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Stats Data And Models 4th Global Edition Richard D. De Veaux, Paul Velleman, David E. Bock - Solutions

Movie output Here is another part of the regression output for the movies in Exercise 3:Source Sum of Squares df Mean Square F-ratio Regression 224995 3 74998.4 34.8 Residual 249799 116 2153.44a) Using the values from the table, show how the value of R2 could be computed. Don’t try to do the
Movie R-squared In the regression model of Exercise 3,a) What is the R2 for this regression? What does it mean?b) Why is the “Adjusted R Square” in the table different from the “R Square”?
More movie testsa) What is the null hypothesis tested for the coefficient of Run Time in the regression of Exercise 3?b) What is the t-statistic corresponding to this test?c) Why is this t-statistic negative?d) What is the P-value corresponding to this t-statistic?e) Complete the hypothesis test.
Movie tests In the regression output for the movies of Exercise 3,a) What is the null hypothesis tested for the coefficient of Stars in this table?b) What is the t-statistic corresponding to this test?c) What is the P-value corresponding to this t-statistic?d) Complete the hypothesis test. Do you
Movie residuals For the movies regression, here is a histogram of the residuals. What does it tell us about these Assumptions and Conditions?a) Linearity conditionb) Nearly Normal conditionc) Equal Spread condition 50 40 30 20 10 -150 -25 100 225 Residuals (U)
More movies For the movies examined in Exercise 4, here is a scatterplot of USGross vs. Budget:What (if anything) does this scatterplot tell us about the following Assumptions and Conditions for the regression?a) Linearity conditionb) Equal Spread conditionc) Normality assumption U.S. Gross ($M)
Movie profits again A middle manager at an entertainment company, upon seeing the analysis of Exercise 3, concludes that longer movies make less money. He argues that his company’s films should all be cut by 30 minutes to improve their gross. Explain the flaw in his interpretation of this model.
Movie profits What can predict how much a motion picture will make? We have data on a number of recent releases that includes the USGross (in $M), the Budget($M), the Run Time (minutes), and the average number of Stars awarded by reviewers. The first several entries in the data table look like
Candy sales A candy maker surveyed chocolate bars available in a local supermarket and found the following least squares regression model:Calories = 28.7 + 11.98Fat1g2 + 3.76Sugar1g2.a) The hand-crafted chocolate she makes has 14g of fat and 25g of sugar. How many calories does the model predict
House prices The following regression model was found for houses in an area of upstate New York:Price = 20,668.96 - 7753.05Bedrooms + 113.74Living Area.a) Find the predicted price of a 3 bedroom, 1750-sq-ft house from this model.b) The house just sold for $271,000. Find the residual corresponding
As a class project, students in a large Statistics class collected publicly available information on recent home sales in their hometowns. There are 894 properties.These are not a random sample, but they may be representative of home sales during a short period of time, nationwide. (Data in Real
Containers one more time Another student performs a one-way ANOVA on the container data of Exercise 20, using the 4 treatments water room, water outside, coffee room, and coffee outside. Perform this analysis and comment on the differences between this analysis and the one in Exercise 20.
Batteries once more Another student analyzed the battery data from Exercise 25, using a one-way ANOVA.He considered the experimental factor to be an 8-level factor consisting of the 8 possible combinations of Brand and Environment. Here are the boxplots for the 8 treatments and a one-way
Peas In an experiment on growing sweet peas, a team of students selected 2 factors at 4 levels each and recorded Weight, Stem Length, and Root Length after 6 12 days of growth. They grew plants using various amounts of Water and Quickgrow solution, a fertilizer designed to help plants grow faster.
Batteries A student experiment was run to test the performance of 4 brands of batteries under 2 different Environments (room temperature and cold). For each of the 8 treatments, 2 batteries of a particular brand were put into a flashlight. The flashlight was then turned on and allowed to run until
Chromatography again Refer back to the experiment in Exercise 22. Instead of Total counts, redo the analysis using log(Total counts) as the response. Do your conclusions change? How? Are the assumptions of the model better satisfied?
