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a course in statistics with r
Mind On Statistics 5th Edition Jessica M Utts, Robert F Heckard - Solutions
2.98 Scores on the Stanford-Binet IQ test have a bell-shaped distribution with mean 100 and standard deviation 16.a. Use the Empirical Rule to specify the intervals into which 68%, 95%, and 99.7% of Stanford-Binet IQ scores fall.b. Draw a picture similar to Figure 2.23 (p. 49) illustrating the
2.97 The scores on the final exam in a course with a large number of students have approximately a bell-shaped distribution.The mean score was 70, the highest score was 98, and the lowest score was 41.a. Find the value of the range for the exam scores.b. Refer to part (a). Use the value of the
2.96 If you learn that your score on an exam was 80 and the mean was 70, would you be more satisfied if the standard deviation was 5 or if it was 15? Explain
2.95 Write a set of seven numbers with a mean of 50 and a standard deviation of 0. Is there more than one possible set of numbers? Explain.
2.94 The data for Exercise 2.66 was this set of systolic blood pressures:110, 123, 132, 150, 127, 118, 102, 122a. Find the mean and standard deviation for these data.b. What is the variance for these data?
2.93 Suppose that the amount spent on textbooks in a semester for college students has a mean of $350 and a standard deviation of $100. In each part, find the value of the standardized score (z-score) for the given amount spent on textbooks.a. $300b. $460c. $650d. $210
2.92 Both of the following lists of n 8 data values have a mean of 20:List 1: 10, 10, 10, 10, 30, 30, 30, 30 List 2: 10, 15, 19, 20, 20, 21, 25, 30 Draw a dotplot comparing the two data lists and explain how the plot shows that the standard deviation for List 1 is greater than the standard
2.91 Refer to Exercise 2.87 about hours of sleep per night for college students. Draw a picture of the distribution. Indicate the locations of the three intervals found in Exercise 2.87.Use Figure 2.24 on p. 51 for guidance.
2.90 Suppose that the mean weight for men 18 to 24 years old is 170 pounds, and the standard deviation is 20 pounds. In each part, find the value of the standardized score (z-score)for the given weight:a. 200 pounds.b. 140 pounds.c. 170 pounds.d. 230 pounds.
2.89 Find the mean and standard deviation for each set of values:a. 22, 27, 30, 21b. 25, 35, 40, 20
2.88 Suppose that the distribution of speeds at an interstate highway location is bell-shaped with a mean of 71 mph and a standard deviation of 5 mph. Use the Empirical Rule to complete each sentence:a. About 68% of vehicles at this location travel between and mph.b. About 95% of vehicles at this
2.87 The typical amount of sleep per night for college students has a bell-shaped distribution with a mean of 7 hours and a standard deviation equal to 1.7 hours. Use the Empirical Rule to complete each sentence:a. About 68% of college students typically sleep between and hours per night.b. About
2.86 Find the mean and standard deviation for each set of values:a. 18, 19, 20, 21, 22b. 20, 20, 20, 20, 20c. 1, 5, 7, 8, 79
2.85 In a statistics class survey, students reported their heights in inches. The instructor entered the data into a computer file and used statistical software to find separate fivenumber summaries for men and women in the class. In the five-number summary for men, the minimum height was 17
2.84 Give an example, not given in Section 2.6, of a situation in which a measurement is an outlier because the individual belongs to a different group than the bulk of individuals measured. Be specific about the variable measured and the way in which the individual may differ from the others who
2.83 Refer to the rainfall data given in Table 2.6 (p. 39). Discuss whether or not there are any outliers, and, if so, whether to discard them or not.
2.82 One of the two authors of this book (one male, one female)has a right handspan measurement of 23.5 cm. Would you consider this value to be an outlier? What additional information do you need to make a decision?General Section Exercises
2.81 A male whose height is 78 inches might be considered to be an outlier among males in a statistics class but not among males who are professional basketball players. Give another example in which the same measurement taken on the same individual would be considered to be an outlier in one
2.80 In the data discussed in Section 2.1, one student reported having slept 16 hours the previous night.a. What additional information do you need to determine whether or not this value is an outlier?b. If you do determine that the data value of 16 hours of sleep is an outlier, what additional
2.79 Find the mean and median for the ages of CEOs of the 50 highest-paid CEOs of Fortune top 500 companies listed in Exercise 2.52 and in the ceodata08 dataset on the companion website. Is the relationship between them what you would typically expect for data with the shape of this
2.78 Create a boxplot for the ages of the 50 highest-paid CEOs of Fortune top 500 companies listed in Exercise 2.52 and in the ceodata08 dataset on the companion website.
