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Statistics The Art And Science Of Learning From Data 4th Global Edition Alan Agresti, Christine A. Franklin, Bernhard Klingenberg - Solutions

For the data set calculate the five-number summary and the interquartile range. Use this information to construct a box plot and identify any outliers.7. n=15 measurements: 19,12,16, 0,14, 9, 6,1, 12,13,10,19, 7, 5,8
For the data set calculate the five-number summary and the interquartile range. Use this information to construct a box plot and identify any outliers.8. n=8 measurements: .23, .30, .35, .41, .56, .58, .76, .80
For the data set calculate the five-number summary and the interquartile range. Use this information to construct a box plot and identify any outliers.9. n=11 measurements: 25, 22, 26, 23, 27, 26, 28,18, 25, 24,12
For the data set, find the mean, the standard deviation, and the five-number summary. Find the z-scores for the minimum and maximum observations. Then construct a box plot and identify any outliers. Are the results using z-scores the same as those based on the box plots?10. n=15 measurements:
For the data set, find the mean, the standard deviation, and the five-number summary. Find the z-scores for the minimum and maximum observations. Then construct a box plot and identify any outliers. Are the results using z-scores the same as those based on the box plots?11. n=13 measurements: 3,
12. You scored 78, which was the 69th percentile on a placement test. What are the percentiles and what do they mean in practical terms?
13. In the U.S. population, about 14.5% of all men are 1.83 meters tall or taller. What are the percentiles and what do they mean in practical terms?
14. A score of 513 on the MCAT (Medical College Admissions Test) is the 90th percentile. What are the percentiles and what do they mean in practical terms?
15. Forty-six percent of all 19-year-old females in a certain height-weight category have a BMI (body mass index) greater than 21.9. What are the percentiles and what do they mean in practical terms?
Find the sample mean and the sample standard deviation and calculate the z-scores for the largest and smallest observations. Are there any unusually large or small observations?16. TV Viewers A sample of 25 households in a particular area gave the following estimates of the number of television
Find the sample mean and the sample standard deviation and calculate the z-scores for the largest and smallest observations. Are there any unusually large or small observations?17. Packaging Hamburger Meat The weights (in pounds) of 27 packages of ground beef are listed here in order from smallest
Find the five-number summary and the IQR. Use this information to construct a box plot and identify any outliers.18. Tuna Fish, again The prices of a 170-gram can or a 200-gram pouch for 14 different brands of water-packed light tuna, based on prices paid nationally in supermarkets, are shown
Find the five-number summary and the IQR. Use this information to construct a box plot and identify any outliers.Polluted Seawater A count of the number of bacteria (per 100 milliliters) in 10 samples of seawater gave these readings: 49, 70, 54, 67, 59, 40, 61, 69, 71, 52
20. Mercury Concentration in Dolphins Scientists are increasingly concerned with the buildup of toxic elements in marine mammals and the transfer of these elements to the animals’offspring. The striped dolphin was the subject of one such study. The mercury concentrations (micrograms/gram) in the
21. Comparing NFL Quarterbacks How does Alex Smith, quarterback for the Kansas City Chiefs, compare to Joe Flacco, quarterback for the Baltimore Ravens? The following table shows the number of completed passes for each athlete during the 2017 NFL football seasona. Calculate five-number summaries
22. Presidential Vetoes The number of vetoes used by each of the 44 presidents is listed here, along with a box plot generated by MINITAB.6 Use the box plot to describe the shape of the distribution and identify any outliers. Washington J. Adams Jefferson Madison Monroe J. Q. Adams Jackson Van
