Statistical Reasoning For Everyday Life 4th International Edition Jeffrey Bennett, William L. Briggs, Mario F. Triola - Solutions

The ages of people who visit Disneyworld.Answer the following questions: a. How many modes would you expect for the distribution? b. Would you expect the distribution to be symmetric, left-skewed, or right-skewed?
The incomes of people sitting in luxury boxes at the Super Bowl.Answer the following questions: a. How many modes would you expect for the distribution? b. Would you expect the distribution to be symmetric, left-skewed, or right-skewed?
The amounts of time that 5000 randomly selected individual taxpayers used to prepare their federal tax returns.Answer the following questions: a. How many modes would you expect for the distribution? b. Would you expect the distribution to be symmetric, left-skewed, or right-skewed?
Assume that you are manufacturing aspirin tablets that are supposed to contain 325 mg of aspirin. If the standard deviation of the amounts of aspirin is calculated, which value would you prefer: a standard deviation of 20 mg or a standard deviation of 10 mg? Why?
For the salaries paid to the 817 professional baseball players in a recent year, the first quartile is $$4,355,101.$ What do we mean when we say that $$4,355,101$ is the first quartile?
The house key lengths of 15 statistics students are measured and rounded to the nearest centimeter, and all 15 values are the same, so the standard deviation is 0 cm.Decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly.
For a recent year, the 817 salaries paid to professional baseball players have a median of $$1,152,000$ and a second quartile with the same value of $$1,152,000$.Decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly.
The following data sets give the ages in years of a sample of cars in a faculty parking lot and a student parking lot at the College of Portland. Faculty: 2 3 1 0 1 2 4 3 3 2 1 Student: 5 6 8 2 7 10 14 6 10 9
The following data sets show the ages of the first seven U.S. Presidents (Washington through Jackson) and seven recent U.S. Presidents (Ford through Obama) at the time of inauguration. First 7: Last 7: 57 61 57 57 58 57 61 61 52 69 64 46 54 47
The following data sets give the approximate lengths of Beethoven’s nine symphonies and Mahler’s nine symphonies (in minutes). Beethoven: Mahler: 28 36 50 33 30 40 38 26 68 52 85 94 50 72 72 80 90 80
You manage a small ice cream shop in which your employees scoop the ice cream by hand. Each night, you total your sales and the total volume of ice cream sold. You find that on nights when an employee named Ben is working, the mean price of the ice cream sold is $$1.75$ per pint with a standard
For the past 100 years, the mean batting average in the major leagues has remained fairly constant at about 0.260. However, the standard deviation of batting averages has decreased from about 0.049 in the 1870s to 0.031 in the present. What does this tell us about the batting averages of players?
At the Web sites of the American Lung Association and the U.S. Environmental Protection Agency, find statistical data concerning the health effects of secondhand (passive) smoke. Write a short summary of your findings and your opinions about whether and how this health issue should be addressed by
A recent study by the Kaiser Family Foundation looked at the role of media (for example, television, books, computers) in the lives of children. The report, which is on the Kaiser Family Foundation Web site, gives many data distributions concerning, for example, how much time children spend daily
The range and standard deviation use different approaches to measure variation in a data set. Construct two different data sets configured so that the range of the first set is greater than the range of the second set (suggesting that the first set has more variation) but the standard deviation of
Find two examples of data distributions in recent news reports; they may be given either as tables or as graphs. In each case, state the range of the distribution and explain its meaning in the context of the news report. Estimate the standard deviation by applying the range rule of thumb.
Find an example of a data distribution given in the form of a table in a recent news report. Make a five-number summary and a boxplot for the distribution.
Jennifer is given a pregnancy test. What does it mean when she is told that the result is positive?
If you apply a test for the presence of alcohol, what is the result called if the test correctly indicates that the subject has not consumed alcohol?
When the Giants and Patriots football teams play each other, can one of the quarterbacks have a higher passing percentage in each half while having a lower passing percentage for the entire game?
