Consumer Reports, three major producers of canned tuna agreed to pay $3,300,000 to settle claims in California that the amount of tuna in their cans was less than the amount printed on the label of the cans. What kind of data do you think was used in
3.1 Not enough tuna. You like to eat tuna sandwiches. Recently you have noticed that there does not seem to be as much tuna as you expect when you open the can. Identify the type of data that this represents and describe how it can or cannot be used to reach a conclusion about the amount of tuna in
The first output shows an expanded dropdown list menu, bivariate fit of Antho 2 by Antho 1. Below it is a scatterplot which plots Antho 2 on the vertical axis, ranging from 0 to 3.5 in increments of 0.25, versus Antho 1 on the horizontal axis, ranging from 0 to 3.5 in increments of 0.25. Hundreds
2.153 Blueberries and anthocyanins. FIGURE 2.41 gives JMP output for using Antho1 to predict Antho2. Use this output to write a summary of this relationship, using the methods and ideas that you learned in this chapter.FIGURE 2.41 Selected JMP outputs for examining the relationship between Antho2
2.152 Blueberries and anthocyanins. Refer to Exercises 1.122 and 1.123 (page 69), where you described the distributions of Antho3 and Antho4. Use Antho3 to predict Antho4. Write a summary of this relationship, using the methods and ideas that you learned in this chapter.
2.151 Survival, class, and sex on the Titanic. Refer to the previous exercise and Exercise 2.100 (page 138). When we looked at survival and class, we ignored sex. When we looked at survival and sex, we ignored class. Are we missing something interesting about these data when we choose this approach
2.150 Survival and sex on the Titanic. In Exercise 2.100 (page 138), you examined the relationship between survival and class on the Titanic. The data file TITANIC contains data on the sex of the Titanic passengers. Examine the relationship between survival and sex and write a short summary of your
2.149 Restricting the range for blueberries and anthocyanins. Refer to Exercises 2.8 and 2.30, where you examined the variables Antho4 and Antho3. Report the least-squares regression line, using Antho3 to predict Antho4. Also report the correlation between these two variables. The data file BERRIER
2.148 Averaged date for blueberries and anthocyanins. Refer to Exercises 2.8 and 2.30, where you examined the variables Antho4 and Antho3. Report the least-squares regression line, using Antho3 to predict Antho4. Also report the correlation between these two variables. The variables Antho4M and
2.147 Recycled product quality. Recycling is supposed to save resources. Some people think recycled products are lower in quality than other products, a fact that makes recycling less practical. People who actually use a recycled product may have different opinions from those who don’t use it.
2.146 More smokers live at least 20 more years! You can see the headlines: “More smokers than nonsmokers live at least 20 more years after being contacted for study!” A medical study contacted randomly chosen people in a district in England. Here are data on the 1314 women contacted who were
2.145 Class size and class level. A university classifies its classes as either“small” (fewer than 40 students) or “large.” A dean sees that 62% of Department A’s classes are small, while Department B has only 40% small classes. She wonders if she should cut Department A’s budget and
2.144 Simpson’s paradox and regression. Simpson’s paradox occurs when a relationship between variables within groups of observations reverses when all of the data are combined. The phenomenon is usually discussed in terms of categorical variables, but it also occurs in other settings. Here is
2.143 An example of Simpson’s paradox. Mountain View University has professional schools in business and law. Here is a three-way table of applicants to these professional schools, categorized by sex, school, and admission decision:Business Law Sex Admit Sex Admit Yes No Yes No Male 400 200 Male
2.142 Distribution of the residuals. Some statistical methods require that the residuals from a regression line have a distribution that is approximately Normal. The residuals for the education spending example are plotted in Example 2.33 (page 117). Is their 38 distribution close to Normal? Make a
2.141 Plywood strength. How strong is a building material such as plywood? To be specific, support a 24-inch by 2-inch strip of plywood at both ends and apply force in the middle until the strip breaks. The modulus of rupture (MOR) is the force needed to break the strip. We would like to be able to
2.140 Predicting text pages. The editor of a statistics text would like to plan for the next edition. A key variable is the number of pages that will be in the final version. Text files are prepared by the authors using a word processor called LaTeX, and separate files contain figures and tables.
