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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
2.66 Add a different outlier. Refer to the previous two exercises. Add an additional observation with y=36 and x=30 to the original data set.a. Repeat the analysis that you performed in Exercise 2.64 and summarize your results, paying particular attention to the effect of this outlier.b. In this
2.65 Add an outlier. Refer to Exercise 2.64. Add an additional observation with y=25 and x=35 to the data set.Repeat the analysis that you performed in Exercise 2.64 and summarize your results, paying particular attention to the effect of this outlier.
2.64 Data generated by software. The following 20 observations on Y and X were generated by a computer program:X Y X Y 23.07 35.49 18.85 28.17 19.88 30.38 19.96 31.17 18.83 26.13 17.87 27.74 22.09 31.85 20.20 30.01 17.19 26.77 20.65 29.61 20.72 29.00 20.32 31.78 18.10 28.92 21.37 32.93 18.01 26.30
2.63 College students by state without the four largest states. Refer to Exercise 2.60, where you eliminated the four largest states that have populations greater than 15 million. FIGURE 2.22 gives software output for these data. Answer the questions in the previous exercise for the data set with
2.62 College students by state. Refer to Exercise 2.59, where you examined the relationship between the number of undergraduate college students and the populations for the 50 states. FIGURE 2.21 gives the output from a software package for the regression. Use this output to answer the following
2.61 Make predictions and compare. Refer to the two previous exercises. Consider a state with a population of 4 million. (This value is approximately the median population for the 50 states.)a. Using the least-squares regression equation for all 50 states, find the predicted number of undergraduate
2.60 College students by state without the four largest states. Refer to the previous exercise. Let’s eliminate the four largest states, which have populations greater than 15 million. Here are the numerical summaries: for number of undergraduate college students, the mean is 220,134 and the
2.59 College students by state. How well does the population of a state predict the number of undergraduates? The National Center for Education Statistics collects data for each of the 50 U.S. states that we can use to address this question.a. Make a scatterplot with population on the x axis and
2.58 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
2.57 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)find the predicted values for the
2.56 Compare the predictions. Refer to the two previous exercises. You have predicted two dominantarm bone strengths: one for a baseball player and one for a person who is not a baseball player. The nondominant bone strengths are both 16.0 Nm/1000.a. Compare the two predictions by computing the
2.55 Predict the bone strength for a baseball player. Refer to Exercise 2.53. A young male who is a baseball player has a bone strength of 16.0 Nm/1000 in his nondominant arm. Predict the bone strength in the dominant arm for this person.
2.54 Predict the bone strength. Refer to Exercise 2.52. A young male who is not a baseball player has a bone strength of 16.0 Nm/1000 in his nondominant arm. Predict the bone strength in the dominant arm for this person.
2.53 Bone strength for baseball players. Refer to the previous exercise. Similar data for baseball players are given in Exercise 2.15 (page 89). Here is the equation of the least-squares line for the baseball players:dominant =0.886+(1.373× nondominant)Answer parts (a) and (c) of the previous
2.52 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.a. Plot the data. Use the bone strength in the nondominant arm as the explanatory variable and bone strength in the dominant arm as the response
2.51 Fuel consumption for different types of vehicles. In Exercise 2.13 (page 89), you examined the relationship between CO2 emissions and highway fuel consumption for 1045 vehicles. You used different plotting symbols for the four different types of fuel used by these vehicles: regular, premium,
2.50 Fuel consumption. In Exercise 2.11 (page 88), you examined the relationship between CO2 emissions and highway fuel consumption for 502 vehicles that use regular fuel. In Exercise 2.32 (page 96), you found the correlation between these two variables.a. Find the equation of the least-squares
2.49 Blueberries and anthocyanins. In Exercise 2.8 (page 88), you examined the relationship between Antho3 and Antho4, two anthocyanins found in blueberries. In Exercise 2.30 (page 96), you found the correlation between these two variables.a. Find the equation of the least-squares regression line
2.48 What’s wrong? Explain what is wrong with each of the following:a. There is a high correlation between the age of American workers and their occupation.b. We found a high correlation(r=1.19)between students’ ratings of faculty teaching and ratings made by other faculty members.c. The