2.77 Create a five-number summary for the ages of the 50 highest-paid CEOs of Fortune top 500 companies listed in Exercise 2.52 and in the ceodata08 dataset on the companion website. Write a few sentences describing the dataset.
2.76 In an experiment conducted by one of this book’s authors, 19 students were asked to estimate (in millions) the population of Canada, which was about 30 million at that time.Before they made their estimates, ten of the students (Group 1) were told that the population of the United States was
2.75 Refer to the sentence-length dataset in Exercise 2.44. Note that you cannot compute exact summary values. Provide as much information as you can about the median, interquartile range, and range for the sample of sentence lengths from the Shorter History of England.
2.74 The football team at the school of one of the authors won 4 of 11 games it played during the 2004 college football season.Point differences between teams in the 11 games were 38, 14, 24, 13, 9, 7, 2, 11, 7, 4, 24 A positive difference indicates that the author’s school won the
2.73 Create a five-number summary for the rainfall data in Example 2.12, Table 2.6 (p. 39). Write a few sentences describing the dataset. The data are in the dataset rainfall on the companion website.
2.72 Refer to Example 2.12, Table 2.6, and Figure 2.18 (p. 39) for the rainfall data. Specify whether the shape is skewed to the left or to the right, and explain whether or not the relationship between the mean and the median (which one is higher) is what you typically expect for data with that
2.71 Refer to Exercise 2.70. Repeat that exercise to describe the rainfall data given in Table 2.6 (p. 39) and also in the dataset rainfall on the companion website.
2.70 Describe the data on first ladies’ ages at death given in Table 2.5 (pp. 27–28) and also in the dataset firstladies on the companion website. Compute whatever numerical summaries you think are appropriate, and then write a narrative summary based on the computed information.Include
2.69 Parts (a) and (b) are the same as Exercise 1.23. Refer to Exercise 2.68, which gives exercise times for men and women in a class.a. Create a five-number summary for the men’s responses.Show how you found your answer.b. Use your five-number summary to describe in words the exercise behavior
2.68 This is the same as parts (a) and (b) of Exercise 1.22. Students in a statistics class were asked, “About how many minutes do you typically exercise in a week?” Responses from the women in the class were 60, 240, 0, 360, 450, 200, 100, 70, 240, 0, 60, 360, 180, 300, 0, 270 Responses from
2.67 Create side-by-side boxplots for the “fastest speed ever driven” described in Case Study 1.1 (p. 2): one for males and one for females. Compare the two sexes based on the boxplots. (Five-number summaries are given in Exercise 2.37 and in Case Study 1.1. The raw data are on page 2 and in
2.66 A set of eight systolic blood pressures follows:110, 123, 132, 150, 127, 118, 102, 122a. Find the median value for the dataset.b. Find the values of the lower and upper quartiles.c. Find the value of the interquartile range (IQR).d. Identify any outliers in the dataset. Use the criterion that
2.65 The weights (in pounds) for nine men on the Cambridge crew team were as follows (The Independent, March 31, 1992; also Hand et al., 1994, p. 337):188.5, 183.0, 194.5, 185.0, 214.0, 203.5, 186.0, 178.5, 109.0 The nine men are comprised of eight rowers and a coxswain, a person who does not row
2.64 The following cholesterol levels for n = 20 individuals were given in Exercise 2.48:196 212 200 242 206 178 184 198 160 182 198 182 222 198 188 166 204 178 164 230a. Create a 5-number summary for these data.b. Draw a boxplot of the cholesterol levels.
2.63 Twenty-two college students recorded the number of hours they studied during a one-week period. The resulting data are:11 15 22 8 6 2 24 7 15 13 4 21 10 9 3 34 16 12 14 18 6 12a. Create a 5-number summary for these data.b. Draw a boxplot of the hours studied.
2.62 Students in a statistics class wrote as many letters of the alphabet as they could in 15 seconds using their nondominant hand. The figure for this exercise is a boxplot that compares the number of letters written by males and females in the sample (Data source: letters dataset on the companion
2.61 Sixty-three college men were asked what they thought was their ideal weight. A five-number summary of the responses(in pounds) follows:Median 175 Quartiles 155 190 Extremes 123 225 Data source: idealwtmen dataset on the companion website.a. Find the value of the range for these data.b. Find
2.60 Refer to part (b) of Exercise 2.59. Explain why there is such a large difference between the mean and median values.
2.59 Find the mean and the median for each list of values:a. 64, 68, 72, 76, 80, 86b. 10, 6, 2, 7, 100c. 30, 10, 40, 30
2.58 The heights (in inches) of seven adult men are 73, 68, 67, 70, 74, 72, and 69.a. Find the median height for this list.b. Find the value of the mean height.