2.139 Firefighters and fire damage. Someone says, “There is a strong positive correlation between the number of firefighters at a fire and the amount of damage the fire does. So sending lots of firefighters just causes more damage.” Explain why this reasoning is wrong.
2.138 Bigger raises for those earning less. Refer to the previous two exercises. The 2019–2020 salaries do an excellent job of predicting the 2020–2021 salaries. Is there anything more that we can learn from these data? In this department, there is a tradition of giving higher-than-average
2.137 Find the line and examine the residuals. Refer to the previous exercise.a. Find the least-squares regression line for predicting 2020–2021 salaries from 2019–2020 salaries.b. Analyze the residuals, paying attention to any outliers or influential observations.Write a summary of your
2.136 Faculty salaries. Here are the salaries for a sample of professors in a mathematics department at a large midwestern university for the academic years 2019–2020 and 2020–2021:2019–2020 salary ($) 2020–2021 salary ($) 2019–2020 salary ($) 2020–2021 salary ($)160,600 163,700 151,650
2.135 Make some predictions. The individual whose salary we have been studying wants to do some financial planning. Specifically, she would like to predict her salary six years into the future—that is, for Year 26. She is willing to assume that her employment situation will be stable for the next
2.134 Try logs. Refer to the previous two exercises. FIGURE 2.39 is a scatterplot with the least-squares regression line for log salary versus year. For this model, r2=0.9995 .a. Compare this plot with Figure 2.37. Write a short summary of the similarities and the differences.b. FIGURE 2.40 is a
2.133 Look at the residuals. Refer to the previous exercise. FIGURE 2.38 is a plot of the residuals versus year.a. Interpret the residual plot.b. Explain how this plot highlights the deviations from the least-squares regression line that you can see in Figure 2.37.FIGURE 2.38 Plot of residuals
2.132 Salaries and raises. For this exercise, we consider a hypothetical employee who starts working in Year 1 with a salary of $50,000. Each year her salary increases by approximately 5%. By Year 20, she is earning $126,000. The following table gives her salary for each year (in thousands of
2.131 Graduation rates. One of the factors used to evaluate undergraduate programs is the proportion of incoming students who graduate. This quantity, called the graduation rate, can be predicted by other variables such as the SAT or ACT scores and the high school records of the incoming students.
2.130 Fields of study by country for college students. In the previous exercise you examined data on fields of study for graduating college students from seven countries.a. Find the seven conditional distributions of graduates in the different fields of study for each country.b. Display the
2.129 Fields of study for college students. The table below gives the number of students(in thousands) graduating from college with degrees in several fields of study for seven countries:a. Calculate the marginal totals and add them to the table.b. Find the marginal distribution of country and give
2.128 Records for men and women in the 10K. TABLE 2.4 shows the progress of world record times (in seconds) for the 10,000-meter run for both men and women.a. Make a scatterplot of world record time against year, using separate symbols for men and women. Describe the pattern for each sex. Then
2.127 Compare the provinces with the territories. Refer to the previous exercise. The three Canadian territories are the Northwest Territories, Nunavut, and the Yukon Territories. All the other entries in Figure 2.35 are provinces.a. Generate a scatterplot of the Canadian demographic data similar
2.126 Nunavut. Refer to the previous exercise and Figures 2.35 and 2.36.a. Do you think that Nunavut is an outlier?b. Make a residual plot for these data. Comment on the size of the residual for Nunavut.Use this information to expand on your answer to part (a).c. Find the value of the correlation
2.125 Population in Canadian provinces and territories. Statistics Canada provides a great deal of demographic data organized in different ways. FIGURE 2.35 gives the percent of the population aged over 65 and the percent aged under 5 for each of the 13 34 Canadian provinces and territories. FIGURE
2.124 Sales and production. Refer to the previous two exercises.a. Make a scatterplot with sales as the response variable and production as the explanatory variable. Describe the relationship. Are there any outliers or influential observations?b. Find the least-squares regression line and add it to
2.123 Dwelling permits and production. Refer to the previous exercise.a. Make a scatterplot with production as the response variable and permits issued for new dwellings as the explanatory variable. Describe the relationship. Are there any outliers or influential observations?b. Find the
2.122 Dwelling permits and sales for 19 countries. The Organisation for Economic Cooperation and Development collects data on main economic indicators (MEIs) for many countries. Each variable is recorded as an index, with the year 2010 serving as a base year.This means that the variable for each
2.121 Effect of a math skills refresher initiative. Students enrolling in an elementary statistics course take a pretest that assesses their math skills. Those who receive low scores are given the opportunity to take three one-hour refresher sessions designed to review the basic math skills needed
2.120 Exercise and mortality. A sign in a fitness center says, “Mortality is halved for men over 65 who walk at least 2 miles a day.”a. Mortality is eventually 100% for everyone. What do you think “mortality is halved” means?b. Assuming that the claim is true, explain why this fact does not
2.119 Artificial sweeteners. People who use artificial sweeteners in place of sugar tend to be heavier than people who use sugar. Does this mean that artificial sweeteners cause weight gain? Give a more plausible explanation for this association.