23. Survival Times Altman and Bland report the survival times for patients with active hepatitis, half treated with prednisone and half receiving no treatment.12 The survival times (in months) are adapted from their data for those treated with prednisone.a. Can you tell by looking at the data
24. Utility Bills in Southern California, again The monthly utility bills for a household in Riverside, California were recorded for 12 consecutive months starting in January 2017:a. Draw a box plot for the monthly utility costs.b. What does the box plot tell you about the distribution of utility
25. Ages of Pennies Here are the ages of 50 pennies, calculated as AGE = CURRENT YEAR - YEAR ON PENNY. The data have been sorted from smallest to largest.a. What is the average age of the pennies?b. What is the median age of the pennies?c. Based on the results of parts a andb, how would you
The following data are the front and rear leg rooms (in inches) for 10 different compact sports utility vehicles1. Since the data involve two variables and a third labeling variable, enter the data into the first three columns of an Excel spreadsheet, using the labels in the table. Select Data ➤
The following data are the front and rear leg rooms (in inches) for 10 different compact sports utility vehicles131. Since the data involve two variables and a third labeling variable, enter the data into the first three columns of a MINITAB worksheet, using the labels in the table. Using the
1. Raisins The number of raisins in each of 14 miniboxes (14-gram size) was counted for a generic brand and for Sunmaid brand raisins. The two data sets are shown here:a. What are the mean and the standard deviation for the generic brand?b. What are the mean and the standard deviation for the
2. Raisins, continued Refer to Exercise 1.a. Find the median, the upper and lower quartiles, and the IQR for each of the two data sets.b. Construct two box plots on the same horizontal scale to compare the two sets of data.c. Draw two stem and leaf plots and describe the shapes of the two data
3. Real Estate Prices The asking prices in thousands of dollars for 25 single family residences listed in Riverside, CA in September 2017 followa. Locate the largest and smallest prices and use the range to approximate the standard deviation.b. Calculate the sample mean x and the sample standard
4. A Recurring Illness The lengths of time (in months) between the onset of a particular illness and its recurrence were recorded as follows:a. Find the range.b. Use the range to approximate s.c. Calculate s for the data and compare it with your approximation from part b. 2.1 4.4 2.7 32.3 9.9 9.0
5. A Recurring Illness, continued Refer to Exercise 4.a. Use the data set to count the number of observations in the intervals x 6s, x 62s, and x 63s.b. Do the percentages in these intervals agree with Tchebysheff’s Theorem? With the Empirical Rule?c. Should the Empirical Rule be used to describe
6. A Recurring Illness, again Find the median and the lower and upper quartiles for the data in Exercise 4.Use these measures to draw a box plot for the data, and use the box plot to describe the distribution.
7. Electrolysis A chemist wanted to determine the number of moles of cupric ions in a given volume of solution. The solution was divided into n530 portions of .2 milliliter each, and each of the portions was tested.The average number of moles of cupric ions for the n530 portions was found to be .17
8. Chloroform According to the EPA, small amounts of chloroform, suspected of being a cancer-causing agent, are present in all of the country’s public water sources.If the mean and the standard deviation of the amounts of chloroform present in the water sources are 34 and 53 micrograms per liter,
9. Sleep and the College Student A group of 10 college students were asked how many hours they slept the previous night:7, 6, 7.25, 7, 8.5, 5, 8, 7, 6.75, 6a. Construct a box plot for the data.b. Is the value x58.5 an outlier? Is this an unusually sleepy college student?