2.47 Internet use and babies. Figure 2.13 (page 90) is a scatterplot of the number of births per 1000 people versus Internet users per 100 people for 106 countries. In Exercise 2.24 (page 90), you described this relationship.a. Make a plot of the data similar to Figure 2.13 and report the
2.46 An interesting set of data. Make a scatterplot of the following data:x 1 2 3 4 10 10 y 1 3 3 5 1 11 Verify that the correlation is about 0.5. What feature of the data is responsible for reducing the correlation to this value despite a strong straight-line association between x and y in most of
2.45 Use the applet. You are going to use the Correlation and Regression applet to make different scatterplots with 10 points that have correlation close to 0.9. Many patterns can have the same correlation. Always plot your data before you trust a correlation.a. Stop after adding the first two
2.44 Use the applet. Go to the Correlation and Regression applet. Click on the scatterplot to create a group of 10 points in the lower-left corner of the scatterplot with a strong straight-line positive pattern (correlation about 0.9).a. Add one point at the upper right that is in line with the
2.43 Compare domestic with imported. In Exercise 2.21 (page 90), you compared domestic beers with imported beers with respect to the relationship between calories and percent alcohol. In that exercise, you used scatterplots to make the comparison. Compute the correlations for these two categories
2.42 Alcohol and calories in beer revisited. Refer to the previous exercise. The data that you used to compute the correlation include an outlier.a. Remove the outlier and recompute the correlation.b. Write a short paragraph about the possible effects of outliers on a correlation, using this
2.41 Alcohol and calories in beer. Figure 2.12 (page 90) gives a scatterplot of the calories versus percent alcohol for 160 brands of domestic beer.a. Compute the correlation for these data.b. Does the correlation do a good job of describing the direction and strength of this relationship? Explain
2.40 Brand names and generic products.a. If a store always prices its generic “store brand” products at 80% of the brand name products’ prices, what would be the correlation between the prices of the brand name products and the store brand products? (Hint: Draw a scatterplot for several
2.39 Decay in the log scale. Refer to the previous exercise and to Exercise 2.23(page 90), where the counts were transformed by a log.a. Find the correlation between the log counts and the time after the start of the first counting period.b. Does the correlation give a good numerical summary of the
2.38 Decay of a radioactive element. Data for an experiment on the decay of barium-137m is given in Exercise 2.22 (page 90).a. Find the correlation between the radioactive counts and the time after the start of the first counting period.b. Does the correlation give a good numerical summary of the
2.37 Student ratings of teachers. A college newspaper interviews a psychologist about student ratings of the teaching of faculty members. The psychologist says,“The evidence indicates that the correlation between the research productivity and teaching rating of faculty members is close to
2.36 Bone strength for baseball players. Refer to the previous exercise. Similar data for baseball players are given in Exercise 2.15 (page 89). Answer parts (a) and(b) of the previous exercise for these data.
2.35 Bone strength. Exercise 2.14 (page 89) gives the bone strengths of the dominant and the nondominant arms of 15 men who were controls in a study.a. Find the correlation between the bone strength of the dominant arm and the bone strength of the nondominant arm.b. Look at the scatterplot for
2.34 Strong association but no correlation. Here is a data set that illustrates an important point about correlation:X 45 55 65 75 85 Y 30 50 70 50 30a. Make a scatterplot of Y versus X.b. Describe the relationship between Y and X. Is it weak or strong? Is it linear?c. Find the correlation between
2.33 Fuel consumption for different types of vehicles. In Exercise 2.13 (page 89), you examined the relationship between CO2 emissions and highway fuel consumption for 1045 vehicles that use four different types of fuel. Find the correlations between CO2 and highway fuel consumption for each of
2.32 Fuel consumption. In Exercise 2.11 (page 88), you used a scatterplot to examine the relationship between CO2 emissions and highway fuel consumption for 502 vehicles that use regular fuel.Find the correlation between these two variables. Use the scatterplot and the correlation to describe the
2.31 Blueberries and anthocyanins with logs. In Exercise 2.9 (page 88), you examined the relationship between Antho4 and Antho3, two anthocyanins found in blueberries, using logs for both variables. Answer the questions in the previous exercise for the variables transformed in this way.