2.118 Watching TV and low grades. Children who watch many hours of television get lower grades in school, on the average, than those who watch less TV. Explain clearly why this fact does not show that watching TV causes poor grades. In particular, suggest some other variables that may be confounded
2.117 Hospital size and length of stay. A study shows that there is a positive correlation between the size of a hospital (measured by its number of beds x) and the median number of days y that patients remain in the hospital. Does this mean that you can shorten a hospital stay by choosing a small
2.116 Computer chip manufacturing and miscarriages. A study showed that women who work in the production of computer chips have abnormally high numbers of miscarriages. The union claimed that exposure to chemicals used in production caused the miscarriages. Another possible explanation is that
2.115 Exercise and self-confidence. A college fitness center offers an exercise program for staff members who choose to participate. The program assesses each participant’s fitness, using a treadmill test, and also administers a personality questionnaire. There is a moderately strong positive
2.114 Marriage and income. Data show that men who are married, and also divorced or widowed men, earn quite a bit more than men who have never been married. This does not mean that a man can raise his income by getting married. Suggest several lurking variables that you think are confounded with
2.113 Online courses. Many colleges offer online versions of courses that are also taught in the classroom. It often happens that the students who enroll in the online version do better than the classroom students on the course exams. This does not show that online instruction is more effective
2.112 Stress and lack of sleep in college students. Studies of college students have shown that stress and lack of sleep are associated. Do you think that lack of sleep causes stress or that stress causes lack of sleep? Write a short paragraph summarizing your opinions.
2.111 Iron and anemia. A lack of adequate iron in the diet is associated with anemia, a condition in which the body does not have enough red blood cells. However, anemia is also associated with malaria and infections from worms called helminths. Discuss these observed associations using the
2.110 The five criteria for establishing causation. Consider the five criteria for establishing causation when an experiment is not possible. Explain how each of these, if not established seriously, weakens the case that an association is due to causation.
2.109 Examples of association. Give three examples of association: one due to causation, one due to common response, and one due to confounding. Use your examples to write a short paragraph explaining the differences among these three explanations for an observed association.
2.108 Construct a table with no association. Construct a 2×4 table of counts where there is no apparent association between the row and column variables.
2.107 Complete the table. Here are the row and column totals for a two-way table with two rows and two columns:a b 400 c d 200 400 200 600 Find two different sets of countsa, b,c, and d for the body of the table that give these same totals. This shows that the relationship between two variables
2.106 Patients in “poor” or “good” condition. Refer to the previous exercise. Not all surgery cases are equally serious. Patients are classified as being in either “poor” or“good” condition before surgery. Here are the data broken down by patient condition.The entries in the
2.105 Which hospital is safer? Insurance companies and consumers are interested in the performance of hospitals. The government releases data about patient outcomes in hospitals that can be useful in making informed health care decisions. Here is a twoway table of data on the survival of patients
2.104 Adequate sleep and exercise. Refer to the previous exercise.a. Find the distribution of exercise for those who get adequate sleep.b. Do the same for those who do not get adequate sleep.c. Write a short summary of the relationship between adequate sleep and exercise, using the results of parts
2.103 Exercise and adequate sleep. A survey of 656 boys and girls, who were 13 to 18 years old, asked about adequate sleep and other health-related behaviors. The recommended amount of sleep is six to eight hours per night. In the survey, 59% of the respondents reported that they got less than this
2.102 Trust and honesty in the workplace. The students surveyed in the study described in the previous exercise were also asked whether they thought trust and honesty are essential in business and the workplace. FIGURE 2.33 gives software output for these data. Use this output to analyze these data
2.101 Lying to a teacher. One of the questions in a survey of high school students asked about lying to teachers. The data set LYING gives the numbers of students who said that they lied to a teacher about something significant at least once during the past year, classified by sex. FIGURE 2.32
200. For second- and third-class passengers who survived, the numbers were 119 and 181, respectively. Let’s look at these data with a two-way table.a. Create a two-way table that you could use to explore the relationship between survival and class.b. Which variable is the explanatory variable,