10. Gas Mileage The miles per gallon for each of 20 medium-sized cars selected from a production line during the month of March are listed here.a. Find the z-scores for the largest and smallest measurements.Would you consider them to be outliers?Why or why not?b. Find the median and the upper and
11. SAT Tests The College Board’s verbal and mathematics scholastic aptitude tests are scored on a scale of 200 to 800. It is reasonable to assume that a distribution of all test scores, either verbal or math, is moundshaped.If s is the standard deviation of one of these distributions, what is
12. Long-Stemmed Roses A strain of long-stemmed roses has an approximate normal distribution with a mean stem length of 38 centimeters and a standard deviation of 6.4 centimeters.a. If one accepts “long-stemmed roses” only with a stem length greater than 31.6 centimeters, what percentage of
13. Drugs for Hypertension A drug company wishes to know if an experimental drug being tested in its laboratories has any effect on systolic blood pressure. Fifteen randomly selected subjects were given the drug, and their systolic blood pressures (in millimeters) are recorded.a. Guess the value of
14. Lumber Rights A company interested in lumbering rights for a certain tract of slash pine trees is told that the mean diameter of these trees is 35 centimeters with a standard deviation of 7 centimeters. Assume the distribution of diameters is roughly mound-shaped.a. What fraction of the trees
15. Social Ambivalence The following data represent the social ambivalence scores for 15 people as measured by a psychological test. (The higher the score, the stronger the ambivalence.)a. Guess the value of s using the range approximation.b. Calculate x and s for the 15 social ambivalence
16. College Teachers Suppose that the number of teachers per college at small 2-year colleges has an average m 5175 and a standard deviation s 515.a. Use Tchebysheff’s Theorem to describe the percentage of colleges that have between 145 and 205 teachers.b. Assume that the population is normally
17. Is It Accurate? From the following data, a student calculated s to be .263. Why might we doubt his accuracy? What is the correct value (to the nearest hundredth)? 17.2 17.1 17.0 17.1 16.9 17.0 17.1 17.0 17.3 17.2 17.1 17.0 17.1 16.9 17.0 17.1 17.3 17.2 17.4 17.1
18. Breathing Patterns Research psychologists want to find out if a person’s breathing patterns are affected by a particular experimental treatment. They collect some baseline measurements on the n530 people in the study before the treatment—the total ventilation in liters of air per minute
19. Arranging Objects The following data are the response times in seconds for n525 first graders to arrange three objects by size.a. Find the mean and the standard deviation for these 25 response times.b. Order the data from smallest to largest.c. Find the z-scores for the smallest and largest
20. Arranging Objects, continued Refer to Exercise 19.a. Find the five-number summary for this data set.b. Draw a box plot for the data.c. Are there any unusually large or small response times identified by the box plot?d. Construct a stem and leaf display for the response times.How would you
21. Calculating the Mean and the Standard Deviation for Grouped Data Suppose that some measurements occur more than once and that the data , ,…, 1 2 x x xk are arranged in a frequency table as shown here:The formulas for the mean and variance for grouped data areNotice that if each value occurs
22. International Baccalaureate High school students in an International Baccalaureate (IB) must take an exam in each of six subject areas at the end of their junior or senior year. Students are scored on a scale of 1 (poor) to 7 (excellent). During its first year of operation at John W. North High
23. A Skewed Distribution To study the usefulness of the Empirical Rule, look at a distribution that is heavily skewed to the right, as shown in the accompanying figure.a. Calculate x and s for the data shown. (NOTE: There are 10 zeros, 5 ones, and so on.)b. Find the intervals x 6s, x 62s, and x
24. Parasites in Foxes A random sample of 100 foxes was examined by a team of veterinarians to determine the prevalence of a particular type of parasite. Counting the number of parasites per fox, the veterinarians found that 69 foxes had no parasites, 17 had one parasite, and so on. A tabulation of
25. What’s Normal? again Refer to Exercise 15(Chapter 1 Review). In addition to the normal body temperature in degrees Celsius for the 130 individuals, the gender of the individuals was recorded. Box plots for the two groups, male and female, are shown next15:How would you describe the
Which is the response/explanatory variable? For the following pairs of variables, which more naturally is the response variable and which is the explanatory variable?a. Carat 1= weight2 and price of a diamondb. Dosage (low/medium/high) and severity of adverse event (mild/moderate/strong/serious) of
