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Introduction To The Practice Of Statistics 6th Edition David S. Moore, George P. McCabe, Bruce A. Craig - Solutions
Quality of life in chronically ill patients.Concern about the quality of life for chronically ill patients is becoming as important as treating their physical symptoms. The SF-36, a questionnaire for measuring the health quality of life, was given to 50 patients with chronic obstructive lung
Standard error and confidence interval for the slope. Refer to the previous two exercises.The standard deviation of the S&P 500 returns for these years is 16.45%. From this and your work in the previous exercise, find the standard error for the least-squares slope b1. Give a 95% confidence interval
Interpreting statistical software output. Refer to the previous exercise. What are the values of the regression standard error s and the squared correlation r2?
Completing an ANOVA table. How are returns on common stocks in overseas markets related to returns in U.S. markets? Measure U.S. returns by the annual rate of return on the Standard &Poor’s 500 stock index and overseas returns by the annual rate of return on the Morgan Stanley Europe,
Parental behavior and self-esteem. Chinese students from public schools in Hong Kong were the subjects of a study designed to investigate the relationship between various measures of parental behavior and other variables. The sample size was 1===+713. The data were obtained from questionnaires
Net flow in stock and bond funds. Is there a nonzero correlation between net flow of money into stock mutual funds and into bond funds? Use the regression analysis you did in Exercise 10.33(page 600) to answer this question with no additional calculations.
Capacity of DRAM. The capacity (bits) of the largest DRAM (dynamic random access memory)chips commonly available at retail has increased as follows:17 Year 1971 1980 1987 1993 1999 2000 Bits 1,024 64,000 1,024,000 16,384,000 256,000,000 512,000,000(a) Make a scatterplot of the data. Growth is much
Is this relationship significant? Refer to the previous exercise. Test the null hypothesis that the correlation between the binge-drinking rate and the average price for a bottle of beer within a 2-mile radius of campus is zero.
Correlation between binge drinking and the average price of beer. A recent study looked at 118 colleges to investigate the association between the binge-drinking rate and the average price for a bottle of beer at establishments within a 2-mile radius of campus.16 A correlation of −0.36 was found.
Predicting the lean in 2009. Refer to the previous two exercises.(a) How would you code the explanatory variable for the year 2009?(b) The engineers working on the Leaning Tower of Pisa were most interested in how much the tower would lean if no corrective action was taken. Use the least-squares
More on the Leaning Tower of Pisa. Refer to the previous exercise.(a) In 1918 the lean was 2.9071 meters. (The coded value is 71.) Using the least-squares equation for the years 1975 to 1987, calculate a predicted value for the lean in 1918. (Note that you must use the coded value 18 for year.)(b)
Leaning Tower of Pisa. The Leaning Tower of Pisa is an architectural wonder. Engineers concerned about the tower’s stability have done extensive studies of its increasing tilt.Measurements of the lean of the tower over time provide much useful information. The following table gives measurements
Do wages rise with experience? Refer to the previous exercise. Analyze the data with the outlier included.(a) How does this change the estimates of the parameters β0, β1, and σ?(b) What effect does the outlier have on the results of the significance test for the slope?(c) How has the width of
Do wages rise with experience? We assume that our wages will increase as we gain experience and become more valuable to our employers. Wages also increase because of inflation. By examining a sample of employees at a given point in time, we can look at part of the picture. How does length of
More on MA and HAV. Refer to the previous exercise. Give a 95% confidence interval for the slope. Explain how this interval can tell you what to conclude from a significance test for this parameter.