2.100 Survival and class on the Titanic. On April 15, 1912, on her maiden voyage, the Titanic collided with an iceberg and sank. The ship was luxurious but did not have enough lifeboats for the 2224 passengers and crew. As a result of the collision, 1502 people died. The level of luxury and the
2.99 Eight is enough. A healthy body needs good food, and healthy teeth are needed to chew our food so that it can nourish our bodies. The U.S. Army has recognized this fact and requires recruits to pass a dental examination. If you wanted to be a soldier in the Spanish American War, which took
2.98 Music and video games. You are planning a study of undergraduates in which you will examine the relationship between listening to music and playing video games.The study subjects will be asked how much time they spend in each of these activities during a typical day. The choices for both
2.97 Does driver’s ed help? A study is planned to look at the effect of driver education programs on accidents. The driving records of all drivers under 18 in a given year will classify each driver as having taken a driver’s education course or not. The drivers will also be classified with
2.96 Dangers of not looking at a plot. Table 2.1 (page 112) presents four sets of data prepared by the statistician Frank Anscombe to illustrate the dangers of calculating without first plotting the data.a. Use x to predict y for each of the four data sets. Find the predicted values and residuals
2.95 Education and income. There is a strong positive correlation between years of education and income for economists employed by business firms. (In particular, economists with doctorates earn more than economists with only a bachelor’s degree.) There is also a strong positive correlation
2.94 Use the applet. Go to the Correlation and Regression applet. Click on the scatterplot to create a group of 15 points in the lower-right corner of the scatterplot with a strong straight-line pattern(correlation about −0.6) .Now display the regression line.a. Add one point at the upper left
2.93 Use the applet. It isn’t easy to guess the position of the least-squares line by eye. Use the Correlation and Regression applet to compare a line you draw with the least-squares line. Create a group of 12 points from lower left to upper right with a clear, positive straight-line pattern
2.92 Price and ounces. In Example 2.2 (page 73) and Check-in question 2.3 (page 74), we examined the relationship between the price and the size of a Mocha Frappuccino®. The 12-ounce Tall drink costs $4.75, the 16-ounce Grande is $5.25, and the 24-ounce Venti is $5.75.a. Plot the data and describe
2.91 Does herbal tea help nursing-home residents? A group of college students believes that herbal tea has remarkable powers. To test this belief, they make weekly visits to a local nursing home, where they visit with the residents and serve them herbal tea. The nursing-home staff report that after
2.90 Are big hospitals bad for you? A study shows that there is a positive correlation between the size of a hospital (measured by its number of beds x) and the median number of days y that patients remain in the hospital. Does this mean that you can shorten a hospital stay by choosing a small
2.89 How’s your self-esteem? People who do well tend to feel good about themselves. Perhaps helping people feel good about themselves will help them do better in their jobs and in life. For a time, raising self-esteem became a goal in many schools and companies. Can you think of explanations for
2.88 A lurking variable. The effect of a lurking variable can be surprising when individuals are divided into groups. In recent years, the mean SAT score of all high school seniors has increased.But the mean SAT score has decreased for students at each level of high school grades (A, B, C, and so
2.87 Internet use and babies. Exercise 2.24 (page 90) explores the relationship between Internet use and birth rate for 106 countries. Figure 2.13 (page 90) is a scatterplot of the data. It shows a negative association between these two variables. Do you think that this plot indicates that Internet
2.86 What’s wrong? Each of the following statements contains an error. Describe each error and explain why the statement is wrong.a. A lurking variable is always quantitative.b. If the residuals are all positive, this implies that there is a positive relationship between the response variable and
2.85 What’s wrong? Each of the following statements contains an error. Describe each error and explain why the statement is wrong.a. If we have data at values of x equal to 11, 12, 13, 14, and 15, and we try to predict the value of y for x=13.5 using a least-squares regression equation, we are
2.84 Make some scatterplots. For each of the following scenarios, make a scatterplot with 12 observations that show a moderate positive association, plus one that illustrates the unusual case.Explain each of your answers.a. An outlier in x that is influential for the regression.b. An outlier in x
2.83 College students by state using logs. Refer to the previous exercise. Answer parts (a) through (f)for that exercise using the logs of both variables. Write a short paragraph summarizing your findings and comparing them with those from the previous exercise.