Ann and Bret are taking the same statistics course, in which the final grade is determined by assignments and exams. Ann’s mean score on the assignments is higher than Bret’s, and Ann’s mean score on the exams is higher than Bret’s. It follows that Ann’s overall mean score in the course
Ann’s batting average for the first half of the softball season is higher than Bret’s, and Ann’s batting average for the second half of the season is higher than Bret’s. It follows that Ann’s batting average for the entire season is higher than Bret’s.Decide whether the statement makes
After taking a test for the presence of a disease, a patient is happy because the physician announces that the test results are positive.Decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly.
Find a recent article in which someone or some group proposes a polygraph test to determine whether a person is being truthful. In light of what you know about polygraph tests, do you think the results will be meaningful? Why or why not?
Eight grocery stores sell the PR energy bar for the following prices:Find the mean, median, and mode for these prices. $1.09 $1.29 $1.29 $1.35 $1.39 $1.49 $1.59 $1.79
A track coach wants to determine an appropriate heart rate for her athletes during their workouts. She chooses five of her best runners and asks them to wear heart monitors during a workout. In the middle of the workout, she reads the following heart rates for the five athletes: 130, 135, 140,
A newspaper surveys wages for workers in regional high-tech companies and reports an average of $$22$ per hour. The workers at one large firm immediately request a pay raise, claiming that they work as hard as employees at other companies but their average wage is only $$19.$ The management
All 100 first-year students at a small college take three courses in the Core Studies program. Two courses are taught in large lectures, with all 100 students in a single class. The third course is taught in 10 classes of 10 students each. Students and administrators get into an argument about
Randall has 38 credits with a grade of A, 22 credits with a grade of B, and 7 credits with a grade of C. What is his grade point average (GPA)? Base the GPA on values of 4.0 points for an A, 3.0 points for a B, and 2.0 points for a C.
Voting in corporate elections is usually weighted by the amount of stock owned by each voter. Suppose a company has five stockholders who vote on whether the company should embark on a new advertising campaign. The votes (Y = yes, N = no) are as follows:According to the company’s bylaws, the
How many modes would you expect for each of the following distributions? Why? Make a rough sketch for each distribution, with clearly labeled axes.a. Heights of 1,000 randomly selected adult womenb. Hours spent watching football on TV in January for 1,000 randomly selected adult Americansc. Weekly
For each of the following situations, state whether you expect the distribution to be symmetric, left-skewed, or right-skewed. Explain.a. Heights of a sample of 100 womenb. Family income in the United Statesc. Speeds of cars on a road where a visible patrol car is using radar to detect speeders.
How would you expect the variation to differ between times in the Olympic marathon and times in the New York City marathon? Explain.
Consider the following two sets of quiz scores for nine students. Which set has the greater range? Would you also say that this set has the greater variation? Quiz 1: 1 10 10 10 10 10 10 10 10 Quiz 2: 2 3 4 5 6 7 8 9 10
One way to study exposure to cigarette smoke is by measuring blood levels of serum cotinine, a metabolic product of nicotine that the body absorbs from cigarette smoke. Table 3 lists serum cotinine levels from samples of 50 smokers (“active smoke”) and 50 nonsmokers who are exposed to cigarette
Answer the following questions concerning the data in Table 3. a. What is the percentile for the data value of 104.54 ng/ml for smokers?b. What is the percentile for the data value of 61.33 ng/ml for nonsmokers?c. What data value marks the 36th percentile for the smokers? For the nonsmokers?Data
Calculate the standard deviations for the waiting times at Big Bank and Best Bank? Calculating the Standard Deviation To calculate the standard deviation for any data set: Step 1. Compute the mean of the data set. Then find the deviation from the mean for every data value by subtracting the mean
Use the range rule of thumb to estimate the standard deviations for the waiting times at Big Bank and Best Bank. Compare the estimates to the actual values found in Example 4.Data From Example 4:-Calculate the standard deviations for the waiting times at Big Bank and Best Bank? Calculating the
Studies of the gas mileage of a Prius under varying driving conditions show that it gets a mean of 45 miles per gallon with a standard deviation of 4 miles per gallon. Estimate the minimum and maximum typical gas mileage amounts that you can expect under ordinary driving conditions.