2.57 The figure for this exercise is a boxplot comparing tip percentages for a male and a female restaurant server, each of whom drew happy faces on the checks of randomly selected dining parties. A dotplot of the data was given as the figure for Exercise 2.39. Discuss the ways in which the tip
2.56 For the following situations, would you be most interested in knowing the average value, the spread, or the maximum value for each dataset? Explain. If you think it would be equally useful to know more than one of these summaries, explain that as well. (Answers may differ for different
2.55 Histograms and boxplots are two types of graphs that were discussed in Section 2.4.a. Explain what features of a dataset are best identified using a histogram.b. Explain what features of a dataset are best identified using a boxplot.
2.54 Construct an example and sketch a histogram for a measurement that you think would be bimodal.
2.53 About 75% of the students in a class score between 80 and 100 on a quiz. The other 25% of the students have scores spread out between 35 and 79. Characterize the shape of the distribution of quiz scores. Explain.
2.52 Here are the ages, arranged in order, for the 50 highestpaid CEOs on the Fortune 500 list of top companies in the United States in 2008 (Data source: http://www.forbes.com/lists/2009/12/best-boss-09_CEO-Compensation_ CompTotDisp.html). These data are part of the ceodata08 dataset on the
2.51 Does a stem-and-leaf plot provide sufficient information to determine whether or not a dataset contains an outlier?Explain.
2.50 Case Study 1.1 (p. 2) presented data on the fastest speed that men and women had driven a car, and dotplots were shown for each sex. Data for the men are also in the pennstate1M dataset on the companion website.a. Create a stem-and-leaf plot for the male speeds.b. Create a histogram for the
2.49 Annual rainfall for Davis, California, for 1951 to 1997, is given in Table 2.6 in Section 2.5 and in the rainfall dataset on the companion website. A histogram is shown in Figure 2.18 (p. 39).a. Create a stem-and-leaf plot for the rainfall data, rounded(not truncated) to the nearest inch.b.
2.48 Cholesterol levels for n 20 individuals follow:196 212 200 242 206 178 184 198 160 182 198 182 222 198 188 166 204 178 164 230a. Draw a histogram of these data. Make the bars cover intervals of cholesterol that are 10 wide beginning at 155 (155 to 165, 165 to 175, and so on).b. Create a
2.47 A set of exam scores is as follows:75, 84, 68, 95, 87, 93, 56, 87, 83, 82, 80, 62, 91, 84, 75a. Draw a stem-and-leaf plot of the scores.b. Draw a dotplot of the scores.
2.46 About how many music CDs do you own? Responses to this question for 24 students in a senior-level statistics course in 1999 follow:220, 20, 50, 450, 300, 30, 20, 50, 200, 35, 25, 50, 250, 100, 0, 100, 20, 13, 200, 2, 125, 150, 90, 60 The data are also given in the musiccds dataset on the
2.45 The following stem-and-leaf plot is for the mean August temperatures (Fahrenheit) in 20 U.S. cities. The “stem” (row label) gives the first digit of a temperature, while the “leaf”gives the second digit (Data source: temperature dataset on the companion website).6 44 6 89 7 01124 7
2.44 Hand et al. (1994, p. 148) provide data on the number of words in each of 600 randomly selected sentences from the book Shorter History of England by G. K. Chesterton. They summarized the data as follows:Number of Words Frequency Number of Words Frequency 1–5 3 31–35 68 6–10 27 36–40
2.43 The figure for this exercise is a histogram summarizing the responses given by 116 college students to a question asking how much they had slept the previous night(Data source: sleepstudy dataset on the companion website).30 20 10 02 3 4 5 6 7 8 Hours of sleep Frequency 9 10 1112a. Describe
2.42 The figure for this exercise is a histogram summarizing the responses given by 137 college women to a question asking how many ear piercings they have (Data source:pennstate2 dataset on the companion website).50 40 30 20 10 00 2 4 6 8 10 12 14 Number of ear piercings Frequencya. Describe the
2.41 Refer to Exercise 2.40.a. Give a value from the five-number summary that characterizes the location of the data.b. Describe the spread of the data using values from the five-number summary.