2.82 College students by state. Refer to Exercise 2.59 (page 110), where you examined the relationship between the number of undergraduate college students and the populations for the 50 U.S.states.a. Make a scatterplot of the data with the least-squares regression line.b. Plot the residuals versus
2.81 Least-squares regression for the log counts. Refer to Exercise 2.23 (page 90), where you analyzed the radioactive decay of barium-137m data using log counts. Here are the data:Time 1 3 5 7 Log count 6.35957 5.75890 5.31321 4.77068a. Using the least-squares regression equation log count
2.80 Least-squares regression for radioactive decay. Refer to Exercise 2.22 (page 90) for the data on radioactive decay of barium-137m. Here are the data:Time 1 3 5 7 Count 578 317 203 118a. Using the least-squares regression equation count =602.8−(74.7× time)and the observed data, find the
2.79 Extrapolation for baseball players’ bone strength. Refer to Exercise 2.76. Would you be concerned that the least-squares regression equation would not be accurate for each of these values of nondominant arm strength: 10.0, 13.0, 16.0, 19.0, 30.0?
2.78 Extrapolation for bone strength. Refer to Exercise 2.76. Would you be concerned that the leastsquares regression equation would not be accurate for each of these values of nondominant arm strength: 10.0, 13.0, 16.0, 19.0, 30.0?
2.77 Bone strength for baseball players. Refer to the previous exercise. Similar data for baseball players is given in Exercise 2.15 (page 89). The equation of the least-squares line for the baseball players is dominant =0.886+(1.373× nondominant)Here are the data for the first four cases:ID
2.76 Bone strength. Exercise 2.14 (page 89) gives the bone strengths of the dominant and the nondominant arms for 15 men who were controls in a study. The least-squares regression line for these data is dominant =2.74+(0.936× nondominant)Here are the data for four cases:ID Nondominant Dominant ID
2.75 Class attendance and grades. A study of class attendance and grades among first-year students at a state university showed that, in general, students who missed a higher percent of their classes earned lower grades. Class attendance explained 25% of the variation in grade index among the
2.74 A property of the least-squares regression line. Use the equation for the least-squares regression line to show that this line always passes through the point(x¯,y¯) .
2.73 Use an applet for progress in math scores. Go to the Two-Variable Statistical Calculator applet. Enter the data for the progress in math scores from Exercise 2.70. Using only the results provided by the applet, write a short report summarizing the analysis of these data.
2.72 Metabolic rate and lean body mass. Compute the mean and the standard deviation of the metabolic rates and lean body masses in Exercise 2.27 (page 91) and the correlation between these two variables. Use these values to find the slope of the regression line of metabolic rate on lean body
2.71 The regression equation. The equation of a least-squares regression line is y=25+8x .a. What is the value of y for x=−3 ?b. If x increases by one unit, what is the corresponding change in y?c. What is the intercept for this equation?
2.70 Progress in math scores. Every few years, the National Assessment of Educational Progress asks a national sample of eighth-graders to perform the same math tasks. The goal is to get an honest picture of progress in math. Here are a few national mean scores, on a scale of 0 to 500:Year 1990
2.69 Always plot your data! Table 2.1 presents four sets of data prepared by the statistician Frank Anscombe to illustrate the dangers of calculating without first plotting the data.a. Without making scatterplots, find the correlation and the least-squares regression line for all four data sets.
2.68 Alcohol and calories in beer revisited. Refer to the previous exercise. The data that you used includes an outlier.a. Remove the outlier and answer parts (a), (b), and (c) for the new set of data.b. Write a short paragraph about the possible effects of outliers on a least-squares regression
2.67 Alcohol and calories in beer. Figure 2.12 (page 90) gives a scatterplot of calories versus percent alcohol in 160 brands of domestic beer.a. Find the equation of the least-squares regression line for these data.b. Find the value of r2 and interpret it in the regression context.c. Write a short

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