Severities of MA and HAV. Metatarsus adductus(call it MA) is a turning in of the front part of the foot that is common in adolescents and usually corrects itself. Hallux abducto valgus (call it HAV)is a deformation of the big toe that is not common in youth and often requires surgery. Perhaps the
Math pretest predicts success? Can a pretest on mathematics skills predict success in a statistics course? The 82 students in an introductory statistics class took a pretest at the beginning of the semester. The least-squares regression line for predicting the score y on the final exam from the
Stocks and bonds. How is the flow of investors’money into stock mutual funds related to the flow of money into bond mutual funds? Here are data on the net new money flowing into stock and bond mutual funds in the years 1985 to 2000, in billions of dollars.12 “Net” means that funds flowing out
School budget and number of students.Suppose that there is a linear relationship between the number of students x in an elementary school and the annual budget y. Write a population regression model to describe this relationship.(a) Which parameter in your model is the fixed cost in the budget (for
CHALL ENGE Neuron responses. Exercise 2.143 (page 163) gives data on neuron responses to pure tones and to monkey calls.(a) Describe each variable graphically and numerically.(b) Plot the data with the pure tone response on the x axis and the monkey call response on the y axis. Describe the
Reading test scores and IQ. In Exercise 2.11(page 95) you examined the relationship between a reading test score and an IQ score for a sample of 60 fifth-grade children.(a) Run the regression and summarize the results of the significance tests.(b) Rerun the analysis with the four possible outliers
TRAP and bone resorption using logs. Refer to the TRAP and VO– data in Exercise 10.27.Reanalyze these data using the logs of both TRAP and VO–. Summarize your results and compare them with those you obtained in Exercise 10.27.
Transforming the data. Refer to the OC and VO+data in Exercise 10.26. For variables such as these, it is common to work with the logarithms of the measured values. Reanalyze these data using the logs of both OC and VO+. Summarize your results and compare them with those you obtained in Exercise
CH ALLENGE TRAP and bone resorption. In Exercise 7.119 (page 482) we looked at the distribution of tartrate resistant acid phosphatase (TRAP), a biomarker for bone resorption. Table 10.7 gives values for this biomarker and a measure of bone resorption VO−. Analyze these data using the questions
CHALLENGE Osteocalcin and bone formation. In Exercise 7.118 (page 482) we looked at the distribution of osteocalcin (OC), a biomarker for bone formation, in a sample of 31 healthy females aged 11 to 32 years. This biomarker is relatively inexpensive to measure, requiring only a single sample of
CRP and serum retinol. In Exercise 7.26 (page 442) we examined the distribution of C-reactive protein (CRP) in a sample of 40 children from Papua New Guinea. Serum retinol values for the same children were studied in Exercise 7.28.One important question that can be addressed with these data is
More on the number of tornadoes. Refer to the previous exercise. The number of tornadoes in 2004 was much larger than expected under the linear model. Remove this observation and rerun the simple linear regression. Compare these results with the results of the previous exercise.
Are the number of tornadoes increasing? Storm Data is a publication of the National Climatic Data Center that contains a listing of tornadoes, thunderstorms, floods, lightning, temperature extremes, and other weather phenomena.Table 10.4 summarizes the annual number of tornadoes in the United
Breaking strength of wood, continued. Refer to the previous exercise. Consider an MOE of 2,000,000.(a) Interpret the confidence interval for mean response and the prediction interval for a future observation for this value of MOE.(b) Which interval will include more values? Give a reason for your
CH ALLENGE Breaking strength of wood. Exercise 2.144 (page 163) gives the modulus of elasticity (MOE) and the modulus of rupture(MOR) for 32 plywood specimens. Because measuring MOR involves breaking the wood but measuring MOE does not, we would like to predict the destructive test result, MOR,
U.S. versus overseas stock returns. Returns on common stocks in the United States and overseas appear to be growing more closely correlated as economies become more interdependent.Suppose that the following population regression line connects the total annual returns (in percent)on two indexes of