Sales and advertising Each month, the owner of Fay’s Tanning Salon records in a data file the monthly total sales receipts and the amount spent that month on advertising.a. Identify the two variables.b. For each variable, indicate whether it is quantitative or categorical.c. Identify the response
Does higher income make you happy? Every General Social Survey (GSS) includes the question, “Taken all together, would you say that you are very happy, pretty happy, or not too happy?” The table below uses the 2010 survey to cross-tabulate happiness with family income, measured as the response
Alcohol and college students The Harvard School of Public Health, in its College Alcohol Study Survey, surveyed college students in about 200 colleges in 1993, 1997, 1999, and 2001. The survey asked students questions about their drinking habits. Binge drinking was defined as five drinks in a row
Effectiveness of government in preventing terrorism In a survey conducted in March 2013 by the National Consortium for the Study of Terrorism and Responses to Terrorism, 1515 adults were asked about the effectiveness of the government in preventing terrorism and whether they believe that it could
In person or over the phone According to data obtained from the General Social Survey (GSS) in 2014, 1644 out of 2532 respondents were female and interviewed in person, 551 were male and interviewed in person, 320 were female and interviewed over the phone and 17 were male and interviewed over the
Surviving the Titanic Was the motto “Women and Children First” followed on the fateful journey of the Titanic? Refer to the following table on surviving the sinking of the Titanic.a. What’s the percentage of children and female adult passengers who survived? What’s the percentage of male
Gender gap in party ID In recent election years, political scientists have analyzed whether a gender gap exists in political beliefs and party identification. The table shows data collected from the 2010 General Social Survey on gender and party identification (ID).a. Identify the response and
Use the GSS Go to the GSS website sda.berkeley.edu/GSS, click GSS, with No Weight Variables predefined(SDA 4.0), type SEX for the row variable and HAPPY for the column variable, put a check in the row box only for percentaging in the output options, and click Run the Table.a. Report the contingency
Used cars and direction of association For the 100 cars on the lot of a used-car dealership, would you expect a positive association, negative association, or no association between each of the following pairs of variables? Explain why.a. The age of the car and the number of miles on the odometerb.
Broadband and GDP The Internet Use data file on the book’s website contains data on the number of individuals with broadband access and Gross Domestic Product (GDP)for 32 nations. Let x represent GDP (in billions of U.S.dollars) and y = number of broadband users (in millions).a. The figure below
Economic development based on GDP The previous problem discusses GDP, which is a commonly used measure of the overall economic activity of a nation. For this group of nations, the GDP data have a mean of 1909 and a standard deviation of 3136 (in billions of U.S. dollars).a. The five-number summary
Email use and number of children According to data selected from GSS in 2014, the correlation between y =email hours per week and x = ideal number of children is-0.0008.a. Would you call this association strong or weak? Explain.b. The correlation between email hours per week and Internet hours per
Internet use correlations For the 32 nations in the Internet Use data file on the book’s website, consider the following correlations:a. Which pair of variables exhibits the strongest linear relationship?b. Which pair of variables exhibits the weakest linear relationship?c. In Example 7, we found
Match the scatterplot with r Match the following scatterplots with the correlation values.1. r = -0.9 2. r = -0.5 3. r = 0 4. r = 0.6 A x P x x
What makes r -1? Consider the data:x 1 3 5 7 9 y 17 11 10 -1 -7a. Sketch a scatterplot.b. If one pair of (x, y) values is removed, the correlation for the remaining four pairs equals -1. Which pair has been removed?c. If one y value is changed, the correlation for the five pairs equals -1.
Gender and Chocolate Preference The following table shows data on gender 1coded as 1 = female, 2 = male2 and preferred type of chocolate 1coded as 1 = white, 2 = milk, 3 = dark2 for a sample of 10 students.The students’ teacher enters the data into software and reports a correlation of 0.640
Provide a data set with five pairs of numeric values for which r 7 0, but r = 0 after one of the points is deleted.
Correlation inappropriate Describe a situation in which it is inappropriate to use the correlation to measure the association between two quantitative variables.
