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Stats Data And Models 3rd Canadian Edition Richard De Veaux, Paul Velleman, David Bock, Augustin Vukov, Augustine Wong - Solutions
7. Sampling University of British Columbia students For each scenario, identify the kind of sample used by the university administrators from Exercise 1:a) Select several dormitories at random and contact everyone living in the selected dorms.b) Using a computer-based list of registered students,
6. Sampling satisfaction A company hoping to assess employee satisfaction surveys employees by assigning computer-generated random numbers to each employee on a list of all employees and then contacting all those whose assigned random number is divisible by 7. Is this a simple random sample?
5. Sampling students A professor teaching a large lecture class of 350 students samples her class by rolling a die. Then, starting with the row number on the die (1 to 6), she passes out a survey to every fourth row of the large lecture hall. She says that this is a Simple Random Sample because
4. Satisfied respondents The company’s annual report states, “Our survey shows that 87.34% of our employees are ‘very happy’ working here.” Comment on that claim. Use appropriate statistics terminology
3. University of British Columbia again The president of the university is planning a speech for an alumni group. He plans to talk about the proportion of students who responded in the survey that they are the first in their family to attend university, but the first draft of his speech treats that
2. Satisfied workers The managers of a large company wished to know the percentage of employees who feel “extremely satisfied” to work there. The company has roughly 24 000 employees. They contacted a random sample of employees and asked them about their job satisfaction, obtaining 437
1. University of British Columbia Administrators at University of British Columbia were interested in estimating the percentage of students who are the first in their family to go to university. The University of British Columbia student body has about 60 000 members. How might the
38. Profit How are a company’s profits related to its sales? Let’s examine data from 71 large U.S. corporations. All amounts are in millions of dollars.a) Histograms of Profits and Sales and histograms of the logarithms of Profits and Sales are seen below. Why are the re-expressed data better
37. Vehicle weights The Minnesota Department of Transportation hoped that they could measure the weights of big trucks without actually stopping the vehicles by using a newly developed “weigh-in-motion” scale. After installation of the scale, a study was conducted to find out whether the
36. Models Find the predicted value of y, using each fitted regression model (some involving re-expressions of y) below for x = 10.a) yn = 2 + 0.8 ln xb) log y = 5 - 0.23xc) 1> 1y = 17.1 - 1.66x
35. Tobacco and alcohol Are people who use tobacco products more likely to consume alcohol? Here are data on household spending (in pounds) taken by the British government on 11 regions in Great Britain. Do tobacco and alcohol spending appear to be related? What questions do you have about these
34. Chips A start-up company has developed an improved electronic chip for use in laboratory equipment. The company needs to project the manufacturing cost, so it develops a spreadsheet model that takes into account the purchase of production equipment, overhead, raw materials, depreciation,
33. Lunchtime Does how long children remain at the lunch table help predict how much they eat? Twenty toddlers were observed over several months at a nursery school. The table and graph show the average number of minutes the kids stayed at the table and the average number of calories they consumed
32. Dollars on education Suppose you want to investigate the relationship between standardized test scores and dollars spent for schools in your province. For each school, an average test score (for the same grade) and the average dollars spent per student in 2013 were determined. Someone suggests
31. French Consider the association between a student’s score on a French vocabulary test and the weight of the student. What direction and strength of correlation would you expect in each of the following situations? Explain.a) The students are all in Grade 3.b) The students are in Grades 3
30. Modelling jumps 2012 Here are the summary statistics for the Olympic long jumps and high jumps displayed in the previous exercise: Event Mean StdDev High Jump 2.148077 0.1938663 Long Jump 8.050000 0.5135913 Correlation = 0.91246a) Write the equation of the line of regression for estimating
29. Jumps 2012 How are Olympic performances in various events related? The following plot shows winning longjump and high-jump distances, in metres, for the Summer Olympics from 1912 through 2012.a) Describe the association.b) Do long-jump performances somehow influence the high-jumpers? How do you
28. Depression The September 1998 issue of the American Psychologist published an article by Kraut et al. that reported 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, 73
27. Winter in the city Summary statistics for the data relating the latitude and average January temperature (degrees Fahrenheit) for 55 large U.S. cities are given below. Variable Mean StdDev Latitude 39.02 5.42 JanTemp 26.44 13.49 Correlation = -0.848a) What percent of the variation in January
26. Correlations The study of U.S. cities in Exercise 25 found the mean January Temperature (degrees Fahrenheit), Altitude (feet above sea level), and Latitude (degrees north of the equator) for 55 cities. Here’s the correlation matrix: Jan. Temp. Latitude Altitude Jan. Temp. 1.000 Latitude
25. U.S. Cities Data from 50 large U.S. cities show the mean January Temperature (in Fahrenheit degrees) and Latitude. Describe what you see in the scatterplot. Avg. Jan. Temp (F) 60 60 45 45 30 15+ 30 35 40 45 Latitude (N)
24. Tips It’s commonly believed that people use tips to reward good service. A researcher for the hospitality industry examined tips and ratings of service quality from 2645 dining parties at 21 different restaurants. The correlation between ratings of service and tip percentages was 0.11.