Gas additives again Refer back to the experiment in Exercise 21. Instead of mpg redo the analysis using log(mpg) as the response. Do your conclusions change?How? Are the assumptions of the model better satisfied?
Chromatography A gas chromatograph is an instrument that measures the amounts of various compounds contained in a sample by separating the various constituents.Because different components are flushed through the system at different rates, chromatographers are able to both measure and distinguish
Gas additives An experiment to test a new gasoline additive, Gasplus, was performed on three different cars: a sports car, a minivan, and a hybrid. Each car was tested with both Gasplus and regular gas on 10 different occasions and their gas mileage was recorded. Here are the partial boxplots:A
Containers revisited Building on the cup experiment of the Chapter 4 Step-By-Step, a student selects one type of container and designs an experiment to see whether the type of Liquid stored and the outside Environment affect the ability of a cup to maintain temperature. He randomly chooses an
Sprouts again The students running the sprouts experiment(Exercise 12) also kept track of the number of beans sprouted (out of 40) for each of the 36 dishes. Here are the partial boxplots of Sprouts plotted against Salinity and Temperature:An ANOVA table shows:An interaction plot shows:A plot of
Washing For his final project, Jonathan examined the effects of two factors on how well stains are removed when washing clothes. On each of 16 new white handkerchiefs, he spread a teaspoon of dirty motor oil (obtained from a local garage). He chose 4 Temperature settings (each of which is a
Basketball shots A student performed an experiment to see if her favorite sneakers and the time of day might affect her free throw percentage. She tried shooting with and without her favorite sneakers and in the early morning and at night. For each treatment combination, she shot 50 baskets on 4
Fish and prostate Refer back to Exercise 14. Perform your own analysis of the data to see if eating fish and contracting prostate cancer are related.
Baldness and heart disease again Refer back to Exercise 13. Perform your own analysis of the data to see if baldness and heart disease are related. Do your conclusions support the claim that baldness is a cause of heart disease? Explain.
Fish and prostate The Chapter 3 Step-By-Step looked at a Swedish study that asked 6272 men how much fish they ate and whether or not they had prostate cancer.Here are the data:Armed with the methods of this chapter, a student performs a two-way ANOVA on the data. Here is her ANOVA table:a) Comment
Baldness and heart disease A retrospective study examined the link between baldness and the incidence of heart disease. In the study, 1435 middle-aged men were selected at random and examined to see whether they showed signs of Heart Disease (or not) and what amount of Baldness they exhibited
Sprouts An experiment on mung beans was performed to investigate the environmental effects of salinity and water temperature on sprouting. Forty beans were randomly allocated to each of 36 petri dishes that were subject to one of four levels of Salinity (0, 4, 8, and 12 ppm)and one of three
Crash analysis The National Highway Transportation Safety Administration runs crash tests in which stock automobiles are crashed into a wall at 35 mph with dummies in both the passenger and the driver’s seats. The THOR Alpha crash dummy is capable of recording 134 channels of data on the impact
Gas mileage again Refer to the experiment in Exercise 8.After analyzing his data the student reports that the F-ratio for Tire Pressure is 4.29 with a P-value of 0.030, the F-ratio for Acceleration is 2.35 with a P-value of 0.143, and the F-ratio for the Interaction effect is 1.54 with a P-value of
Popcorn again Refer to the experiment in Exercise 7.After collecting her data and analyzing the results, the student reports that the F-ratio for Power is 13.56 and the F-ratio for Time is 9.36.a) What are the P-values?b) What would you conclude?c) What else about the data would you like to see in
Gas mileage revisited In Chapter 26 we saw a student’s experiment to study the effect of Tire Pressure and Acceleration on gas mileage. He devises a system so that his Jeep Wagoneer uses gasoline from a one-liter container.He uses 3 levels of Tire Pressure (low, medium, and full)and 2 levels of
Popcorn revisited In the previous chapter we saw a two-factor experiment to test how microwave power and temperature affect popping. She chooses 3 levels of Power (low, medium, and high) and 3 Times (3 minutes, 4 minutes, and 5 minutes), running one bag at each condition.She counts the number of