2.30 Blueberries and anthocyanins. In Exercise 2.8 (page 88), you examined the relationship between Antho4 and Antho3, two anthocyanins found in blueberries.a. Find the correlation between these two anthocyanins.b. Look at the scatterplot for these data that you made in part (a) of Exercise 2.8(or
2.29 Interpret some correlations. For each of the following correlations, describe the relationship between the two quantitative variables in terms of the direction and the strength of the linear relationship.a. r=0.01.b. r=0.8.c. r=−0.8.d. r=−0.2.
2.28 What’s wrong? Explain what is wrong with each of the following:a. A correlation of 2.0 indicates a very strong positive relationship.b. When reporting a correlation, you should always give its units.c. The correlation between two quantitative variables is always positive.d. Ashley obtains
2.27 Body mass and metabolic rate. Metabolic rate, the rate at which the body consumes energy, is important in studies of weight gain, dieting, and exercise. The following table gives data on the lean body mass and resting metabolic rate for 12 women and 7 men who are subjects in a study of
2.26 Make another plot. Refer to Exercise 2.24.a. Make a new data set that has Internet users expressed as users per 10,000 people and births as births per 10,000 people.b. Explain why these transformations to give new variables are linear transformations. (Hint: See linear transformations on page
2.25 Try a log. Refer to the previous exercise.a. Make a scatterplot of the log of births per 1000 people versus Internet users per 100 people.b. Describe the relationship that you see in this plot and compare it with Figure 2.13.c. Which plot do you prefer? Give reasons for your answer.
2.24 Internet use and babies. The World Bank collects data on many variables related to world development for countries throughout the world. Two of these variables are Internet use, in number of users per 100 people, and births per 1000 people.FIGURE 2.13 is a scatterplot of birth rate versus
2.23 Use a log for the radioactive decay. Refer to the previous exercise. Transform the counts using a log transformation. Then repeat parts (a) through (e) for the transformed data and compare your results with those from the previous exercise.
2.22 Decay of a radioactive element. Barium-137m is a radioactive form of the element barium that decays very rapidly. It is easy and safe to use for lab experiments in schools and colleges. In a typical experiment, the radioactivity of a sample of barium-137m is measured for one minute. It is then
2.21 Compare domestic with imported. Plot calories versus percent alcohol for domestic and imported beers on the same scatterplot. Use different colors or symbols for the two types of beers. Summarize what this plot tells you about the relationship and the difference between the two types of beer.
2.20 Imported beer. The beer100.com website also gives data for imported beers. Describe the relationship between calories and percent alcohol for these imported beers. Use percent alcohol as the explanatory variable and calories as the response variable.
2.19 More beer. Refer to the previous exercise.a. Make a scatterplot of calories versus percent alcohol using the data set without the outlier.b. Describe the relationship between these two variables. If your software is capable, use a line and smoothers to explore the relationship.
2.18 What’s in the beer? The website beer100.com advertises itself as “Your Place for All Things Beer.” One of their “things” is a list of 160 domestic beer brands with the percent alcohol, calories per 12 ounces, and carbohydrates per 12 ounces (in grams).a. FIGURE 2.12 gives a
2.17 Graduation in four years and undergraduate major. How well does your undergraduate major predict the chance that you will graduate in four years? Data for a sample of 1200 recent college graduates were analyzed to address this question. What are the explanatory and response variables? Are
2.16 Compare the baseball players with the controls. Refer to the previous two exercises.a. Plot the data for the two groups on the same graph, using different symbols for the baseball players and the controls.b. Use your plot to describe and compare the relationships for the two variables. Write a
2.15 Bone strength for baseball players. Refer to the previous exercise. The study collected arm bone strength information for two groups of young men. The data in the previous exercise were for a control group. The second group (Group=“Baseball”) in the study comprised men who played baseball.
