Question: Using the same survey as in Exercise

> Exercise 15 describes a regression model that estimates a cereal potassium content from the amount of fiber it contains. In this context, what does it mean to say that a cereal has a negative residual?

> In Chapter 6, Exercise 41 we examined We can examine the relationship between the fuel economy (Combined MPG) and Displacement (in liters) for 1211 models of cars. (Data in Fuel economy 2016) Further analysis produces the regression model Combined MPG^=3

> For many people, breakfast cereal is an important source of fiber in their diets. Cereals also contain potassium, a mineral shown to be associated with maintaining a healthy blood pressure. An analysis of the amount of fiber (in grams) and the potassium

> Agricultural scientists are working on developing an improved variety of Roma tomatoes. Marketing research indicates that customers are likely to bypass Romas that weigh less than 70 grams. The current variety of Roma plants produces fruit that averages

> Hens usually begin laying eggs when they are about 6 months old. Young hens tend to lay smaller eggs, often weighing less than the desired minimum weight of 54 grams. 1. The average weight of the eggs produced by the young hens is 50.9 grams, and only 28

> Most people think that the normal adult body temperature is 98.6F. That figure, based on a 19th-century study, has recently been challenged. In a 1992 article in the Journal of the American Medical Association, researchers reported that a more accurate f

> Companies that design furniture for elementary school classrooms produce a variety of sizes for kids of different ages. Suppose the heights of kindergarten children can be described by a Normal model with a mean of 38.2 inches and standard deviation of 1

> A tire manufacturer believes that the tread life of its snow tires can be described by a Normal model with a mean of 32,000 miles and standard deviation of 2500 miles. 1. If you buy one of these tires, would it be reasonable for you to hope it will last

> Assume the cholesterol levels of adult American women can be described by a Normal model with a mean of 188 mg/dL and a standard deviation of 24. 1. Draw and label the Normal model. 2. What percent of adult women do you expect to have cholesterol levels

> Consider the IQ model N(100,15) one last time. 1. What IQ represents the 15th percentile? 2. What IQ represents the 98th percentile? 3. What the IQR of the IQs?

> Here are several scatterplots. The calculated correlations are 0.923,0.487,0.006, and 0.777. Which is which?

> Consider the Angus weights model N(1152,84) one last time. 1. What weight represents the 40th percentile? 2. What weight represents the 99th percentile? 3. What the IQR of the weights of these Angus steers?

> In the Normal model N(100,15) from Exercise 10 , what cutoff value bounds 1. the highest 5% of all IQs? 2. the lowest 30% of the IQs? 3. the middle 80% of the IQs?

> Based on the model N(1152,84) describing Angus steer weights from Exercise 29 , what are the cutoff values for 1. the highest 10% of the weights? 2. the lowest 20% of the weights? 3. the middle 40% of the weights?

> Suppose we take logarithms of the CEO compensations in Exercise 47 . The histogram of log Compensation looks like this: with a mean of 1.07 and a standard deviation of 0.26. 1. According to the Normal model, what percent of CEOs would you expect to earn

> The Glassdoor Economic Research Blog published the compensation (in millions of dollars) for the CEOs of large companies. The distribution looks like this: The mean CEO compensation is $14.1M and the standard deviation is $11.32M. 1. According to the Nor

> A large philanthropic organization keeps records on the people who have contributed. In addition to keeping records of past giving, the organization buys demographic data on neighborhoods from the U.S. Census Bureau. Eighteen of these variables concern e

> NFL data from the 2015 football season reported the number of yards gained by each of the league 488 receivers: The mean is 274.73 yards, with a standard deviation of 327.32 yards. 1. According to the Normal model, what percent of receivers would you exp

> The mean of the 100 car speeds in Exercise 30 was 23.84 mph, with a standard deviation of 3.56 mph. 1. Using a Normal model, what values should border the middle 95% of all car speeds? 2. Here are some summary statistics. From your answer in part a, how

> Fifty-three men completed the men alpine downhill at the 2018 winter Olympics in PyeongChang. The gold medal winner finished in 100.25 seconds. Here are the times (in seconds) for all competitors. 1. The mean time was 103.883 seconds, with a standard dev

> For the car speed data in Exercise 30 , here are the histogram, boxplot, and Normal probability plot of the 100 readings. Do you think it is appropriate to apply a Normal model here? Explain.

