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Statistics The Exploration And Analysis Of Data 6th Edition John M Scheb, Jay Devore, Roxy Peck - Solutions

=+a. For this study, what is the dependent variable? What is the predictor variable?
=+5.19 A sample of 548 ethnically diverse students from Massachusetts were followed over a 19-month period from 1995 and 1997 in a study of the relationship between TV viewing and eating habits (Pediatrics [2003]: 1321–1326). For each additional hour of television viewed per day, the number of
=+a. Construct a scatterplot of y 5 percentage who said they were more likely to purchase and x 5 grade. Does there appear to be a linear relationship between x and y?
=+Percentage That Said They Grade Were More Likely to Purchase 6 32.7 8 46.1 10 75.0 12 83.6
=+5.18 ● Researchers asked each child in a sample of 411 school-age children if they were more or less likely to purchase a lottery ticket at a store if lottery tickets were visible on the counter. The percentage that said that they were more likely to purchase a ticket by grade level are as
=+who live in more polluted areas have higher medical costs? Explain.
=+d. Do the scatterplot and the equation of the least-squares line support the researchers’ conclusion that elderly people
=+c. Is the slope of the least-squares line positive or negative? Is this consistent with your description of the relationship in Part (a)?
=+b. Find the equation of the least-squares line describing the relationship between y 5 medical cost and x 5 pollution.
=+a. Construct a scatterplot of the data. Describe any interesting features of the scatterplot.
=+Region Pollution Cost of Medical Care North 30.0 915 Upper South 31.8 891 Deep South 32.1 968 West South 26.8 972 Big Sky 30.4 952 West 40.0 899
=+5.17 ● ▼ The article “Air Pollution and Medical Care Use by Older Americans” (Health Affairs [2002]: 207–214)gave data on a measure of pollution (in micrograms of particulate matter per cubic meter of air) and the cost of medical care per person over age 65 for six geographical regions
=+5.16 A sample of automobiles traversing a certain stretch of highway is selected. Each one travels at roughly a constant rate of speed, although speed does vary from auto to auto. Let x 5 speed and y 5 time needed to traverse this segment of highway. Would the sample correlation coefficient be
=+5.15 Each individual in a sample was asked to indicate on a quantitative scale how willing he or she was to spend money on the environment and also how strongly he or she believed in God (“Religion and Attitudes Toward the Environment,” Journal for the Scientific Study of Religion[1993]:
=+5.14 An auction house released a list of 25 recently sold paintings. Eight artists were represented in these sales.The sale price of each painting appears on the list. Would the correlation coefficient be an appropriate way to summarize the relationship between artist (x) and sale price(y)? Why
=+An alternative formula for computing the correlation coefficient that is based on raw data and is algebraically equivalent to the one given in the text is Use this formula to compute the value of the correlation coefficient, and interpret this value.
=+5.13 According to the article “First-Year Academic Success: A Prediction Combining Cognitive and Psychosocial Variables for Caucasian and African American Students”(Journal of College Student Development [1999]: 599–605), there is a mild correlation between high school GPA(x) and
=+d. Is it reasonable to conclude that test anxiety caused poor exam performance? Explain.
=+c. Compute the value of the correlation coefficient. Is the value of r consistent with your answer to Part (b)?
=+b. Does there appear to be a linear relationship between the two variables? How would you characterize the relationship?
=+a. Construct a scatterplot, and comment on the features of the plot.
=+5.12 ● The following data on x 5 score on a measure of test anxiety and y 5 exam score for a sample of n 5 9 students are consistent with summary quantities given in the paper “Effects of Humor on Test Anxiety and Performance” (Psychological Reports [1999]: 1203–1212):x 23 14 14 0 17 20
=+c. The line pictured in the scatterplot has a slope of 1 and passes through (0, 0). If x and y were always identical, all points would lie exactly on this line. The authors of the paper claimed that perfect correlation (r 5 1) would result in this line. Do you agree? Explain your reasoning.
=+b. The paper reported that r 5 .9366. How would you describe the relationship between the two variables?