Compare the predictions. Case 21 in Table 10.2 and Table 10.3 corresponds to the same watershed area. For this case the area is 10 km2 and the percent forest is 25%. A predicted index of biotic integrity based on area was computed in Exercise 10.14, while one based on percent forest was computed in
Predicting water quality for an area of 30 km2.Refer to Exercise 10.14.(a) Find a 95% confidence interval for mean response corresponding to an area of 30 km2.(b) Find a 95% prediction interval for a future response.(c) Write a short paragraph interpreting the meaning of the intervals in terms of
How an outlier can affect statistical significance. Consider the data in Table 10.3 and the relationship between IBI and the percent of watershed area that was forest. The relationship between these two variables is almost significant at the .05 level. In this exercise you will demonstrate the
Comparing the analyses. In Exercises 10.14 and 10.15, you used two different explanatory variables to predict IBI. Summarize the two analyses and compare the results. If you had to choose between the two explanatory variables for predicting IBI, which one would you prefer? Give reasons for your
CHALLENGE More on predicting water quality. The researchers who conducted the study described in the previous exercise also recorded the percent of the watershed area that was forest for each of the streams. The data are given in Table 10.3. Analyze these data using the questions in the previous
CHALL ENGE Predicting water quality. The index of biotic integrity (IBI) is a measure of the water quality in streams. IBI and land use measures for a collection of streams in the Ozark Highland ecoregion of Arkansas were collected as part of a study.10 Table 10.2 gives the data for IBI and the
Beer and blood alcohol. How well does the number of beers a student drinks predict his or her blood alcohol content? Sixteen student volunteers at Ohio State University drank a randomly assigned number of 12-ounce cans of beer. Thirty minutes later, a police officer measured their blood alcohol
Are the two fuel efficiency measurements similar? Refer to Exercise 7.24. In addition to the computer calculating mpg, the driver also recorded the mpg by dividing the miles driven by the amount of gallons at fill-up. The driver wants to determine if these calculations are different.Fill-up 1 2 3 4
More on public university tuition. Refer to Exercise 10.10.(a) Construct a 95% confidence interval for the slope. What does this interval tell you about the percent increase in tuition between 2000 and 2005?(b) The tuition at Stat U was $5000 in 2000. What is the predicted tuition in 2005?(c) Find
Public university tuition: 2000 versus 2005.Table 10.1 shows the in-state undergraduate tuition and required fees for 34 public universities in 2000 and 2005.8(a) Plot the data with the 2000 tuition on the x-axis and describe the relationship. Are there any outliers or unusual values? Does a linear
Significance test for the slope. For each of the settings in the previous exercise, test the null hypothesis that the slope is zero versus the two-sided alternative
95% confidence intervals for the slope. Find a 95% confidence interval for the slope in each of the following settings:(a) n = 25, ˆy = 1.3 + 12.10x, and SEb1= 6.31(b) n = 25, ˆy = 13.0 + 6.10x, and SEb1= 6.31(c) n = 100, ˆy = 1.3 + 12.10x, and SEb1= 6.31
What’s wrong? For each of the following, explain what is wrong and why.(a) The parameters of the simple linear regression model are b0, b1, and s.(b) To test H0: b1 = 0, use a t test.(c) For a particular value of the explanatory variable x, the confidence interval for the mean response will be
What’s wrong? For each of the following, explain what is wrong and why.(a) The slope describes the change in x for a change in y.(b) The population regression line is y = b0 + b1x.(c) A 95% confidence interval for the mean response is the same width regardless of x.
Research and development spending. The National Science Foundation collects data on the research and development spending by universities and colleges in the United States.7 Here are the data for the years 1999 to 2001 (using 1996 dollars):Year 1999 2000 2001 Spending (billions of dollars) 26.4
Standard error for the mean response. Refer to Example 10.10.What is the standard error of ˆy when x = 30 mph?Would you expect the standard error of ˆy to be larger, smaller, or the same when x = 40 mph? Explain.