Have ANOVA cookie Here is the ANOVA table for the cookie experiment of Exercise 2 along with an interaction plot. What does the interaction term say about the cookie recipes? Analysis of Variance For Score Sums of Mean Source DF Squares Square F-ratio P-value Intercept 1 2515.16 2515.16 677.74
Student TV interactions Here is an ANOVA table with an interaction term and the corresponding interaction plot for the TV watching data of Exercise 1. What does the interaction term mean here? Analysis of Variance For TVhours No Selector Sums of Mean Source DF Squares Square F-ratio P-value
Cookie assumptions The student performing the chocolate chip cookie experiment of Exercise 2 planned to analyze his results with an Analysis of Variance on two factors. Here are some displays. Do you think the Assumptions for ANOVA are satisfied? 8 6 4 Score Score 2 8 6 4 2 0 Milk chocolate chips 0
Student TV assumptions The TV watching study of Exercise 1 was collected as a survey of students at a small college. Do the assumptions of ANOVA appear to be met? Here are some displays to help in your decision: Tv hours 15 12 6 3 Women Men Tv hours 25 20 20 15 10 10 5 0 Women Men
Cookies A student performed an experiment to compare chocolate chip cookie recipes. He baked batches of cookies with different amounts of Sugar: 0.5, 0.375, and 0.25 cups, and with different kinds of chips: milk, semisweet, and dark chocolate. Cookie quality was scored on a 0 to 10 scale by other
Students set up an experiment to investigate factors that determine how far a paper airplane will fly. Among the factors are whether the plane is constructed of copier paper or heavier construction paper, whether it is a “dart” or a glider, and whether the ends of the wings are folded up into
Analgesics A pharmaceutical company tested three formulations of a pain relief medicine for migraine headache sufferers. For the experiment, 27 volunteers were selected and 9 were randomly assigned to one of three drug formulations. The subjects were instructed to take the drug during their next
Downloading To see how much of a difference time of day made on the speed at which he could download files, a college sophomore performed an experiment. He placed a file on a remote server and then proceeded to download it at three different time periods of the day. He downloaded the file 48 times
Cereals, redux We also have data on the protein content of the cereals in Exercise 19 by their shelf number. Here are the boxplot and ANOVA table:a) What are the null and alternative hypotheses?b) What does the ANOVA table say about the null hypothesis? (Be sure to report this in terms of protein
Cereals once more We first saw data on breakfast cereals in Chapter 7. Supermarkets often place similar types of cereal on the same supermarket shelf. We have data on the shelf as well as the sugar, sodium, and calorie content of 77 cereals. Does sugar content vary by shelf? At the top of the next
Fertilizers A biology student is studying the effect of 10 different fertilizers on the growth of mung bean sprouts.She sprouts 12 beans in each of 10 different petri dishes, and adds the same amount of fertilizer to each dish. After one week she measures the heights of the 120 sprouts in
School system A school district superintendent wants to test a new method of teaching arithmetic in the fourth grade at his 15 schools. He plans to select 8 students from each school to take part in the experiment, but to make sure they are roughly of the same ability, he first gives a test to all
Auto noise filters In a statement to a Senate Public Works Committee, a senior executive of Texaco, Inc., cited a study on the effectiveness of auto filters on reducing noise.Because of concerns about performance, two types of filters were studied, a standard silencer and a new device developed by
Eggs A student wants to investigate the effects of real vs.substitute eggs on his favorite brownie recipe. He enlists the help of 10 friends and asks them to rank each of 8 batches on a scale from 1 to 10. Four of the batches were made with real eggs, four with substitute eggs. The judges tasted
Smokestack scrubbers Particulate matter is a serious form of air pollution often arising from industrial production.One way to reduce the pollution is to put a filter, or scrubber, at the end of the smokestack to trap the particulates.An experiment to determine which smokestack scrubber design is
Yogurt An experiment to determine the effect of several methods of preparing cultures for use in commercial yogurt was conducted by a food science research group.Three batches of yogurt were prepared using each of three methods: traditional, ultrafiltration, and reverse osmosis. A trained expert
ZIP codes, revisited The intern from the marketing department at the Holes R Us online piercing salon (Chapter 3, Exercise 55) has recently finished a study of the company’s 500 customers. He wanted to know whether people’s ZIP codes vary by the last product they bought. They have 16 different