2.14 Bone strength. Osteoporosis is a condition where bones become weak. It affects more than 200 million people worldwide.Exercise is one way to produce strong bones and to prevent osteoporosis. Because we use our dominant arm (the right arm for most people) more than our nondominant arm, we
2.13 Fuel consumption for different types of vehicles. Refer to the previous two exercises. Those exercises examined data for vehicles that used regular fuel. Data are also available for vehicles that use several other types of fuel. There are 1045 vehicles in total. The variable Fuel has four
2.12 Fuel consumption with a line. Refer to the previous exercise.a. Add a line to the plot. To what extent to you think that the line does a good job of summarizing the relationship?b. If your have the appropriate software, use smooth curves to examine the relationship. Does your analysis support
2.11 Fuel consumption. Natural Resources Canada tests new vehicles each year and reports several variables related to fuel consumption for vehicles in different classes. For 2018 the group provides data for 502 vehicles that use regular fuel. Two variables reported are carbon dioxide
2.10 Blueberries and anthocyanins: Raw data or logs. Refer to Exercises 2.8 and 2.9.a. Compare your results from the two exercises.b. For exploring and explaining the relationship between Antho4 and Antho3, do you prefer the analysis you performed in Exercise 2.8 or the one you performed in
2.9 Blueberries and anthocyanins with logs. Refer to the previous exercise. In Exercises 1.124 and 1.125 (page 69), you examined the distributions of Antho3 and Antho4. Transform each of the variables with a log, make a scatterplot, and answer the questions in the previous exercise for the
2.8 Blueberries and anthocyanins. Anthocyanins are compounds that appear to have some health benefits for bones, the heart, and the brain. Blueberries are a good source of many different anthocyanins.Researchers at the Piedmont Research Station of North Carolina State University have assembled a
2.7 What’s wrong? Explain what is wrong with each of the following:a. In a scatterplot, we put the response variable on the x axis and the categorical variable on the y axis.b. If two variables are positively associated, then high values of one variable are associated with low values of the other
2.6 Make some sketches. For each of the following situations, make a scatterplot that illustrates the given relationship between two variables.a. A weak negative linear relationship.b. No apparent relationship.c. A strong positive relationship that is not linear.d. A more complicated relationship.
2.5 Volleyball tickets and performance. For the teams in the Atlantic Coast Conference last year, plan a study of the relationship between the average number of tickets sold for women’s home volleyball matches and the percent of games won.Give the key characteristics of the data that could be
2.4 Driver’s education. Think about a study designed to examine the relationship between whether a driver aged 18 or less completed a driver’s education program and the number of accidents they had in the year after they received their license.Describe a data set that could be used for this
2.3 Buy and sell prices of used textbooks. Think about a study designed to compare the prices of textbooks for third- and fourthyear college courses in five different majors. For each text, you compute the difference between the price paid for a used textbook and the price the seller gives back
2.2 Explanatory or response? For each of the following scenarios, classify each of the pair of variables as explanatory or response or neither. Give reasons for your answers.a. The quality rating of a laundry detergent and the price per load of the detergent.b. The day of the week and the amount of
2.1 High click counts on Twitter. A study was done to identify variables that might produce high click counts on Twitter. You and 14 of your friends collect data on all of your tweets for a week. You record the number of click counts, the length of each tweet, the outside temperature, whether it is
1.125 Blueberries and anthocyanins, Antho4. Refer to Exercise 1.122.Generate your own output for the analysis of Antho4 and use your output to write a summary of the distribution of Antho4 using the methods and ideas that you learned in this chapter.