> Owners of a new coffee shop tracked sales for the first 20 days and displayed the data in a scatterplot (by day). 1. Make a histogram of the daily sales since the shop has been in business. 2. State one fact that is obvious from the scatterplot, but not

> Later on, the forester in Exercise 39 shows you a histogram of the tree diameters he used in analyzing the woods that was for sale. Do you think he was justified in using a Normal model? Explain, citing some specific concerns.

> A company that manufactures rivets believes the shear strength (in pounds) is modeled by N(800,50). 1. Draw and label the Normal model. 2. Would it be safe to use these rivets in a situation requiring a shear strength of 750 pounds? Explain. 3. About wha

> A forester measured 27 of the trees in a large woods that is up for sale. He found a mean diameter of 10.4 inches and a standard deviation of 4.7 inches. Suppose that these trees provide an accurate description of the whole forest and that a Normal model

> Exercise 10 proposes modeling IQ scores with N(100,15). What IQ would you consider to be unusually high? Explain.

> In Exercise 29 , we suggested the model N(1152,84) for weights in pounds of yearling Angus steers. What weight would you consider to be unusually low for such an animal? Explain.

> A popular band on tour played a series of concerts in large venues. They always drew a large crowd, averaging 21,359 fans. While the band did not announce (and probably never calculated) the standard deviation, which of these values do you think is most

> A friend tells you about a recent study dealing with the number of years of teaching experience among current college professors. He remembers the mean but can’t recall whether the standard deviation was 6 months, 6 years, or 16 years. Tell him which one

> Suppose police set up radar surveillance on the Stanford street described in Exercise 30 . They handed out a large number of tickets to speeders going a mean of 28 mph, with a standard deviation of 2.4 mph, a maximum of 33 mph, and an IQR of 3.2 mph. Loc

> Suppose the auctioneer in Exercise 31 sold a herd of cattle whose minimum weight was 980 pounds, median was 1140 pounds, standard deviation 84 pounds, and IQR 102 pounds. They sold for 40 cents a pound, and the auctioneer took a $20 commission on each an

> For the car speed data in Exercise 30 , recall that the mean speed recorded was 23.84 mph, with a standard deviation of 3.56 mph. To see how many cars are speeding, John subtracts 20 mph from all speeds. 1. What is the mean speed now? What is the new sta

> A ceramics factory can fire eight large batches of pottery a day. Sometimes a few of the pieces break in the process. In order to understand the problem better, the factory records the number of broken pieces in each batch for 3 days and then creates the

> Beanstalk Clubs are social clubs for very tall people. To join, a man must be over 6²2³ tall, and a woman over 5²10³. The National Health Survey suggests that heights of adults may be Normally distributed, with mean heights of 69.1³ for men and 64.0³ for

> Recall that the beef cattle described in Exercise 29 had a mean weight of 1152 pounds, with a standard deviation of 84 pounds. 1. Cattle buyers hope that yearling Angus steers will weigh at least 1000 pounds. To see how much over (or under) that goal the

> In a study of dialysis, researchers found that of the three patients who were currently on dialysis, 67% had developed blindness and 33% had their toes amputated. What kind of display might be appropriate for these data? Explain.

> The boxplots display the heights (in inches) of 130 members of a choir by the part they sing. 1. It appears that the median height for sopranos is missing, but actually the median and the upper quartile are equal. How could that happen? 2. Write a few se

> Results of a 1996 American Medical Association report about the infant mortality rate for twins carried for the full term of a normal pregnancy are shown on the next page, broken down by the level of prenatal care the mother had received. 1. Is the overa

> Here are the prices (in cents per pound) of bananas reported from 15 markets surveyed by the U.S. Department of Agriculture. 1. Display these data with an appropriate graph. 2. Report appropriate summary statistics. 3. Write a few sentences about this di

> A student runs an experiment to test how different factors affect his reaction time while playing video games. He uses a specified race course with random hazards and times how long it takes him (in seconds) to finish 4 laps under a variety of experiment

> A student runs an experiment to test how different factors affect her bowling performance. She uses 3 levels for the weight of the ball (low, medium, and high) and 2 approaches (standing and walking), throwing 4 balls at each condition and choosing the c

> The Bureau of Transportation Statistics of the U.S. Department of Transportation reports statistics about airline performance. For September 2018 they report the following number of bags lost per 1000 passengers. Are the airlines roughly equal in their b

> The data on water hardness and mortality considered in Part VI Review Exercise 30 also included information on whether the town is north or south of Derby. When that information is coded in a variable as 1 for north of Derby and 0 for south of Derby, and

> In an attempt to control the growth of the herds of wild horses, managers sterilized some of the stallions. The variable Sterilized is coded 0 for herds and years in which no stallions were sterilized and 1 for herds and years in which some stallions wer