Eye and hair color In Chapter 4, Exercise 32, we saw a survey of 1021 school-age children conducted by randomly selecting children from several large urban elementary schools. Two of the questions concerned eye and hair color. In the survey, the following codes were used:The students analyzing the
Hearing A researcher investigated four different wordlists for use in hearing assessment. She wanted to know whether the lists were equally difficult to understand in the presence of a noisy background. To find out, she tested 96 subjects with normal hearing randomly assigning 24 to each of the
Tellers A bank is studying the time that it takes 6 of its tellers to serve an average customer. Customers line up in the queue and then go to the next available teller. Here is a boxplot of the last 200 customers and the times it took each teller:a) What are the null and alternative hypotheses?b)
Finger Lakes wines 2014 Here are bottle prices (in dollars)of wines produced by wineries along three of the Finger Lakes.a) What null and alternative hypotheses would you test for these data? Talk about prices and location, not symbols.b) Do the conditions for an ANOVA seem to be met here? Why or
Fuel economy by cylinders, revisited Here are boxplots, first seen in Chapter 4 Exercise 28, that show the relationship between the number of cylinders a car’s engine has and the car’s fuel economy.a) State the null and alternative hypotheses that you might consider for these data.b) Do the
Frisbee throws A student performed an experiment with three different grips to see what effect it might have on the distance of a backhanded Frisbee throw. She tried it with her normal grip, with one finger out, and with the Frisbee inverted. She measured in paces how far her throw went. The
Activating baking yeast To shorten the time it takes him to make his favorite pizza, a student designed an experiment to test the effect of sugar and milk on the activation times for baking yeast. Specifically, he tested four different recipes and measured how many seconds it took for the same
Darts A student interested in improving her dart-throwing technique designs an experiment to test 4 different stances to see whether they affect her accuracy. After warming up for several minutes, she randomizes the order of the 4 stances, throws a dart at a target using each stance, and measures
Gas mileage A student runs an experiment to study the effect of three different mufflers on gas mileage. He devises a system so that his Jeep Wagoneer uses gasoline from a one-liter container. He tests each muffler 10 times, carefully recording the number of miles he can go in his Jeep Wagoneer on
Skating A figure skater tried various approaches to her Salchow jump in a designed experiment using 5 different places for her focus (arms, free leg, midsection, takeoff leg, and free). She tried each jump 6 times in random order, using two of her skating partners to judge the jumps on a scale from
Popcorn A student runs an experiment to test four different popcorn brands, recording the number of kernels left unpopped. She pops measured batches of each brand 3 times, using the same popcorn popper and randomizing the order of the brands. After collecting her data and analyzing the results, she
Contrast baths are a treatment commonly used in hand clinics to reduce swelling and stiffness after surgery. Patients’ hands are immersed alternately in warm and cool water. (That’s the contrast in the name.) Sometimes, the treatment is combined with mild exercise. Although the treatment is
Newspapers Who reads the newspaper more, men or women? Eurostat, an agency of the European Union (EU), conducts surveys on several aspects of daily life in EU countries. Recently, the agency asked samples of 1000 respondents in each of 14 European countries whether they read the newspaper on a
Hearing Fitting someone for a hearing aid requires assessing the patient’s hearing ability. In one method of assessment, the patient listens to a tape of 50 English words. The tape is played at low volume, and the patient is asked to repeat the words. The patient’s hearing ability score is the
Cramming Students in two basic Spanish classes were required to learn 50 new vocabulary words. One group of 45 students received the list on Monday and studied the words all week. Statistics summarizing this group’s scores on Friday’s quiz are given. The other group of 25 students did not get
Diet Thirteen overweight women volunteered for a study to determine whether eating specially prepared crackers before a meal could help them lose weight. The subjects were randomly assigned to eat crackers with different types of fiber (bran fiber, gum fiber, both, and a control cracker).