Which mountain bike to buy? Is there a relationship between the weight of a mountain bike and its price?A lighter bike is often preferred, but do lighter bikes tend to be more expensive? The following table, from the Mountain Bike data file on the book’s website, gives data on price, weight, and
Prices and protein revisited Is there a relationship between the protein content and the cost of Subway sandwiches? Use software to analyze the data in the following tablea. Construct a scatterplot to show how protein depends on cost. Is the association positive or negative? Do you notice any
Buchanan vote Refer to Example 6 and the Buchanan and the Butterfly Ballot data file on the book’s website.Let y = Buchanan vote and x = Gore vote.a. Construct a box plot for each variable. Summarize what you learn.b. Construct a scatterplot. Identify any unusual points.What can you learn from a
Sketch plots of lines Identify the values of the y-intercept a and the slopeb, and sketch the following regression lines, for values of x between 0 and 10.a. yn = 7 + 0.5xb. yn = 7 + xc. yn = 7 - xd. yn = 7
Sit-ups and the 40-yard dash Is there a relationship between how many sit-ups you can do and how fast you can run 40 yards? The EXCEL output shows the relationship between these variables for a study of female athletes to be discussed in Chapter 12.a. The regression equation is yn = 6.71- 0.024x.
Wage bill of Premier League Clubs Data of the Premier League Clubs’ wage bills was obtained from www.tsmplug.com. For the response variable y = wage bill in millions of pounds in 2014 and the explanatory variable x = wage bill in millions of pounds in 2013, yn = -1.537 + 1.056x.a. How much do you
Rating restaurants Zagat restaurant guides publish ratings of restaurants for many large cities around the world(see www.zagat.com). The review for each restaurant gives a verbal summary as well as a 0- to 30-point rating of the quality of food, décor, service, and the cost of a dinner with one
Predicting cost of meal from rating Refer to the previous exercise. The correlation with the cost of a dinner is 0.68 for food quality rating, 0.69 for service rating, and 0.56 for décor rating. According to the definition of r2 as a measure for the reduction in the prediction error, which of
Internet and email use According to data selected from GSS in 2014, the correlation between y = email hours per week and x = Internet hours per week is 0.33. The regression equation is predicted email hours = 3.54 + 0.25 Internet hoursa. Based on the correlation value, the slope had to be positive.
Government debt and population Data used in this exercise was published by www.bloomberg.com for the most government debt per person for 58 countries and their respective population sizes in 2014. When using population size (in millions) as the explanatory variable x, and government debt per person
Diamond weight and price The weight (in carats)and the price (in millions of dollars) of the 9 most expensive diamonds in the world was collected from www.elitetraveler.com. Let the explanatory variable x = weight and the response variable y = price. The regression equation is yn = 109.618+
How much do seat belts help? In 2013, data was collected from the U.S. Department of Transportation and the Insurance Institute for Highway Safety. According to the collected data, the number of deaths per 100,000 individuals in the U.S would decrease by 24.45 for every 1 percentage point gain in
Regression between cereal sodium and sugar The following figure shows the result of a regression analysis of the explanatory variable x = sugar and the response variable y = sodium for the breakfast cereal data set discussed in Chapter 2 (the Cereal data file on the book’s website).a. What
Expected time for weight loss In 2014, the statistical summary of a weight loss survey was created and published on www.statcrunch.com.a. In this study, it seemed that the desired weight loss (in pounds) was a good predictor of the expected time (in weeks) to achieve the desired weight loss. Do you
Advertising and sales Each month, the owner of Fay’s Tanning Salon records in a data file y = monthly total sales receipts and x = amount spent that month on advertising, both in thousands of dollars. For the first three months of operation, the observations are as shown in the table.Advertising
Midterm–final correlation For students who take Statistics 101 at Lake Wobegon College in Minnesota, both the midterm and final exams have mean = 75 and standard deviation = 10. The professor explores using the midterm exam score to predict the final exam score.The regression equation relating y
Predict final exam from midterm In an introductory statistics course, x = midterm exam score and y = final exam score. Both have mean = 80 and standard deviation = 10.The correlation between the exam scores is 0.70.a. Find the regression equation.b. Find the predicted final exam score for a student
NL baseball Example 9 related y = team scoring (per game) and x = team batting average for American League teams. For National League teams in 2010, yn = -6.25 + 41.5x. (Data available on the book’s website in the NL team statistics file.)a. The team batting averages fell between 0.242 and 0.272.