Table 6 gives the shooting performance of two players in each half of a basketball game. Shaq had a higher shooting percentage in both the first half (40% to 25%) and the second half (75% to 70%). Can Shaq claim that he had the better game? TABLE 6 Basketball Shots First half Player Baskets
Suppose you are a doctor seeing a patient with a breast tumor. Her mammogram comes back negative. Based on the numbers in Table 7, what is the chance that she has cancer? TABLE 7 Summary of Results for 10,000 Mammograms (when in fact 100 tumors are malignant and 9,900 are benign) Tumor is malignant
All athletes participating in a regional high school track and field championship must provide a urine sample for a drug test. Those who fail are eliminated from the meet and suspended from competition for the following year. Studies show that, at the laboratory selected, the drug tests are 95%
The first class in a frequency table of incomes shows a frequency of 24 corresponding to the range of values from $$0$ to $$999.$ Using only this information about the frequency table, is it possible to identify the original 24 sample values that are summarized by this class? Explain.
A friend tells you that her frequency table has two columns labeled State and Median Income.Decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly.
The relative frequency of category A in a table is 0.27 or 27%.Decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly.
What do we mean by the distribution of data?
What is an important advantage of a Pareto chart over a pie chart?
I used a pie chart to illustrate a data set showing how the cost of college has changed over time.Decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly.
A quality control engineer wants to draw attention to the most serious causes of defects, so sheuses a Pareto chart to illustrate the frequencies of the different causes of defects.Decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain
I made both a histogram and a line chart for a data set of the crime rate (number of crimes committed) each year from 1960 to 2010. The histogram showed that the crime rate peaked in 1982, while the line chart showed that it peaked in 1983.Decide whether the statement makes sense (or is clearly
Incomes of college graduates who took a statistics course.
The political party affiliations of 1000 survey subjects.
Number of movie theatres for each year since 1960.
Ages of people who died in car crashes last year.
Construct a Pareto chart of the data given in Exercise 21. Compare the Pareto chart to the pie chart. Which graph is more effective in showing the relative importance of the mistakes made by job applicants?Data From Exercise 21:-Chief financial officers of U.S. companies were surveyed about areas
Refer to the QWERTY data in Exercise 19 in Section 1 and construct a dotplot.Data From Exercise 19 in Section 1:-The traditional keyboard configuration is called a Qwerty keyboard because of the positioning of the letters QWERTY on the top row of letters. Developed in 1872, the Qwerty configuration
Refer to the Dvorak data in Exercise 19 in Section 1 and construct a dotplot. Compare the result to the dotplot in Exercise 23. Based on the results, does either keyboard configuration appear to be better? Explain.Data From Exercise 23:-Refer to the QWERTY data in Exercise 19 in Section 1 and
Can every histogram be converted to a three-dimensional graphic? Does the three-dimensional version of a histogram have more visual appeal? Does the three-dimensional version of a histogram provide any information not provided by the original histogram?
What is a multiple bar graph, and how is it helpful?
A quality control engineer claims that because cars are three-dimensional objects, she needs a three-dimensional graph to display the production cost of a Corvette for each of the past 10 years.Decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly
A contour map could be used to display the ages of all full-time students at your college.Decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly.
A multiple bar graph could be used to show the numbers of males, females, and total students at your college for each of the past 10 years.Decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly.