Education vs. income 2009 The information below examines the median income and education level(percent of population with at least a Bachelor’s degree)for several large U.S. cities in 2009.a) Do you think the assumptions for inference are met?Explain.b) Does there appear to be an association
Infliximab In an article appearing in the journal The Lancet, medical researchers reported on the experimental use of the arthritis drug infliximab in treating Crohn’s disease. In a trial, 573 patients were given initial 5-mg injections of the drug. Two weeks later, 335 had responded positively.
Dairy sales Peninsula Creameries sells both cottage cheese and ice cream. The CEO recently noticed that in months when the company sells more cottage cheese, it seems to sell more ice cream as well. Two of his aides were assigned to test whether this is true or not. The first aide’s plot and
Juvenile offenders According to a 2011 article in the Journal of Consulting and Clinical Psychology, Charles Borduin pioneered a treatment called Multisystemic Therapy (MST) as a way to prevent serious mental health problems in adolescents. The therapy involves a total support network including
Learning math Developers of a new math curriculum called “Accelerated Math” compared performances of students taught by their system with control groups of students in the same schools who were taught using traditional instructional methods and materials. Statistics about pretest and posttest
Togetherness Are good grades in high school associated with family togetherness? A simple random sample of 142 high-school students was asked how many meals per week their families ate together. Their responses produced a mean of 3.78 meals per week, with a standard deviation of 2.2. Researchers
Old Faithful Old Faithful eruptions do not occur at uniform intervals and may vary greatly. Can we improve our chances of predicting the time of the next eruption if we know how long the previous eruption lasted?a) Describe what you see in this scatterplot.b) Write an appropriate hypothesis.c) Here
Family planning A 1954 study of 1438 pregnant women examined the association between the woman’s education level and the occurrence of unplanned pregnancies, producing these data:Do these data provide evidence of an association between family planning and education level? (Source: Fertility
Pregnancy A San Diego reproductive clinic reported 42 live births to 157 women under the age of 38, but only 7 successes for 89 clients aged 38 and older. Is this evidence of a difference in the effectiveness of the clinic’s methods for older women?a) Test the appropriate hypotheses, using the
Depression and the Internet The September 1998 issue of the American Psychologist published an article reporting on an experiment examining “the social and psychological impact of the Internet on 169 people in 73 households during their first 1 to 2 years online.” In the experiment, a sample of
Eye and hair color A survey of 1021 school-age children was conducted by randomly selecting children from several large urban elementary schools. Two of the questions concerned eye and hair color. In the survey, the following codes were used:The Statistics students analyzing the data were asked to
Age and party 2011 The Pew Research Center conducted a representative telephone survey during 2011. Among the reported results was the following table concerning the preferred political party affiliation of respondents and their ages for white voters. Is there evidence of age-based differences in
Retirement planning According to the 2011 Retirement Confidence Survey, run by the Employee Benefit Research Institute, 37% of men reported being “a lot behind schedule” while 43% of women answered in the same way. Is this evidence that in general, more women are feeling this way when it comes
Twins, again After reading of the JAMA study in Exercise 34, a large city hospital examined their records of twin births for several years and found the data summarized in the table below. Is there evidence that the way the hospital deals with pregnancies involving twins may have changed?
Twins In 2000, the Journal of the American Medical Association published a study that examined a sample of pregnancies that resulted in the birth of twins. Births were classified as preterm with intervention (induced labor or cesarean), preterm without such procedures, or term or
AP Statistics scores 2010 In 2010, almost 130,000 Statistics students nationwide took the Advanced Placement Examination in Statistics. The national distribution of scores and the results at Ithaca High School are shown in the table.a) Is the distribution of scores at this high school significantly
Lefties and music In an experiment to see if left- and right-handed people have different abilities in music, subjects heard a tone and were then asked to identify which of several other tones matched the first. Of 76 righthanded subjects, 38 were successful in completing this test, compared with
Wild horses Large herds of wild horses can become a problem on some federal lands in the West. Researchers hoping to improve the management of these herds collected data to see if they could predict the number of foals that would be born based on the size of the current herd. Their attempt to model
Wealth distribution The following table is based on a June 2011 Gallup Poll in which Americans were classified as high income (over $75,000), middle income($30k–$75k), or low income (less than $30k). Those polled were asked for their views on redistributing U.S. wealth by heavily taxing the rich.