1.124 Blueberries and anthocyanins, Antho3. Refer to Exercise 1.122.FIGURE 1.36 gives the JMP output for Antho3. Use this output to write a summary of the distribution of Antho3 using the methods and ideas that you learned in this chapter.FIGURE 1.36 JMP descriptive statistics for Antho3, Exercise
1.123 Blueberries and anthocyanins, Antho2. Refer to the previous exercise. Generate your own output for the analysis of Antho2 and use your output to write a summary of the distribution of Antho2 using the methods and ideas that you learned in this chapter.
1.122 Blueberries and anthocyanins. Anthocyanins are compounds that have been associated with health benefits to the heart, bones, and brain.40 Blueberries are a good source of many different anthocyanins. Researchers at the Piedmont Research Station of North Carolina State University have
1.121 Phish. One of the most favored songs of the band Phish is“Divided Sky.” The band plays this song at many of their concerts.Frequently, after the main theme, Trey, the guitarist, pauses before playing the resolving note. The data file PHISH gives the date of each concert where “Divided
1.120 Spam filters. A university department installed a spam filter on its computer system. During a 21-day period, 6693 messages were tagged as spam. How much spam you get depends on what your online habits are.Here are the counts for some students and faculty in this department (with log-in IDs
1.119 Time spent studying. Do women study more than men? We asked the students in a large first-year college class how many minutes they studied on a typical weeknight. Here are the responses of random samples of 30 women and 30 men from the class:Women Men 170 120 180 360 240 80 120 30 90 200 120
1.118 How much vitamin C do men consume? To evaluate whether or not the intake of a vitamin or mineral is adequate, comparisons are made between the intake distribution and the requirement distribution.Here is some information about the distribution of vitamin C intake, in milligrams per day, for
1.117 How much vitamin C do women consume? To evaluate whether or not the intake of a vitamin or mineral is adequate, comparisons are made between the intake distribution and the requirement distribution.Here is some information about the distribution of vitamin C intake, in milligrams per day, for
1.116 How much vitamin C do men need? Refer to the previous exercise. For men aged 19 to 30 years, the EAR is 75 milligrams per day(mg/d), the RDA is 90 mg/d, and the UL is 2000 mg/d. Answer the questions in the previous exercise for this population.
1.115 How much vitamin C is needed? The Food and Nutrition Board of the Institute of Medicine, working in cooperation with scientists from Canada, have used scientific data to answer this question for a variety of vitamins and minerals. Their methodology assumes that needs, or requirements, follow
1.114 Leisure time for college students. You want to measure the amount of “leisure time” that college students enjoy. Write a brief discussion of two issues:a. How will you define “leisure time”?b. Once you have defined leisure time, how will you measure it?
1.113 Travel and tourism in Canada. Refer to the previous exercise.Under the “Subjects” tab, choose “Travel and tourism.” Pick some data from the resources listed and use the methods that you learned in this chapter to create graphical and numerical summaries. Write a report summarizing
1.112 Canadian international trade. The government organization Statistics Canada provides data on many topics related to Canada’s population, resources, economy, society, and culture. Go to the web page statcan.gc.ca/start-debut-eng.html. Under the “Subjects” tab, choose“International
1.111 What graph would you use? What type of graph or graphs would you plan to make in a study of each of the following issues?a. What makes of cars do students drive? How old are their cars?b. How many hours per week do students study? How does the number of study hours change during a semester?c.
1.110 Flopping in the World Cup. Soccer players are often accused of spending an excessive amount of time dramatically falling to the ground followed by other activities, in attempts to show that a possible injury is very serious. It has been suggested that these tactics are often designed to
1.109 Highway fuel consumption. Refer to the previous exercise. Use graphical and numerical summaries to describe the distribution of highway fuel consumption for these vehicles. Be sure to justify your choice of summaries.