23. Down the drain Most water tanks have a drain plug so that the tank may be emptied when it’s to be moved or repaired. How long it takes a certain size of tank to drain depends on the size of the plug, as shown in the table below. Create a model. (Hint: Replace Drain Time by 1> 1Drain Time)
22. Smoking and pregnancy 2011 The Child Trends Data Bank monitors issues related to children. The table shows a 50-state average of the percent of expectant mothers who smoked cigarettes during their pregnancies.a) Create a scatterplot and describe the trend you see.b) Find the correlation.c) How
21. Big screen An electronics website collects data on the size of new HD flat panel televisions (measuring the diagonal of the screen in inches) to predict the cost (in hundreds of dollars). Which of these is most likely to be the slope of the regression line: 0.03, 0.3, 3, 30? Explain.
20. Improving trees In the last exercise, you saw that the linear model had some deficiencies. Let’s create a better model.a) Perhaps the cross-sectional area of a tree would be a better predictor of its age. Since area is measured in square units, try re-expressing the data by squaring the
19. How old is that tree? One can determine how old a tree is by counting its rings, but that requires cutting the tree down. Can we estimate the tree’s age simply from its diameter? A forester measured 27 trees of the same species that had been cut down, and counted the rings to determine the
18. Crocodile lengths The ranges inhabited by the Indian gharial crocodile and the Australian saltwater crocodile overlap in Bangladesh. Suppose a very large crocodile skeleton is found there, and we wish to determine the species of the animal. Wildlife scientists have measured the lengths of the
17. Old Faithful There is evidence that eruptions of Old Faithful can best be predicted by knowing the duration of the previous eruption.a) Describe what you see in the scatterplot of Intervals between eruptions vs. Duration of the previous eruption.b) Write the equation of the line of best fit.
16. Colourblind Although some women are colourblind, this condition is found primarily in men. Why is it wrong to say there’s a strong correlation between sex and colourblindness?