=+a. Does it appear that x and y are highly correlated?
=+5.11 The accompanying scatterplot shows observations on hemoglobin level, determined both by the standard spectrophotometric method (y) and by a new, simpler method based on a color scale (x) (“A Simple and Reliable Method for Estimating Hemoglobin,” Bulletin of the World Health Organization
=+c. With x 5 300-yd peak rate and y 5 shuttle run peak rate, how does the value of r compare to what you calculated in Part (b)?
=+b. With x 5 shuttle run peak rate and y 5 300-yd run peak rate, calculate r. Is the value of r consistent with your answer in Part (a)?
=+a. Construct a scatterplot of the data. What does the scatterplot suggest about the nature of the relationship between the two variables?
=+5.10 ● Peak heart rate (beats per minute) was determined both during a shuttle run and during a 300-yard run for a sample of n 5 10 individuals with Down syndrome(“Heart Rate Responses to Two Field Exercise Tests by Adolescents and Young Adults with Down Syndrome,”Adapted Physical Activity
=+b. The article concludes that “heavier logging led to large forest fires.” Do you think this conclusion is justified based on the given data? Explain.
=+a. Is there a correlation between timber sales and acres burned in forest fires? Compute and interpret the value of the correlation coefficient.
=+5.9 ● ▼ The accompanying data were read from graphs that appeared in the article “Bush Timber Proposal Runs Counter to the Record” (San Luis Obispo Tribune, September 22, 2002). The variables shown are the number of acres burned in forest fires in the western United States and timber
=+b. Is it reasonable to conclude in this case that there is no strong relationship between the variables (linear or otherwise)? Use a graphical display to support your answer.
=+a. What is the value of the correlation coefficient for this data set?
=+5.8 ● Data from the U.S. Federal Reserve Board (Household Debt Service Burden, 2002) on the percentage of disposable personal income required to meet consumer loan payments and mortgage payments for selected years are shown in the following table:Consumer Household Consumer Household Debt
=+Based on the time-series plot, would the correlation coefficient between household debt and corporate debt be positive or negative? Weak or strong? What aspect of the time-series plot supports your answer?
=+5.7 The following time-series plot is based on data from the article “Bubble Talk Expands: Corporate Debt Is Latest Concern Turning Heads” (San Luis Obispo Tribune, September 13, 2002) and shows how household debt and corporate debt have changed over the time period from 1991 (year 1 in the
=+c. Suppose that the observation for Harney District was removed from the data set. Would the correlation coefficient for the new data set be greater than or less than the one computed in Part (a)? Explain.
=+b. Are any unusual features of the data evident in the scatterplot?
=+a. Does there appear to be a strong linear relationship between the cost-to-charge ratio for inpatient and outpatient services? Justify your answer based on the value of the correlation coefficient and examination of a scatterplot of the data.
=+5.6 ● Cost-to-charge ratios (the percentage of the amount billed that represents the actual cost) for 11 Oregon hospitals of similar size were reported separately for inpatient and outpatient services. The data are Cost-to-Charge Ratio Hospital Inpatient Outpatient Blue Mountain 80 62 Curry
=+c. Do you have any concerns about this study that would make you hesitant to generalize these conclusions to other countries?
=+b. Is it reasonable to conclude that increasing sugar consumption leads to higher rates of depression? Explain.
=+a. Compute and interpret the correlation coefficient for this data set.
=+The fo in the Country Consumption Rate Korea 150 2.3 United States 300 3.0 France 350 4.4 Germany 375 5.0 Canada 390 5.2 New Zealand 480 5.7
=+5.5 ● The paper “A Cross-National Relationship Between Sugar Consumption and Major Depression?” (Depression and Anxiety [2002]: 118–120) concluded that there was a correlation between refined sugar consumption (calories per person per day) and annual rate of major depression(cases per 100
=+5.4 The article “That’s Rich: More You Drink, More You Earn” (Calgary Herald, April 16, 2002) reported that there was a positive correlation between alcohol consumption and income. Is it reasonable to conclude that increasing alcohol consumption will increase income? Give at least two
=+5.3 Draw two scatterplots, one for which r 5 1 and a second for which r 5 21.