2.40 This is the same as Exercise 1.2. A five-number summary for the heights in inches of the women who participated in the survey described in Section 2.1 follows:Female Heights(inches)Median 65 Quartiles 63.5 67.5 Extremes 59 71a. What is the median height for these women?b. What is the range of
2.39 In an experiment, one female and one male restaurant server drew happy faces on the checks of randomly chosen dining parties. The figure for this exercise is a dotplot comparing tip percentages for the female (n 22 checks) to the tip percentages for the male (n 23 checks).Tip percentage
2.38 Refer to the five-number summaries given in Exercise 2.37.a. Using the appropriate summary value, compare the location of the fastest speed ever driven response for males to the location for females.b. Explain whether the spread is greater for one sex than the other or whether it is about the
2.37 This is the same as Exercise 1.1. The five-number summaries of the fastest speed ever driven data given in Case Study 1.1(page 2) were as follows:Males(87 students)Female(102 Students)Median 110 89 Quartiles 95 120 80 95 Extremes 55 150 30 130 Give a numerical value for each of the
2.36 Refer to Exercise 2.35.a. Reconstruct the table using the two categorical variables“letter listed first (S or Q)” and “ordering of letter chosen(listed first or second).”b. Draw an appropriate picture to accompany your numerical summary.c. Explain whether you think the variables used
2.35 In the sample survey described in Section 2.1, there were 92 students who responded to “Randomly pick a letter —S or Q.” Of these 92 students, 61 picked S and 31 picked Q.The order of the letter choices was reversed for another 98 students who responded to “Randomly pick a letter —Q
2.34 Refer to Exercise 2.33 concerning feelings about weight.To compare the men and women, draw a bar graph of the percents found in parts (c) and (d). Use Figure 2.4(p. 23) for guidance.General Section Exercises
2.33 A sample of college students was asked how they felt about their weight. Of the 143 women in the sample who responded, 38 women said that they felt overweight, 99 felt that their weight was about right, and 6 felt that they were underweight. Of the 78 men in the sample, 18 men felt that they
2.32 In 2006 the age distribution for mothers in the United States who had a first child that year was as follows (Martin et al., p. 30):Under 20 20–24 25–29 30–34 35 and Over 20.9% 30.6% 24.7% 15.7% 8.1%a. Draw a bar graph to represent the data.b. Draw a pie chart to represent the data.c.
2.31 For each of the following situations, which is the explanatory variable and which is the response variable?a. The two variables are whether or not someone smoked and whether or not the person developed Alzheimer’s disease.b. The two variables are whether or not somebody voted in the last
2.30 Refer to Exercise 2.27. Students also were asked what grades they usually get in school. For twelfth-grade students who responded to this question and the question about how often they wear seatbelts when driving, a summary of frequency counts for combinations of responses to the two questions
2.29 In a survey done in 2010, students in a statistics class were asked, “How do you prefer to use your cell phone—to talk or to text?” Of the 106 women who responded, 22 women said to talk and 84 said to text. Of the 83 men who responded, 34 men said to talk and 49 men said to text.a.
2.28 In the 2008 General Social Survey, participants were asked,“Would you say that you are very happy, pretty happy, or not too happy?” The results were that 599 people said very happy, 1100 people said pretty happy, and 316 people said not too happy (Data source: http://sda.berkeley.edu).a.
2.27 Table 2.1 (p. 20) summarized frequency of seatbelt use while driving for twelfth-grade participants in the 2003 Youth Risk Behavior Surveillance System (YRBSS) survey. In 2001, YRBSS survey students were asked the same question. For the 2001 survey, a summary of responses given by 2530
2.26 To answer the following questions, researchers would measure two variables for each individual unit in the study. In each case, specify the two variables, and the variable type for each. Then, specify which is the explanatory variable and which is the response variable.a. For college students,
2.25 To answer the following questions, researchers would measure two variables for each individual unit in the study. In each case, specify the two variables, and the variable type for each. Then, specify which is the explanatory variable and which is the response variable.a. Is the average IQ of
2.24 Find an example of a study that uses statistics in a magazine, newspaper, or website. Determine what variables were measured, and, for each variable, determine its type. Which of the questions listed under “Asking the Right Questions” (p. 18)were addressed in this study? Describe the
2.23 Give an example of an ordinal variable for which a numerical summary like the average would make sense.
2.22 Give an example of an ordinal variable that is likely to be treated as a categorical variable because numerical summaries like the average would not make much sense.
2.21 A physiologist records the pulse rates of 30 men and 30 women.a. Specify the two variables measured in this situation.b. For each variable, explain whether it is categorical or quantitative.c. Using the examples under the “Asking the Right Questions” heading in Section 2.2 (p. 18) as a
2.20 According to the Associated Press (June 19, 1998), “Smokers are twice as likely as lifetime nonsmokers to develop Alzheimer’s disease and other forms of dementia . . . [according to a study that] followed 6,870 men and women ages 55 and older.” For this situation, specify the explanatory
2.19 For each of the following situations reported in the news, specify what variable(s) were measured on each individual and whether they are best described as categorical, ordinal, or quantitative.a. A Los Angeles Times survey found that 60% of the 1515 adult Californians polled supported a state
2.18 For each pair of variables, specify which variable is the explanatory variable and which is the response variable in the relationship between them.a. Amount a person walks or runs per day and performance on a test of lung function.b. Feeling about importance of religion and age of
2.17 For each of the following quantitative variables, explain whether the variable is continuous or not.a. Number of classes a student misses in a week.b. Head circumference (in centimeters).c. Time it takes students to walk from their dorm to a classroom.