15. Cars with horses Can we predict the horsepower of the engine that manufacturers will put in a car by knowing the weight of the car? Here are the regression analysis and residual plot:a) Write the equation of the regression line.b) Do you think the car’s weight is measured in pounds or
14. Quebec abortions Below are annual rates of abortion performed on females under the age of 20, per 1000 Quebec females (aged 15–49) over the period 1974–2005 (data not available for 1991).a) Plot the rate versus the year. Describe the trend.b) Calculate the correlation.c) Fit a straight line
13. Indigenous populations rising 2011 The data below show Indigenous populations in a sample of Canadian cities.a) Plot the 2011 percents versus the 2001 percents. Guess the correlation, and confirm your guess.b) Fit a regression model to predict the 2011 percent from the 2001 percent.c) Interpret
12. Cramming One Thursday, researchers gave students enrolled in a section of basic Spanish a set of 50 new vocabulary words to memorize. On Friday, the students took a vocabulary test. When they returned to class the following Monday, they were retested—without advance warning. Here are the
11. Traffic Highway planners investigated the relationship between traffic density (number of automobiles per mile) and the average speed (in miles per hour) of the traffic on a moderately large city thoroughfare. The data were collected at the same location at 10 different times over a span of
10. Grades A Statistics instructor created a linear regression equation to predict students’ final exam scores from their midterm exam scores. The regression equation was Fin = 10 + 0.9 Mid.a) If Susan scored a 70 on the midterm, what did the instructor predict for her score on the final?b) Susan
9. A manatee model 2013 Continue your analysis of the manatee situation from the previous exercise.a) Create a linear model of the association between Manatee Deaths and Powerboat Registrations.b) Interpret the slope of your model.c) Interpret the y-intercept of your model.d) How accurately did
8. Manatees 2013 Marine biologists warn that the growing number of powerboats registered in Florida threatens the existence of manatees. The data below come from the Florida Fish and Wildlife Conservation Commission (myfwc.com/research/manatee/) and the National Marine Manufacturers Association
7. Acid rain Biologists studying the effects of acid rain on wildlife collected data from 163 streams in the Adirondack Mountains. They recorded the pH (acidity) of the water and the BCI, a measure of biological divera) What is the correlation between pH and BCI?b) Describe the association between
6. Residuals Below is a plot of primary school enrollment percentage of females (in the population in the correct age group) versus gross national income per capita for a number of countries. Also shown is the least squares straight-line fit.a) Show and describe by drawing on the plot and with
5. Lurking variables Each of the following scatterplots contains two distinct subgroups (+’s for males, o’s for females). In each case, estimate the correlation between y and x:a) ignoring genderb) taking gender into account, i.e., separately by gender (iv) x x x
4. Vineyards again Instead of Age, perhaps the Size of the vineyard (in acres) is associated with the price of the wines. Look at the scatterplot:a) Do you see any evidence of an association?b) What concern do you have about this scatterplot?c) If the red “+” data point is removed, would you
3. Vineyards Here are the scatterplot and regression analysis for Case Prices of 36 wines from vineyards in the Finger Lakes region of New York State and the Ages of the vineyards.a) Does it appear that vineyards in business longer get higher prices for their wines? Explain.b) What does this
2. Togetherness Are good grades in high school associated with family togetherness? A 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 then
1. College Every year, US News and World Report publishes a special issue on many U.S. colleges and universities. The scatterplots below have Student/Faculty Ratio (number of students per faculty member) for the colleges and universities on the y-axes plotted against 4 other variables. The correct
60. Placental mammals again Continuing with the previous exercise, the species listed in the last 7 rows of the table were all carnivores, while primates occupy the first 16 rows. Enter into a new column in your data worksheet—”p” or “c” for each species, to denote whether primate or
59. Placental mammals In the introductory example in Chapter 6, we plotted (average) neonatal brain weight versus (average) gestation period for a number of placental mammal species. We are interested in finding a good model for predicting the neonatal brain weight of a species from its gestation
58. Asian immigrants 2012 Below are data on immigration to Canada from countries in Asia:a) We want to predict the percentage of total immigrants who are from Asia based on the year. You may use two straight line models (which we call piecewise linear) depending on the time period. Draw your fitted
57. Planet distances and years 2006 At a meeting of the International Astronomical Union (IAU) in Prague in 2006, Pluto was determined not to be a planet, but rather the largest member of the Kuiper belt of icy objects (http://www.enchantedlearning.com/subjects/ astronomy/planets/). Let’s examine
56. Census at school, boys versus girls Separate the CensusAtSchool data in the previous exercise according to gender, and run the two regressions of armspan on height, once for each gender.a) Describe the differences suggested by the two fitted models.b) Estimate the difference in armspan between
55. Census at school The International CensusAtSchool Project collects data on primary and secondary school students from various countries, including Canada. We selected a random sample of 111 Canadian secondary school students, age 14 and over, from 2006–2007. Below are the first four rows of
54. More Mandarin 2011 Mandarin speakers in Canada are increasing rapidly. Here are 2001 and 2011 Census figures on Mandarin mother-tongue residents in some urban areas:a) Plot the 2011 count against the 2001 count. Would you fit a regression line for predicting 2011 counts from 2001 counts?