=+5.2 Is the following statement correct? Explain why or why not.A correlation coefficient of 0 implies that no relationship exists between the two variables under study.
=+h. Amount of fertilizer used per acre and crop yield(Hint: As the amount of fertilizer is increased, yield tends to increase for a while but then tends to start decreasing.)
=+g. Time spent on homework and time spent watching television during the same day by elementary school children
=+f. Score on the math section of the SAT exam and score on the verbal section of the same test
=+c. Incomes of husbands and wives when both have fulltime jobsd. Height and IQe. Height and shoe size
=+b. Interest rate and number of loan applications
=+a. Maximum daily temperature and cooling costs
=+5.1 For each of the following pairs of variables, indicate whether you would expect a positive correlation, a negative correlation, or a correlation close to 0. Explain your choice.
=+ What is the probability that a randomly selected group of 50 shoppers will spend a total of more than$5300? (Hint: The total will be more than $5300 when the sample average exceeds what value?)
=+b. Suppose you were told that at least 60 of the 100 employees in a sample from your state participated in such a plan. Would you think p 5 .40 for your state? Explain.8.37 The amount of money spent by a customer at a discount store has a mean of $100 and a standard deviation of $30.
=+a. In a random sample of 100 employees, what is the approximate probability that at least half of those in the sample participate in such a plan?
=+8.36 Newsweek (November 23, 1992) reported that 40%of all U.S. employees participate in “self-insurance”health plans (p 5 .40).
=+b. If the permeability index is to be determined for each specimen in a random sample of size 10, how likely is it that the sample average permeability index will be between 950 and 1100? between 850 and 1300?
=+a. How likely is it that a single randomly selected specimen will have a permeability index between 850 and 1300?
=+8.35 Water permeability of concrete can be measured by letting water flow across the surface and determining the amount lost (in inches per hour). Suppose that the permeability index x for a randomly selected concrete specimen xx of a particular type is normally distributed with mean value 1000
=+8.34 Suppose that 20% of the subscribers of a cable television company watch the shopping channel at least once a week. The cable company is trying to decide whether to replace this channel with a new local station. A survey of 100 subscribers will be undertaken. The cable company has decided to
=+c. What is the probability that the sample mean is less than 50 lb?
=+b. What is the probability that the sample mean is between 49.75 lb and 50.25 lb?
=+8.32 The nicotine content in a single cigarette of a particular brand has a distribution with mean 0.8 mg and standard deviation 0.1 mg. If 100 of these cigarettes are analyzed, what is the probability that the resulting sample mean nicotine content will be less than 0.79? less than 0.77?8.33
=+e. If you were writing admission procedures for a selective university, would you recommend using the maximum test score, the average test score, or the most recent test score in making admission decisions? Write a paragraph explaining your choice.
=+d. Does a student who takes the exam five times have a big advantage over a student of equal ability who takes the exam only twice if the maximum score is used for college admission decisions? Explain.
=+c. Now consider the approximate sampling distributions of the maximum score for two-time and for five-time test takers. How do these two distributions compare?
=+b. Based on the three distributions from Part 1, for a twotime test taker, describe the advantage of using the maximum score compared to using either the average score or the most recent score.
=+a. The statistic that is the average of the test scores is just a sample mean (for a sample of size 2 in Part 1 and for a sample of size 5 in Part 2). How do the sampling distributions of mean2 and mean5 compare to what is expected based on the general properties of the distribution given in
=+Part 3: Now use the approximate sampling distributions constructed in Parts 1 and 2 to answer the following questions.
=+c. Construct density histograms for max5, mean5, and recent5.
=+b. Recent will just be the values in C15; name this column recent5. Compute the Max and Mean values, and store them in columns C16 and C17. Name these columns max5 and mean5.
=+a. Obtain 500 sets of 5 test scores, and store these values in columns C11– C15.