> A student runs an experiment to test four different clubs on her putting accuracy, recording the distance in centimeters from a small target that she places on the green. She randomizes the club used each time by drawing numbers out of a hat until each c

> John Beale of Stanford, California, recorded the speeds of cars driving past his house, where the speed limit read 20 mph. The mean of 100 readings was 23.84 mph, with a standard deviation of 3.56 mph. (He actually recorded every car for a two-month peri

> 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 scores on Friday quiz are given. The other group

> A student runs an experiment to test four different grips on his football throwing distance, recording the distance in yards that he can throw the football using each grip. He randomizes the grip used each time by drawing numbers out of a hat until each

> A weight loss clinic advertises that its program of diet and exercise will allow clients to lose 10 pounds in one month. A local reporter investigating weight reduction gets permission to interview a randomly selected sample of clients who report the giv

> Using a Simple Random Sample, a student asked 200 students questions about their study and workout habits, and received 124 responses. One of the questions asked, Do you participate in intramural (IM) athletics, varsity athletics, or no athletics? while

> The Los Angeles Almanac website reports recent annual rainfall (in inches), as shown in the table. 1. Create a 90% confidence interval for the mean annual rainfall in LA. 2. If you wanted to estimate the mean annual rainfall with a margin of error of onl

> Brianna, a member of the track team, runs an experiment to test how different factors affect her javelin throw. She wants to know if the more expensive (premium) javelin is worth the extra price and is curious to know how much warming up helps her distan

> A student runs an experiment to test how different factors affect his score while playing video pinball. Here are the results of 16 runs of an experiment performed in random order. Factor Eyes has two levels: both open and right eye closed. Factor Tilt h

> A study published in the journal Environmental Health Perspectives examined the sex ratios of children born to workers exposed to dioxin in Russian pesticide factories. The data covered the years 1961 to 1988 in the city of Ufa, Bashkortostan, Russia. Of

> 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 abo

> Using N(1152,84), the Normal model for weights of Angus steers in Exercise 13 , 1. How many standard deviations from the mean would a steer weighing 1000 pounds be? 2. Which would be more unusual, a steer weighing 1000 pounds or one weighing 1250 pounds?

> The New York Times reported the results of the 2003 NY Marathon by listing time brackets and the number of racers who finished within that bracket. Because the brackets are of different sizes, we look at the number of racers finishing per minute against

> Nick (see Exercise 19) designed a follow-up experiment to see if having Music or Television on would affect his typing speed. In particular, he’d like to know if he can type just as effectively with the music and/or the TV on while he t

> How accurate are pollsters in predicting the outcomes of Congressional elections? The table shows the actual number of Democrat seats in the House of Representatives and the number predicted by the Gallup organization for nonpresidential election years s

> For a class project, Nick M. designed and carried out an experiment to see if the room Temperature and the wearing of Gloves affected his typing speed. He ran each combination of hot and cold temperature and gloves on and off 8 times, recording the net n

> The National Vital Statistics Report provides information on live Births (per 1000 women), according to the age of the woman (in 5-year brackets Age used here is the midpoint of the bracket) and the Year from 1990 to 1999. The report isolates births to w

> The Insurance Institute for Highway Safety publishes data on a variety of traffic related risks. One report gives the numbers of people killed in highway accidents during each year from 1975 to 2013. Here is a regression predicting Total traffic fataliti

> We have data on Old Faithful eruptions that includes another variable recording the Day on which the eruption occurred (where 1 is the first day and each successive day just counts one more). The correlation of Interval (minutes until the next eruption)

> The survey in Exercise 14 also asked students about the number of hours they studied. Those doing the survey wanted to know if the average amount of studying varied by sex or by class of the respondent. Partial boxplots of the Hours Studied last night by

> Using a Simple Random Sample, a student group asked 450 students about their sleep and study habits and received about 200 responses. The group wanted to know if the average amount of sleep varied by sex (F or M) or by year (Freshman, Sophomore, Junior,

> At a barbershop music singing competition, choruses are judged on three scales: Music (quality of the arrangement, etc.), Performance, and Singing. The scales are supposed to be independent of each other, and each is scored by a different judge, but a fr

> Two companies market new batteries targeted at owners of personal music players. DuraTunes claims a mean battery life of 11 hours, while RockReady advertises 12 hours. 1. Explain why you would also like to know the standard deviations of the battery life