The stack plot in Figure 21 shows the numbers of male and female higher education students for different years. Projections are from the U.S. National Center for Education Statistics.a. In words, discuss the trends revealed on this graphic.b. Redraw the graph as a multiple line chart. Briefly
The graph in Figure 22 shows home prices in different regions of the United States. Note that the data have not been adjusted for the effects of inflation.a. In words, describe the general trends that apply to the home price data for all regions.b. In words, describe any differences that you notice
Under standard test conditions, the braking distance for a Honda Civic is 136 feet and the braking distance for a VW Jetta is 137 feet. Is that difference meaningful? How could a graph be constructed so that the difference is greatly exaggerated?
A line chart has a vertical scale with values of 0, 1, 10, 100, 1000 and 10,000. What is the name of such a scale? What is an advantage of such a scale?
Constant Dollars. The graph in Figure 41 shows the minimum wage in the United States, together with its purchasing power, which is adjusted for inflation with 1996 used as the reference year. The graph represents the years from 1955 to 2011. Summarize what the graph shows. $8 $7 $6 $5 Minimum Wage
The graph in Figure 42 shows simultaneously the number of births in this country during two time periods: 1946–1964 and 1977–1994. When did the first baby boom peak? When did the second baby boom peak? Why do you think the designer of this display chose to superimpose the two time intervals,
The Rocky Mountain Beverage Company wants feedback on its new product, Coral Cola, and sets up a taste test with 20 people. Each individual is asked to rate the taste of the cola on a 5-point scale:The 20 ratings are as follows:Construct a frequency table for these data. (bad taste) 1 2 3 4 5
Using the taste test data from Example 1, create a frequency table with columns for the relative and cumulative frequencies. What percentage of the respondents gave the cola the highest rating? What percentage gave the cola one of the three lowest ratings?Data From Example 1:-The Rocky Mountain
Consider the following set of 20 scores from a 100-point exam:Determine appropriate bins and make a frequency table. Include columns for relative and cumulative frequency, and interpret the cumulative frequency for this case. 76 80 78 76 94 75 98 77 84 88 81 72 91 72 74 86 79 88 72 75
Carbon dioxide (CO2) is released into the atmosphere by the combustion of fossil fuels (oil, coal, natural gas). Table 6 lists the eight countries that emit the most carbon dioxide each year. Construct Pareto charts for the total emissions and for the average emissions per person. Why do the two
The following data show the ages (at the time when they won the award) of all Academy Award–winning actresses through 2012, sorted into age order. Display the data using 10-year bins. Discuss the results. Ages of Actresses at Time of Academy Award (through 2012) 21 22 24 24 25 25 25 25 26 26 26
Make a stemplot for the data from Example 3. Discuss the pros and cons of the stemplot over a histogram.Data From Example 3:-The following data show the ages (at the time when they won the award) of all Academy Award–winning actresses through 2012, sorted into age order. Display the data using
Figure 10 shows a time-series graph for the death rate (deaths per 1,000 people) in the United States since 1900. (For example, the 1905 death rate of 16 means that, for each 1,000 people living at the beginning of 1905, 16 people died during the year.) Discuss the general trend. Also consider the
Study Figures 13 and 14. What general messages do they reveal? Comment on how the use of the multiple bar and line graphics helps convey these messages.Data From Figure 13 and 14:- Professional Degree Median Annual Earnings of Full-Time Workers (Ages 25 and up), by Educational Attainment and Gender
As you are undoubtedly aware, the government currently spends much more money than it takes in; in fact, in recent years the revenue has been about one-third less than the spending. Therefore, balancing the budget requires either a dramatic reduction in spending, a substantial increase in tax
Study Figures 16 and 17 and use them to answer the following questions.a. Do you see any geographical trends that might explain the states with the lowest energy usage per person?b. Were there any temperatures above 80°F in the United States on the date shown in Figure 17?Data From Figure 16 and
Based on Figure 19, at about what time was the largest number of birds flying over the east-west line marked by the seven cities? Over what part of New York did most of the birds fly? Approximately how many birds passed over Oneonta around 12:00 midnight?