2.16 For each of the following, indicate whether the variable is ordinal or not. If the variable is not ordinal, indicate its variable type.a. Whether or not the person believes in love at first sight.b. Student rating of teacher effectiveness on a 7-point scale where 1 not at all effective and 7
2.15 For each pair of variables, specify which variable is the explanatory variable and which is the response variable in the relationship between them.a. Score on the final exam and final course grade in a psychology course.b. Opinion about the death penalty (favor or oppose), and sex (male or
2.14 For each of the following quantitative variables, explain whether the variable is continuous or not.a. Body weight (in pounds).b. Number of text messages a person sends in a day.c. Number of coins presently in someone’s pockets and/or purse.
2.13 For each of the following, indicate whether the variable is ordinal or not. If the variable is not ordinal, indicate its variable type.a. Opinion about a new tax law (favor or oppose).b. Letter grade in a statistics course (A, B, and so on).c. Heights of men (in inches).
2.12 For each of the following characteristics of an individual, indicate whether the variable is categorical or quantitative.a. Length of forearm from elbow to wrist (in centimeters).b. Whether or not the person has ever been the victim of a crime.c. Number of songs on his or her digital music
2.11 For each of the following variables, indicate whether the variable is categorical or quantitative.a. Importance of religion to respondent (very, somewhat, or not very important).b. Hours of sleep last night.c. Weights of adult women, measured in pounds.d. Favorite color for an automobile.
2.10 Read Case Study 1.6 (p. 5) about aspirin and heart attack rates.a. What two variables are measured on each individual in Case Study 1.6?b. Describe the observational units in this study.c. What was the sample size for the study?d. Explain whether you think the researchers treated the observed
2.9 Case Study 1.2 (p. 3) gave the information that the rate of errors made by air traffic controllers in the United States during fiscal year 1998 was 5.5 errors per million flights.Discuss whether this summary value is a population summary(a parameter) or a sample summary (a statistic).
2.8 Read Case Study 1.5 (p. 4) about prayer and blood pressure.a. What was the sample size for the observational study conducted by the National Institutes of Health?b. Describe the observational units in this study.c. Describe two variables that the researchers related to each other in Case Study
2.7 Case Study 1.1 (p. 2) was about the fastest speeds that students in a statistics class claimed they have ever driven.a. What variables are described in Case Study 1.1?b. What are the observational units in the study?c. Explain whether you think it would be more appropriate to treat the data as
2.6 For each of the following statistical summaries, explain whether it is a population parameter or a sample statistic.a. A highway safety researcher wants to estimate the average distance at which all drivers can read a highway sign at night. She measures the distance for a sample of 50 drivers;
2.5 For each of the following statistical summaries, explain whether it is a population parameter or a sample statistic.a. In the 2000 census of the United States, it was determined that the average household size was 2.59 persons per household (http://www.census.gov).b. In an ABC News poll
2.4 In each situation, explain whether it would be more appropriate to treat the observed dataset as sample data or as population data.a. A historian summarizes the ages at death for all deceased past presidents of the United States.b. A nutritionist wants to determine which of two weightloss
2.3 In each situation, explain whether it would be more appropriate to treat the observed data as a sample from a larger population or as data from the whole population.a. An instructor surveys all the students in her class to determine whether students would prefer a take-home exam or an in-class
2.2 Suppose that in a national survey of 620 randomly selected adults, each person is asked how important religion is to him or her (very, fairly, not very), and whether the person favors or opposes stricter regulation of what can be broadcast on network television.a. How many variables are
2.1 A sociologist assembles a dataset consisting of the poverty rate, per capita income, serious crime rate, and teen birth rate for the 50 states of the United States.a. How many variables are in this dataset?b. What is an observational unit in this dataset?c. What is the sample size for the
1.44 Refer to Case Study 1.6. Go through the five steps listed under“The Discovery of Knowledge” in Section 1.3, and show how each step was addressed in this study.
1.43 Refer to Case Study 1.5. Explain what mistakes were made in the implementation of steps 4 and 5 of “The Discovery of Knowledge” when USA Today reported the results of this study.
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