> Here are data on 32 light water nuclear power plants. The variables are: Cost: In $100,000, adjusted to 1976 base. Date: Date that construction permit was issued in years after 1900. Thus, 68.58 is roughly halfway through 1968. Mwatts: Power plant net ca

> In preparation for a regional paper airplane competition, a student tried out her latest design. The distances her plane traveled (in feet) in 11 trial flights are given here. (The world record is an astounding 193.01 feet!) The data were 62, 52, 68, 23,

> In 2002 the Veritas Software company found out that its chief financial officer did not actually have the MBA he had listed on his resume. They fired him, and the value of the company stock dropped 19%. Kroll, Inc., a firm that specializes in investigati

> We have a sample of municipal mutual funds that report their return (%) in the previous 3years and the previous 5 years. 1. Create a 95% confidence interval for the difference in rate of return for the 3- and 5-year periods covered by these data. Clearly

> A corporation with a fleet of vehicles wanted to test the cost-effectiveness of using Motor Silk oil additive. For the study, 6100 delivery and passenger vehicles were tested for the same 3-month period in one year and then again in the subsequent year.

> A recent study of perfect pitch tested 2700 students in American music conservatories. It found that 7% of non-Asian and 32% of Asian students have perfect pitch. A test of the difference in proportions resulted in a P-value of

> Refer again to the research summarized in Exercise R6.6. Is there any evidence that when eclampsia does occur, the magnesium sulfide treatment may help prevent the woman death? 1. Write an appropriate hypothesis. 2. Check the assumptions and conditions.

> It estimated that 50,000 pregnant women worldwide die each year of eclampsia, a condition involving elevated blood pressure and seizures. A research team from 175 hospitals in 33 countries investigated the effectiveness of magnesium sulfate in preventing

> 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

> Fitting someone for a hearing aid requires assessing the patient 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

> Anna, a language major, took final exams in both French and Spanish and scored 83 on each. Her roommate Megan, also taking both courses, scored 77 on the French exam and 95 on the Spanish exam. Overall, student scores on the French exam had a mean of 81

> 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 scores on Friday quiz are given. The other group

> There is some indication in medical literature that doctors may have become more aggressive in inducing labor or doing preterm cesarean sections when a woman is carrying twins. Records at a large hospital show that, of the 43 sets of twins born in 2000,

> 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,

> 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.

> According to an 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

> 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. S

> 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

> We saw in Part II Review Exercise R2.21 that Old Faithful eruptions do not occur at constant intervals and the intervals may vary greatly depending on the duration of the previous eruption. In that exercise, we fit a regression model, which we can now im

> Cereals with bran Exercise R6.41 looked at regressions to model calories in breakfast cereals based on their carbohydrates and fiber content. Here is a scatterplot of carbohydrates vs. fiber content for these cereals: The cereals plotted with green x are

> A 1954 study of 1438 pregnant women examined the association between the woman 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

> The first Stat exam had a mean of 80 and a standard deviation of 4 points; the second had a mean of 70 and a standard deviation of 15 points. Reginald scored an 80 on the first test and an 85 on the second. Sara scored an 88 on the first but only a 65 on

> A regression of the calories in breakfast cereals on their carbohydrate content (g) looks like this: Response variable is: calories A second regression with fiber content included gives this model: Response variable is: calories 1. Give an interpretation

> At a barbershop music singing competition, choruses are judged on three scales: Music (quality of the arrangement, etc.), Performance, and Singing. The scales are supposed to be independent of each other, and each is scored by a different judge, but a fr

> At the middle of the 2016–2017 NBA season, James Hardin led the league by making 468 of 544 free throws, for a success rate of 86%. But Russell Westbook was close behind with 425 of 517 (82.2%). 1. Find a 95% confidence interval for the difference in t

> 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 analyz

> The Pew Research Center conducted a representative telephone survey in October of 2016. Among the reported results was the following table concerning the preferred political party affiliation of respondents and their ages for white voters. Is there evide

> 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

> Are twin births becoming more common? Part II Review Exercise R2.5 looked at the number of twin births by year from 1980 to 2014. Now we can include some inference: Response variable is: TwinBirths/1000 1. State and test the standard null hypothesis for

> 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 pr

> In 2016, about 200,000 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. Is the distribution of scores at this high scho

> 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 right-handed subjects, 38 were successful in completin

> The first Stats exam had a mean of 65 and a standard deviation of 10 points; the second had a mean of 80 and a standard deviation of 5 points. Derrick scored an 80 on both tests. Julie scored a 70 on the first test and a 90 on the second. They both total