Hard water In an investigation of environmental causes of disease, data were collected on the annual mortality rate (deaths per 100,000) for males in 61 large towns in England and Wales. In addition, the water hardness was recorded as the calcium concentration (parts per million, or ppm) in the
Tableware Nambe Mills manufactures plates, bowls, and other tableware made from an alloy of several metals.Each item must go through several steps, including polishing.To better understand the production process and its impact on pricing, the company checked the polishing time (in minutes) and the
Genetics Two human traits controlled by a single gene are the ability to roll one’s tongue and whether one’s ear lobes are free or attached to the neck. Genetic theory says that people will have neither, one, or both of these traits in the ratio 1:3:3:9 (1 attached, noncurling; 3 attached,
Rainmakers? In an experiment to determine whether seeding clouds with silver iodide increases rainfall, 52 clouds were randomly assigned to be seeded or not.The amount of rain they generated was then measured(in acre-feet). Create a 95% confidence interval for the average amount of additional rain
Insulin and diet A study published in the Journal of the American Medical Association examined people to see if they showed any signs of IRS (insulin resistance syndrome)involving major risk factors for Type 2 diabetes and heart disease. Among 102 subjects who consumed dairy products more than 35
Irises Can measurements of the petal length of flowers be of value when you need to determine the species of a certain flower? Here are the summary statistics from measurements of the petals of two species of irises.(Source: R. A. Fisher, “The Use of Multiple Measurements in Axonomic Problems.”
Teach for America, part II The study described in Exercise 21 also looked at scores in mathematics and language. Here are software outputs for the appropriate tests. Explain what they show. Mathematics T-TEST OF MU (1) - Mu(2) = 0 Mu(Cert) Mu(NoCert) = 4.53 t (86) = 2.95 p = 0.002 Language T-TEST
Legionnaires’ disease In 1974, the Bellevue-Stratford Hotel in Philadelphia was the scene of an outbreak of what later became known as legionnaires’ disease. The cause of the disease was finally discovered to be bacteria that thrived in the air-conditioning units of the hotel.Owners of the Rip
Teach for America Several programs attempt to address the shortage of qualified teachers by placing uncertified instructors in schools with acute needs—often in inner cities. A study compared students taught by certified teachers to others taught by uncertified teachers in the same schools.
Cesareans Some people fear that differences in insurance coverage can affect healthcare decisions. A survey of several randomly selected hospitals found that 16.6% of 223 recent births in Vermont involved cesarean deliveries, compared to 18.8% of 186 births in New Hampshire. Is this evidence that
Eating disorders A study conducted in the multicultural Spanish city of Ceuta investigated the relationship between religion and the prevalence of eating disorders.Students aged 12–20 were selected from three public schools. In the study, suppose there were 150 Muslim students and 46 were
Smoking In the depression and heart attack research described in Exercise 17, 32% of the diseased group were smokers, compared with only 23.7% of those free of heart disease.a) Create a 95% confidence interval for the difference in the proportions of smokers in the two groups.b) Is this evidence
Age In a study of how depression may affect one’s ability to survive a heart attack, the researchers reported the ages of the two groups they examined. The mean age of 2397 patients without cardiac disease was 69.8 years(SD = 8.7 years), while for the 450 patients with cardiac disease, the mean
Driving fatalities 2011 The U.S. Census compiled data from each state in 2011 to record the number of deaths per 100 million vehicle miles traveled. Wondering if the death rate is different in New England when compared to the Mountain states, we hope to create a 95% confidence interval for the
Feeding fish In the midwestern United States, a large aquaculture industry raises largemouth bass. Researchers wanted to know whether the fish would grow better if fed a natural diet of fathead minnows or an artificial diet of food pellets. They stocked six ponds with bass fingerlings weighing

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