Constructing confidence intervals for the mean response. Refer to Example 10.6. For the following three changes in average speed, construct a 95% confidence interval for the change in mpg.(a) LOGMPH increases from 2.9 to 3.9 (18.2 to 49.4 mph).(b) LOGMPH decreases from 3.7 to 2.7 (40.4 to 14.9
More on speed’s effect on fuel efficiency. Refer to Example 10.4.(a) What is the predicted mpg for the car when it averages 35 mph?(b) If the observed mpg when x = 35 mph were 21.0, what is the residual?(c) Suppose you wanted to use the estimated population regression line to examine the average
Understanding a linear regression model. Consider a linear regression model with μy = 40.5 − 2.5x and standard deviation σ =2.0.(a) What is the slope of the population regression line?(b) Explain clearly what this slope says about the change in the mean of y for a change in x.(c) What is the
CHALLENGE Suspicious results? An instructor who assigned an exercise similar to the one described in the previous exercise received homework from a student who reported a P-value of 0.999. The instructor suspected that the student did not use the computer for the assignment but just made up some
More on goodness of fit to the uniform distribution. Refer to the previous exercise.Use software to generate your own sample of 500 uniform random variables on the interval from 0 to 1, and perform the goodness of fit test. Choose a different set of intervals from the ones used in the previous
Goodness of fit to the uniform distribution.Computer software generated 500 random numbers that should look like they are from the uniform distribution on the interval 0 to 1 (see page 263).They are categorized into five groups: (1) less than or equal to 0.2, (2) greater than 0.2 and less than or
More on the goodness of fit to a standard Normal distribution. Refer to the previous exercise. Use software to generate your own sample of 500 standard Normal random variables, and perform the goodness of fit test. Choose a different set of intervals from the ones used in the previous exercise.
Goodness of fit to a standard Normal distribution. Computer software generated 500 random numbers that should look like they are from the standard Normal distribution. They are categorized into five groups: (1) less than or equal to −0.6, (2) greater than −0.6 and less than or equal to −0.1,
Use of academic assistance services. The 2005 National Survey of Student Engagement reported on the use of campus services during the first year of college. 34 In terms of academic assistance (for example tutoring, writing lab), 43% never used the services, 35% sometimes used the services, 15%
Is there a random distribution of trees? In Example 6.1 (page 354) we examined data concerning the longleaf pine trees in the Wade Tract and concluded that the distribution of trees in the tract was not random. Here is another way to examine the same question. First, we divide the tract into four
CHALLENGE Evaluation of an herbal remedy. A study designed to evaluate the effects of the herbal remedy Echinacea purpurea randomly assigned healthy children who were 2 to 11 years old to receive either echinacea or a placebo.32 Each time a child had an upper respiratory infection(URI) treatment
CHALLENGE More on why animals are brought to animal shelters. Refer to Exercise 9.33(page 554) concerning the case-control study of factors associated with bringing a cat to an animal shelter and the similar study for dogs. The last category for the source of the pet was given as“Other” and
Are Mexican Americans less likely to be selected as jurors? Refer to Exercise 8.81 (page 523)concerning Castaneda v. Partida, the case where the Supreme Court review used the phrase “two or three standard deviations” as a criterion for statistical significance. Recall that there were 181,535
CH ALLENGE“No Sweat” label. Following complaints about the working conditions in some apparel factories both in the United States and abroad, a joint government and industry commission recommended in 1998 that companies that monitor and enforce proper standards be allowed to display a “No
Altruism and field of study. In one part of the study described in the previous exercise, students were asked to respond to some questions regarding their interests and attitudes. Some of these questions form a scale called PEOPLE that measures altruism, or an interest in the welfare of others.