53. Bigger and bigger According to the UK National Sizing Survey, women’s average body size measurements have increased over time as follows:a) Compute all correlations among all pairs of the four variables.b) Why are the correlations so high?c) Predict the average waist size for UK women in 1950
52. Mandarin or Cantonese 2011 Below are data on Canadian cities, showing mother-tongue counts from the 2011 Census.a) Plot Cantonese speaker count versus Mandarin speaker count. Would you fit a regression line for predicting Cantonese speakers from Mandarin speakers? Explain.b) Take the log (base
51. Math and gender 2009 Below are mean PISA (Programme for International Student Assessment) math scores for samples of 15-year-old male and female students from a number of randomly selected schools in each of various OECD and other industrialized nations (4000–10 000 per country).Country Male
50. Interprovincial migration 2015 In Chapter 6 exercises, we examined data showing the net interprovincial migration each year for Ontario and Alberta (number arriving minus number leaving). Below are the first few and last few lines of the data file available at www.pearsoncanada. ca/deveaux.few
49. Gender gap 2011 Below is the difference in median income, for full-time, full-year workers, between males and females in Canada, by year (in constant 2011 dollars):a) Plot the difference in median earnings versus year. Describe the relationship.b) Fit a straight line and assess your model by
48. Second stage 2014 Look once more at the data from the Tour de France. In Exercise 46, we looked at the whole history of the race, but now let’s consider just the postWorld War II era.a) Find the regression of Avg Speed by Year only for years from 1947 to the present. Are the conditions for
47. Rich getting richer 2011 Below are annual percentages of Canadian families that earned over $150 000 (in constant 2011 dollars) from 1986–2011. This percentage has gone up, but alas, we’re not all getting richer! During the same period, the percentage earning under $40 000 increased from
46. Tour de France 2014 We met the Tour de France data set in Chapter 1 (in Just Checking). One hundred years ago, the fastest rider finished the course at an average speed of about 25.3 kph (around 15.8 mph). By the 21st century, riders were averaging over 40 kph (nearly 25 mph).a) Make a
45. Life expectancy 2013 Data for 26 Western Hemisphere countries can be used to examine the association between life expectancy and the birth rate (number of births per 1000 population).Country Birth Rate (births/ 1000 population) Life Expectancy Argentina 17.12 76.1 Barbados 12.1 77 Belize 25.58
44. South American Immigrants Below are data on immigration to Canada from South America compared with total immigrants, by year: Year Total immigrants South America 1986 99 343 6 699 1987 152 031 10 798 1988 161 534 7 237 1989 191 516 8 663 1990 216 424 8 986 1991 232 776 10 674 1992 254 856 10
43. Marriage age 2011 revisited Suppose you wanted to predict the trend in marriage age for American women into the early part of this century.a) How could you use the data graphed in Exercise 15 to get a good prediction? Marriage ages in selected years starting in 1900 are listed below. Use all or
42. Another swim 2013 In Exercise 40, we saw that Vicki Keith’s round-trip swim of Lake Ontario was an obvious outlier among the other one-way times. Here is the new regression after this unusual point is removed: Dependent variable is Time R-Squared = 4.5% s = 322.7 Variable Coefficient
41. Elephants and hippos We removed humans from the scatterplot in Exercise 39 because our species was an outlier in life expectancy. The resulting scatterplot shows two points that now may be of concern. The point in the upper right corner of this scatterplot is for elephants, and the other point
40. Swim the lake 2013 People swam across Lake Ontario 52 times between 1974 and 2013 (www.soloswims.com). We might be interested in whether they are getting any faster or slower. Here are the regression of the crossing Times (minutes) against the Year since 1974 of the crossing and the residuals
39. Gestation For humans, pregnancy lasts about nine months. In other species of animals, the length of time from conception to birth varies. Is there any evidence that the gestation period is related to the animal’s lifespan? The first scatterplot shows Gestation Period (in days) vs. Life
38. Marriage age 2011 again Has the trend of decreasing difference in age at first marriage seen in Exercise 36 gotten stronger recently? The scatterplot and residual plot for the data from 1980 through 2011, along with a regression for just those years, are below.a) Is this linear model