A statistics class consists of 24 students, all but one of whom are unemployed or are employed in low-paying part-time jobs. One student works as an executive secretary earning $$75,000$ per year. Which does a better job of describing the income of a typical student in the class: the mean or the
An economist wants to find the mean annual income for all adults in the United States. She knows that it is not practical to survey each member of the adult population, so she refers to an almanac and finds the mean income listed for each of the 50 states. She adds the 50 state means and divides by
The number on the jersey of each New York Giants football player is recorded, then the mean of those numbers is computed.Decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly.
A professor calculates final grades using a weighted mean in which the final exam counts twice as much as the midterm.Decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly.
The following ages (years) of survey respondents: 22, 19, 21, 27, “over 65,” “over 80”.State whether the mean or median would give a better description of the “average.” Explain your reasoning.
An instructor has a first-period class with 25 students, and they had a mean score of 86% on the midterm exam. The second-period class has 30 students, and they had a mean score of 84% on the same exam. Does it follow that the mean score for both classes combined is 85%? Explain.
A batting average in baseball is determined by dividing the total number of hits by the total number of at-bats (neglecting walks, sacrifices, and a few other special cases). A player goes 2 for 4 (2 hits in 4 at-bats) in the first game, 0 for 3 in the second game, and 3 for 5 in the third game.
Suppose a player has a batting average over many games of 0.200 (he’s not very good). In his next game, he goes 2 for 4, which is a batting average of 0.500 for the game. Does it follow that his new batting average is 10.200 + 0.5002/2 = 0.350? Explain.
For data collected on car driving fatalities, a researcher claims that while many fatalities are recorded as involving alcohol, many others are missed because the deceased are not tested for alcohol consumption. If this is true, what kind of error is introduced and how does it affect the values of
A store is having a “25% off ” sale. How does a sale price compare to an original price?
Researchers doing statistical studies in biology, psychology, and sociology are grateful for the existence of twins. Twins can be used to study whether certain traits are inherited from parents (nature) or acquired from one’s surroundings during upbringing (nurture). Identical twins are formed
When recording the weight of a watermelon, a supermarket clerk writes the wrong number. Is this type of error a random error or a systematic error? Explain.
At a particular moment, the U.S. Census Bureau population clock shows that the global population is 7,118,233,027 people. Describe the accuracy and precision of that population number.Data From Exercise 2:-A standard weight defined to represent exactly 1 kg is kept by the National Institute of
There are 24,627 species of fish on Earth.Decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly.
The Jenkins supermarket manager claims that the scanning errors on purchased items are random, and about half of the errors are in favor of the supermarket.Decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly.
An American Airlines agent tells you that you must pay a surcharge because your checked bag weighs 23.018 kg, which exceeds the limit of 23 kg, and that there’s no doubt that the scale is correct because it measures to the thousandth of a kilogram.Decide whether the statement makes sense (or is
A tax auditor reviewing a tax return looks for several kinds of problems, including these two: (1) mistakes made in entering or calculating numbers on the tax return and (2) places where the taxpayer reported income dishonestly. Discuss whether each problem involves random or systematic errors.
For a flight on a small plane, the pilot asks passengers what they weigh.Identify at least one likely source of random errors and also identify at least one likely source of systematic errors.
The weights of individual M&M plain candies were obtained by placing each candy in a paper cup, then obtaining the weight without accounting for the weight of the cup.Identify at least one likely source of random errors and also identify at least one likely source of systematic errors.
You receive a Visa credit card bill for $$2,995,$ but it includes a charge of $$1,750$ that was not valid. (That is, the true value is $$1,750$ less than the bill claims.)Find the values of the absolute and relative errors.
A steak at a restaurant actually weighs 18 ounces (the true value), but the menu claims that it is a 20-ounce steak.Find the values of the absolute and relative errors.

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Statistical Reasoning For Everyday Life 4th International Edition Jeffrey Bennett, William L. Briggs, Mario F. Triola - Solutions

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