1.108 CO2 emissions in vehicles. Natural Resources Canada tests new vehicles each year and reports several variables related to fuel consumption for vehicles in different classes. For 2018, it provides data for 502 vehicles that use conventional fuel. Two variables reported are carbon
1.107 Sources of renewable energy consumed. Refer to the previous exercise. Renewable energy is classified into five sources. Here are the 2008 amd 2018 energy data for these sources:Amount Source 2008 2018 Hydroelectric 2.511 2.688 Geothermal 0.192 0.218 Solar 0.074 0.951 Wind 0.546 2.533 Biomass
1.106 Sources of energy consumed. Energy consumed in the United States can be classified as coming from one of three sources: fossil fuels, nuclear and electric power, and renewable energy. In 2018, the energy from these three sources was 81.0, 8.4, and 11.5 quadrillion Btu, respectively. In 2008,
1.105 Potassium from a supplement. Refer to Exercise 1.16 (page 22), where you used a stemplot to examine the potassium absorption of a group of 29 adults who ate a controlled diet that included 40 mEq of potassium from a supplement for five days. In Exercise 1.34 (page 43), you compared the
1.104 Potassium from potatoes. Refer to Exercise 1.15 (page 22), where you used s stemplot to examine the potassium absorption of a group of 27 adults who ate a controlled diet that included 40 mEq of potassium from potatoes for five days. In Exercise 1.33 (page 43), you compared the stemplot, the
1.103 Longleaf pine trees. Exercise 1.56 (page 46) gives the diameter at breast height (DBH) for 40 longleaf pine trees from the Wade Tract in Thomas County, Georgia. Make a Normal quantile plot for these data and write a short paragraph interpreting what it describes.
1.102 Deciles of HDL cholesterol. The deciles of any distribution are the 10th, 20th, . . . , 90th percentiles. Refer to Exercise 1.95 where we assumed that the distribution of HDL cholesterol in U.S.women aged 20 and over is Normal with mean 55 mg/dl and standard deviation 15.5 mg/dl. Find the
1.101 Outliers for Normal distributions. Continue your work from the previous two exercises.The percent of the observations that are suspected outliers according to the 1.5 × IQR rule is the same for any Normal distribution. What is this percent?
1.100 IQR for Normal distributions. Continue your work from the previous exercise. The interquartile range IQR is the distance between the first and third quartiles of a distribution.a. What is the value of the IQR for the standard Normal distribution?b. There is a constant c such that IQR = cσ
1.99 Quartiles for Normal distributions. The quartiles of any distribution are the values with cumulative proportions 0.25 and 0.75.a. What are the quartiles of the standard Normal distribution?b. Using your numerical values from (a), write an equation that gives the quartiles of the N(μ, σ)
1.98 Deciles of Normal distributions. The deciles of any distribution are the 10th, 20th, . . . , 90th percentiles. The first and last deciles are the 10th and 90th percentiles, respectively.a. What are the first and last deciles of the standard Normal distribution?b. The weights of 9-ounce potato
1.97 Diagnosing osteoporosis. Osteoporosis is a condition in which the bones become brittle due to loss of minerals. To diagnose osteoporosis, an elaborate apparatus measures bone mineral density (BMD).BMD is usually reported in standardized form. The standardization is based on a population of
1.96 Men and HDL cholesterol. HDL cholesterol levels for men have a mean of 46 mg/dl, with a standard deviation of 13.6 mg/dl. Assume that the distribution is Normal. Answer the questions given in the previous exercise for the population of men.
1.95 Do you have enough “good cholesterol”? High-density lipoprotein (HDL) is sometimes called the“good cholesterol” because high values are associated with a reduced risk of heart disease. According to the American Heart Association, people over the age of 20 years should have at least 40
1.94 Find the SAT quartiles. The quartiles of any distribution are the values with cumulative proportions 0.25 and 0.75. What are the quartiles of the distribution of SAT scores?
1.93 Find the ACT quintiles. The quintiles of any distribution are the values with cumulative proportions 0.20, 0.40, 0.60, and 0.80. What are the quintiles of the distribution of ACT scores?
1.92 How low is the bottom 15%? What SAT scores make up the bottom 15% of all scores?
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