Study time and college GPA A graduate teaching assistant (Euijung Ryu) for Introduction to Statistics (STA 2023) at the University of Florida collected data from one of her classes in spring 2007 to investigate the relationship between using the explanatory variable x = study time per week (average
Oil and GDP An article in the September 16, 2006, issue of The Economist showed a scatterplot for many nations relating the response variable y = annual oil consumption per person (in barrels) and the explanatory variable x = gross domestic product (GDP, per person, in thousands of dollars). The
Mountain bikes revisited Is there a relationship between the weight and price of a mountain bike? This question was considered in Exercise 3.21. We will analyze the Mountain Bike data file on the book’s website. (The data also were shown in Exercise 3.21.)a. Construct a scatterplot. Interpret.b.
Mountain bike and suspension type Refer to the previous exercise. The data file contains price, weight, and type of suspension system (FU = full, FE = front@end in the scatterplot shown).a. Do you observe a linear relationship? Is the single regression line, which is yn = 1896 - 40.45x, the best
Fuel Consumption Most cars are fuel efficient when running at a steady speed of around 40 to 50 mph. A scatterplot relating fuel consumption (measured in mpg) and steady driving speed (measured in mph) for a mid-sized car is shown below. The data are available in the Fuel file on the book’s Web
Extrapolating murder The SPSS figure shows the data and regression line for the 50 states in Table 3.6 relating x = percentage of single-parent families to y = annual murder rate (number of murders per 100,000 people in the population).a. The lowest x value was for Utah and the highest was for
Men’s Olympic long jumps The Olympic winning men’s long jump distances (in meters) from 1896 to 2012 and the fitted regression line for predicting them using x = year are displayed in the graph below (data on website).a. Identify an observation that may influence the fit of the regression line.
U.S. average annual temperatures Use the U.S.Temperatures data file on the book’s website. (Source:National Climatic Data Center).a. Construct a scatterplot, fit a trend line, and interpret the slope.b. Predict the annual mean U.S. temperature for the year(i) 2016 and (ii) 2500.c. In which
Murder and education Example 13 found the regression line yn = -3.1 + 0.33x for all 51 observations on y = murder rate and x = percent with a college education.a. Show that the predicted murder rates increase from 1.85 to 10.1 as percent with a college education increases from x = 15% to x = 40%,
Murder and poverty For Table 3.6, the regression equation for the 50 states and D.C. relating y = murder rate and x = percent of people who live below the poverty level is yn = -4.1 + 0.81x. For D.C., x = 17.4 and y = 41.8.a. When the observation for D.C. is removed from the data set, yn = 0.4+
TV watching and the birth rate The figure shows recent data on x = the number of televisions per 100 people and y = the birth rate (number of births per 1000 people) for six African and Asian nations. The regression line, yn = 29.8- 0.024x, applies to the data for these six countries. For
Looking for outliers Using software, analyze the relationship between x = college education and y = percentage single-parent families, for the data in Table 3.6, which are in the U.S. Statewide Crime data file on the book’s website.a. Construct a scatterplot. Based on your plot, identify two
Regression between cereal sodium and sugar Let x = sodium and y = sugar for the breakfast cereal data in the Cereal data file on the book’s website and in Table 2.3 in Chapter 2.a. Construct a scatterplot. Do any points satisfy the two criteria for a point to be potentially influential on the
Gestational period and life expectancy Does the life expectancy of animals depend on the length of their gestational period? The data in the Animals file on the book’s website show observations on the average longevity (in years) and average gestational period (in days) for 21 animals. (Source:
GPA and hours spent watching TV A study conducted among sophomores at Fairfield University showed a correlation of -0.69 between the number of hours spent watching TV and GPA. It was found that for each additional hour a week you spent watching TV, you could expect on average to see a drop of
Hospital size and length of stay A study shows that there is a positive correlation between x = size of a hospital (measured by its numbers of beds) and y = median number of days that patients remain in that hospital.a. Does this mean that you can shorten a hospital stay by choosing a small
Does ice cream prevent flu? Statistical studies show that a negative correlation exists between the number of flu cases reported each week throughout the year and the amount of ice cream sold in that particular week. Based on these findings, should physicians prescribe ice cream to patients who

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