=+Part 2: Now you will produce approximate sampling distributions for these same three statistics, but for the case of a student who takes the exam five times.Follow the same steps as in Part 1, with the following modifications:
=+Click on the Frame drop-down menu, and select Multiple Graphs.Select Same X and Same Y. (This will cause MINITAB to use the same scales for all three histograms, so that they can be easily compared.)Click on OK.
=+MINITAB: Graph S Histogram Enter max2, mean2, and recent2 into the first three rows of the Graph Variables box Click on the Options button. Select Density. Click on OK. (This will produce histograms that use the density scale rather than the frequency scale.)
=+c. Construct density histograms for each of the three statistics (these density histograms approximate the sampling distributions of the three statistics), as follows:
=+Enter C1-C2 in the Input Variables box Enter C4 in the Store Result In box.Click on OK You should now see the average for each pair in C4. Name this column mean2.
=+iii. Compute the average test score (Mean) for each pair of scores, and store the values in C4, as follows:MINITAB: Calc S Row statistics Click the button for mean
=+Enter C1-C2 in the Input variables box Enter C3 in the Store Result In box.Click on OK You should now see the maximum value for each pair in C3. Name this column max2.
=+ii. Compute the maximum test score (Max) for each pair of scores, and store the values in C3, as follows:MINITAB: Calc S Row statistics Click the button for maximum
=+i. Recent is just the last test score, so the values in C2 are the values of Recent. Name this column recent2 by typing the name into the gray box at the top of C2.
=+b. Looking at the MINITAB worksheet, you should now see 500 rows of values in each of the first two columns.The two values in any particular row can be regarded as the test scores that might be observed when the student takes the test twice. For each pair of test scores, we now calculate the
=+a normal distribution with mean 1200)Enter 30 in the Standard Deviation box (because we want scores from a normal distribution with standard deviation 30)Click on OK
=+a. Obtain 500 sets of 2 test scores by generating observations from a normal distribution with mean 1200 and standard deviation 30.MINITAB: Calc S Random Data S Normal Enter 500 in the Generate box (to get 500 sets of scores)Enter C1-C2 in the Store in Columns box (to get two test scores in each
=+The instructions that follow assume the use of MINITAB. If you are using a different software package or a graphing calculator, your instructor will provide alternative instructions.
=+Part 1: Begin by considering what happens if this student takes the exam twice. You will use simulation to generate samples of two test scores, Score1 and Score2, for this student. Then you will compute the values of Max, Mean, and Recent for each pair of scores. The resulting values of Max,
=+30. If we select a sample from this normal distribution, the resulting set of observations can be viewed as a collection of test scores that might have been obtained by this student.
=+An individual’s score on the SAT exam fluctuates between test administrations. Suppose that a particular student’s “true ability” is reflected by an SAT score of 1200 but, because of chance fluctuations, the test score on any particular administration of the exam can be considered a
=+In this activity, you will investigate the differences between the three possibilities by looking at the sampling distributions of three statistics for a test taker who takes the exam twice and for a test taker who takes the exam five times. The three statistics are Max 5 maximum score Mean 5
=+families with higher incomes (who can afford to take the exam many times). The author proposed two alternatives that he believes would be fairer than using the highest score: (1) Use the average of all test scores, or (2) use only the most recent score.
=+American Prospect web site titled “College Try: Why Universities Should Stop Encouraging Applicants to Take the SATs Over and Over Again.” This paper argued that current college admission policies that permit applicants to take the SAT exam multiple times and then use the highest score for
=+Technology activity: Requires use of a computer or a graphing calculator.Background: The Chronicle of Higher Education (January 29, 2003) summarized an article that appeared on the
=+b. What is the approximate probability that a shipment will not be returned if the true proportion of defective cartridges in the shipment is .10?
=+a. What is the approximate probability that a shipment will be returned if the true proportion of defective cartridges in the shipment is .05?
=+8.31 ▼ A manufacturer of computer printers purchases plastic ink cartridges from a vendor. When a large shipment is received, a random sample of 200 cartridges is selected, and each cartridge is inspected. If the sample proportion of defective cartridges is more than .02, the entire shipment

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