37. Interest rates 2014 revisited In Exercise 35, you investigated the federal rate on 3-month Treasury bills between 1950 and 1980. The scatterplot below shows that the trend changed dramatically after 1980, so we computed a new regression model for the years 1981 to 2013.Here’s the model for
36. Marriage age, 2011 The graph shows the ages of both men and women at first marriage (www.census.gov).Clearly, the patterns for men and women are similar. But are the two lines getting closer together?Here’s a timeplot showing the difference in average age (men’s age–women’s age) at
35. Interest rates 2014 Here’s a plot showing the federal rate on 3-month Treasury bills from 1950 to 1980, and a regression model fit to the relationship between the Rate (in %) and Years Since 1950 (www.gpoaccess. gov/eop/).a) What is the correlation between Rate and Year?b) Interpret the slope
34. Speed How does the speed at which you drive affect your fuel economy? To find out, researchers in the United States drove a compact car for 200 miles at speeds ranging from 35 to 75 miles per hour, and measured fuel efficiency in miles per gallon (mpg). From their data, they created the model
33. Heating After keeping track of his heating expenses for several winters, a homeowner in the U.S. believes he can estimate the monthly cost from the average daily Fahrenheit temperature by using the model Cost = 133 - 2.13 Temp. The residuals plot for his data is shown.a) Interpret the slope of
32. Grades A U.S. college admissions officer, defending the college’s use of SAT scores in the admissions process, produced the graph below. It shows the mean GPAs for last year’s freshmen, grouped by SAT scores. How strong is the evidence that SAT Score is a good predictor of GPA? What
31. Reading To measure progress in reading ability, students at an elementary school take a reading comprehension test every year. Scores are measured in “grade-level” units; that is, a score of 4.2 means that a student is reading at slightly above the expected level for a Grade 4 student. The
30. What’s the effect? A researcher studying violent behaviour in elementary-school children asks the children’s parents how much time each child spends playing computer games and has their teachers rate each child on the level of aggressiveness they display while playing with other children.
29. What’s the cause? Suppose a researcher studying health issues measures blood pressure and the percentage of body fat for several adult males and finds a strong positive association. Describe three different possible causeand-effect relationships that might be present.
28. The extra point revisited The original five points in Exercise 27 produce a regression line with slope 0. Match each of the green points (a–e) with the slope of the line after that one point is added:a) -0.45b) -0.30c) 0.00d) 0.05e) 0.85
27. The extra point The scatterplot below shows five small blue data points at the left. Not surprisingly, the correlation for these points is r = 0. Suppose one additional data point is added at one of the five positions (a–e) suggested below in green. Match each point (a–e) with the correct
26. More unusual points Each of the following scatterplots shows a cluster of points and one “stray” point. For each, answer these questions:a) In what way is the point unusual? Does it have high leverage, a large residual, or both?b) Do you think that point is an influential point?c) If that
25. Unusual points Each of these four scatterplots shows a cluster of points and one “stray” point. For each, answer these questions:a) In what way is the point unusual? Does it have high leverage, a large residual, or both?b) Do you think that point is an influential point?c) If that points
24. Tracking hurricanes 2012 In a previous chapter, we saw data on the errors (in nautical miles) made by the National Hurricane Center in predicting the path of hurricanes. The following scatterplot shows the trend in the 24-hour tracking errors since 1970 (www.nhc.noaa.gov). Dependent variable
23. Oakland passengers 2013 The scatterplot below shows the number of passengers at Oakland (CA) airport month by month since 1997. (www.oaklandairport.com)a) Describe the patterns in passengers at Oakland airport that you see in this time plot.b) Until 2009, analysts got fairly good predictions
22. Smoking 2011, women and men In Exercise 16, we examined the percentage of men aged 18–24 who smoked from 1965 to 2011 according to the Centers for Disease Control and Prevention. How about women? Here’s a scatterplot showing the corresponding percentages for both men and women: 1970 20
21. Movie dramas Here’s a scatterplot of the production budgets (in millions of dollars) versus the running time (in minutes) for major release movies in 2005. Dramas are plotted as red x’s and all other genres are plotted as blue dots. (The re-make of King Kong is plotted as a black “–.”