Student loans. A study of 865 college students found that 42.5% had student loans.30 The students were randomly selected from the approximately 30,000 undergraduates enrolled in a large public university. The overall purpose of the study was to examine the effects of student loan burdens on the
CHALLENGE Why are animals brought to animal shelters? Euthanasia of healthy but unwanted pets by animal shelters is believed to be the leading cause of death for cats and dogs.A study designed to find factors associated with bringing a cat to an animal shelter compared data on cats that were
CHALLENGE Cracks in veneer. Many furniture pieces are built with veneer, a thin layer of fine wood that is fastened to less expensive wood products underneath. Face checks are cracks that sometimes develop in the veneer. When face checks appear, the furniture needs to be reconstructed. Because this
More on secondhand stores. The study of shoppers in secondhand stores cited in the previous exercise also compared the income distributions of shoppers in the two stores. Here is the two-way table of counts:Income City 1 City 2 Under $10,000 70 62$10,000 to $19,999 52 63$20,000 to $24,999 69
Secondhand stores. Shopping at secondhand stores is becoming more popular and has even attracted the attention of business schools. A study of customers’ attitudes toward secondhand stores interviewed samples of shoppers at two secondhand stores of the same chain in two cities.The breakdown of
Changing majors. A task force set up to examine retention of students in the majors that they chose when starting college examined data on transfers to other majors.25 Here are some data giving counts of students classified by initial major and the area that they transferred to:Area transferred to
Pet ownership and gender. Refer to the previous exercise. Here are similar data giving the relationship between pet ownership status and gender:Pet ownership status Gender Non–pet owners Dog owners Cat owners Female 1024 157 85 Male 915 171 82 Analyze the data. Include numerical and graphical
Pet ownership and education level. The Health, Aging, and Body Composition (Health ABC) study is a 10-year study of older adults. A research project based on this study examined the relationship between physical activity and pet ownership.24 The data collected included information concerning pet
Internet references in prominent journals. The World Wide Web (WWW) has led to an enormous increase in the amount of information that is easily available to anyone with Internet access.References to Internet pages are becoming quite common in the scientific literature. One study examined Internet
Hummingbirds of Santa Lucia. E. jugularis is a type of hummingbird that lives in the forest preserves of the Carribean island of Santa Lucia.The males and the females of this species have bills that are shaped somewhat differently. Researchers who study these birds thought that the bill shape might
Which model? Refer to Exercises 9.17, 9.18, 9.20, and 9.23. For each, state whether you are comparing two or more populations (the first model for two-way tables) or testing independence between two categorical variables (the second model).
CHALLENGE Student-athletes and gambling. A survey of student-athletes that asked questions about gambling behavior classified students according to the National Collegiate Athletic Association (NCAA) division.21 For male studentathletes, the percents who reported wagering on collegiate sports are
Identity theft. A study of identity theft looked at how well consumers protect themselves from this increasingly prevalent crime. The behaviors of 61 college students were compared with the behaviors of 59 nonstudents.20 One of the questions was “When asked to create a password, I have used
Dieting trends among male and female undergraduates. A recent study of undergraduates looked at gender differences in dieting trends.19 There were 181 women and 105 men who participated in the survey. The table below summarizes whether a student tried a low-fat diet or not by gender:Gender Tried
Air pollution from a steel mill. One possible effect of air pollution is genetic damage. A study designed to examine this problem exposed one group of mice to air near a steel mill and another group to air in a rural area and compared the numbers of mutations in each group.18 Here are the data for
Intended readership of ads with sexual imagery.The ads in the study described in the previous exercise were also classified according to the age group of the intended readership. Here is a summary of the data:Magazine readership age group Model dress Young adult Mature adult Not sexual 72.3%
Sexual imagery in magazine ads. In what ways do advertisers in magazines use sexual imagery to appeal to youth? One study classified each of 1509 full-page or larger ads as “not sexual” or “sexual,”according to the amount and style of the dress of the male or female model in the ad. The ads
Drinking status and class attendance. As part of the 1999 College Alcohol Study, students who drank alcohol in the last year were asked if drinking ever resulted in missing a class.16 The data are given in the following table:Drinking status Missed Occasional Frequent a class Nonbinger binger
CHALLENGE Gender versus motivation for volunteer service, continued. Refer to the previous exercise. Recompute the table for volunteers only.To do this take the entries for each motivation and divide by the percent of volunteers. Do this separately for each gender. Verify that the percents sum to
CHALLENGE Gender versus motivation for volunteer service. A study examined patterns and characteristics of volunteer-service for young people from high school through early adulthood.15 Here are some data that can be used to compare males and females on participation in unpaid volunteer service or
Construct a table with no association. Construct a 3 × 2 table of counts where there is no apparent association between the row and column variables.
Can you construct the joint distribution from the marginal distributions? Here are the row and column totals for a two-way table with two rows and two columns:a b 50 c d 150 100 100 200 Find two different sets of countsa, b,c, and d for the body of the table. This demonstrates that the relationship
Find the degrees of freedom and P-value. For each of the following situations give the degrees of freedom and an appropriate bound on the P-value(give the exact value if you have software available)for the X2 statistic for testing the null hypothesis of no association between the row and column
New treatment for cocaine addiction. Cocaine addiction is difficult to overcome. Addicts have been reported to have a significant depletion of stimulating neurotransmitters and thus continue to take cocaine to avoid feelings of depression and anxiety. A 3-year study with 72 chronic cocaine users
Waking versus bedtime symptoms. As part of the study on ongoing fright symptoms due to exposure to horror movies at a young age, the following table was presented to describe the lasting impact these movies have had during bedtime and waking life:Waking symptoms Bedtime symptoms Yes No Yes 36 33 No
Does using Rodham matter? In April 2006, the Opinion Research Corporation conducted a telephone poll for CNN of 1012 adult Americans.13 Half those polled were asked their opinion of Hillary Rodham Clinton. The other half were asked their opinion of Hillary Clinton. The table below summarizes the
Time status versus gender for the 20–24 age category. Refer to Exercise 9.7. The table below breaks down the 20–24 age category by gender.Gender Status Male Female Total Full-time 2719 2991 5710 Part-time 535 680 1215 Total 3254 3671 6925(a) Compute the marginal distribution for gender.Display
Age and time status of U.S. college students.The Census Bureau provides estimates of numbers of people in the United States classified in various ways.12 Let’s look at college students. The following table gives us data to examine the relation between age and full-time or part-time status. The
Why not use a chi-square test? As part of the study on ongoing fright symptoms due to exposure to horror movies at a young age, the following table Percent of students who reported each problem Type of Problem Bedtime Waking Short Short Movie or video term Enduring term Enduring Poltergeist (n =
Distribution of M&M colors. M&M Mars Company has varied the mix of colors for M&M’sMilk Chocolate Candies over the years. These changes in color blends are the result of consumer preference tests.Most recently, the color distribution is reported to be 13% brown, 14%yellow, 13% red, 20% orange,
Frequent binge drinking and gender: the chi-square test. Refer to Example 9.2 (page 526). Use the chi-square test to assess if frequ binge drinking is associated with gender. Also, compare the chi-square statistic with the z statistic in Example 8.11 (page 513). State your conclusions.
Find the P-value. For each of the following give the degrees of freedom and an appropriate bound on the P-value for the X2 statistic.(a) X2 = 2.5 for a 2 by 2 table(b) X2 = 6.5 for a 2 by 2 table(c) X2 = 16.3 for a 3 by 5 table(d) X2 = 16.3 for a 5 by 3 table
Expected cell counts and the chi-square test. Refer to Exercise 9.1.You decide to use the chi-square test to compare these two conditional distributions.(a) What is the expected count for the first cell (observed count is 75)?(b) Computer software gives you X2 = 4.09. What are the degrees of
Comparison of conditional distributions. Consider the following 2 × 2 table.Observed counts Explanatory variable Response variable 1 2 Yes 75 95 170 No 125 105 230 Total 200 200 400(a) Compute the conditional distribution of the response variable for each of the two explanatory-variable
% said they would borrow less.(c) “Since leaving school, my education loans have not caused me more financial hardship than I had anticipated at the time I took out the loans.” 34.3%disagreed.(d) “Making loan payments is unpleasant but I know that the benefits of education loans are worth
CHALLENGE Attitudes toward student loan debt. The National Student Loan Survey asked the student loan borrowers in their sample about attitudes toward debt.37 Here are some of the questions they asked, with the percent who responded in a particular way:(a) “To what extent do you feel burdened by
CHALLENGE Home court advantage. In many sports there is a home field or home court advantage. This means that the home team is more likely to win when playing at home than they are to win when playing at an opponent’s field or court, all other things being equal. Go to the Web site of your
CHALLENGE Statistics and the law. Castaneda v. Partida is an important court case in which statistical methods were used as part of a legal argument.36 When reviewing this case, the Supreme Court used the phrase “two or three standard deviations” as a criterion for statistical significance.
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