20. Bad model? A student who has created a linear model is disappointed to find that her R2 value is a very low 13%.a) Does this mean that a linear model is not appropriate? Explain.b) Does this model allow the student to make accurate predictions? Explain.
19. Good model? In justifying his choice of a model, a student wrote, “I know this is the correct model because R2 = 99.4%.”a) Is this reasoning correct? Explain.b) Does this model allow the student to make accurate predictions? Explain.
18. Gas mileage revisited Let’s try the re-expressed variable fuel consumption (gal/100 mi) to examine the fuel efficiency of the 11 cars in Exercise 17. Here are the revised regression analysis and residual plot: Dependent variable is: Fuel Consumption R-squared = 89.2% Variable Coefficient
17. Gas mileage One of the important factors determining a car’s fuel efficiency is its weight. Let’s examine this relationship for 11 cars. In this exercise, we are using the U.S. units for fuel efficiency, miles per (U.S.) gallon.a) Describe the association between these variables shown in
16. Smoking 2011 The Centers for Disease Control and Prevention track cigarette smoking in the United States. How has the percentage of people who smoke changed since the danger became clear during the last half of the 20th century? The scatterplot shows percentages of smokers among men 18–24
15. Marriage age 2011 Is there evidence that the age at which women get married has changed over the past 100 years? The scatterplot shows the trend in age at first marriage for American women (Adapted from Bureau of the Census (2010). Median age at first marriage: 1890 to present. From
14. Average GPA An athletic director proudly states that he has used the average GPAs of the university’s sports teams and is predicting a high graduation rate for the teams. Why is this method unsafe?
13. Grading A team of Calculus teachers is analyzing student scores on a final exam compared to the midterm scores. One teacher proposes that they already have every teacher’s class averages and they should just work with those averages. Explain why this is problematic.
12. Cell phones and life expectancy The correlation between cell phone usage and life expectancy is very high. Should we buy cell phones to help people live longer?
11. Skinned knees There is a strong correlation between the temperature and the number of skinned knees on playgrounds. Does this tell us that warm weather causes children to trip?
10. Revenue and advanced sales The production company of Exercise 9 offers advanced sales to “Frequent Buyers” through its website. Here’s a relevant scatterplot:One performer refused to permit advanced sales. What effect would that point have if we were to fit a regression line to predict
9. Revenue and large venues A regression of Total Revenue on Ticket Sales by the concert production company of Exercises 2 and 4 finds the model Revenue = -14 228 + 36.87 TicketSales.a) Management is considering adding a stadium-style venue that would seat 10 000. What does this model predict that
8. Stopping times Using data from 20 compact cars, a consumer group develops a model that predicts the stopping time for a vehicle by using its weight. You consider using this model to predict the stopping time for your large SUV. Explain why this is not advisable.
7. Cell phone costs Noting a recent study predicting the increase in cell phone costs, a friend remarks that by the time he’s a grandfather, no one will be able to afford a cell phone. Explain where his thinking went awry.
6. Abalone again The researcher in Exercise 5 is content with the second regression. But he has found a number of shells that have large residuals and is considering removing them all. Is this good practice?
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