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

An article titled “Does Vasectomy Cause Prostate Cancer?” (Chance, Vol. 10, No. 1)reports on several large studies that found an increased risk of prostate cancer among men with vasectomies. In the absence of a direct cause, several researchers attribute the correlation to detection bias, in
Starting from the Web site of the National Highway Traffic Safety Administration, research the latest studies on the safety of air bags, especially with regard to children. Write a short report summarizing your findings and offering recommendations for improving child safety in cars.
In the largest study of how dietary fiber prevents coronary heart disease(CHD) in women (Journal of the American Medical Association, Vol. 281, No. 21), researchers detected a reduced risk of CHD among women who have a high-fiber diet. Find the research paper, summarize its findings, and discuss
Writing in the Journal of the American Medical Association (Vol. 281, No. 22), researchers reported finding a negative correlation between incidence of gallstone disease and coffee consumption in men. Find the research paper, summarize its findings, and discuss whether a cause for the correlation
Researchers reported in the Journal of the American Medical Association (Vol. 281, No. 1)that moderate alcohol consumption is correlated with a decreased risk of stroke in people 40 years of age and older.(Heavy consumption of alcohol was correlated with deleterious effects.) Find the research
Tobacco companies have been the subject of many lawsuits related to the dangers of smoking.Research one recent lawsuit. What were the plaintiffs trying to prove? What statistical evidence did they use? How well do you think they established causality? Did they win?Summarize your findings in one to
Find a recent news report in which a statistical study led to a conclusion of causation.Describe the study and the claimed causation. Do you think the claim of causation is legitimate? Explain.
Find a news report concerning an ongoing legal case, either civil or criminal, in which establishing causality is important to the outcome.Briefly describe the issue of causation in the case and how the ability to establish or refute causality will influence the outcome of the case.
Can we conclude that the old ratings have a direct causal effect on the new ratings? Explain briefly.For Exercises 1–3, refer to the combined city–highway fuel economy ratings (mi/gal) for different cars. The old ratings are based on tests used before 2008 and the new ratings are based on tests
In a study of casino size (square feet) and revenue, the value of r = 0.445 is obtained. Find the value of r2. What does that value tell us?
In a study of global warming, assume that we have found a strong positive correlation between carbon dioxide concentration and temperature. Identify three possible explanations for this correlation.
For 10 pairs of sample data, the correlation coefficient is computed to be r = -1. What do you know about the scatterplot?
Using the data in Table 1, create a scatterplot to look for a correlation between a diamond’s color and price. Comment on the correlation. TABLE 1 Prices and Characteristics of a Sample of 23 Diamonds from Gem Dealers Diamond Price Weight (carats) Depth Table Color Clarity 1 $6,958 1.00 60.5 65 3
Figure 4 shows a scatterplot for the variables life expectancy and infant mortality in 16 countries. What type of correlation does it show? Does this correlation make sense? Does it imply causality? Explain. Infant mortality (deaths per 1,000 live births) 120 100 80 Life Expectancy and Infant
Figure 5 shows a scatterplot for the variables number of farms and mean farm size in the United States. Each dot represents data from a single year between 1950 and 2000; on this diagram, the earlier years generally are on the right and the later years on the left. Estimate the correlation
The scatterplots in Figure 6 show two weeks of data comparing the actual high temperature for the day with the same-day forecast (part a) and the three-day forecast (part b). Estimate the correlation coefficient for each data set and discuss what these coefficients imply about weather forecasts. 70
You’ve conducted a study to determine how the number of calories a person consumes in a day correlates with time spent in vigorous bicycling. Your sample consisted of ten women cyclists, all of approximately the same height and weight. Over a period of two weeks, you asked each woman to record
Every financial advisor has a strategy for predicting the direction of the stock market. Most focus on fundamental economic data, such as interest rates and corporate profits. But an alternative strategy might rely on a famous correlation between the Super Bowl winner in January and the direction
State whether the prediction (or implied prediction) should be trusted in each of the following cases, and explain why or why not.a. You’ve found a best-fit line for a correlation between the number of hours per day that people exercise and the number of calories they consume each day. You’ve
Figure 20 shows data and best-fit lines for both men’s and women’s world record times in the 1-mile race. Based on these data, predict when the women’s world record will be faster than the men’s world record. Comment on the prediction. Record (seconds) 280 270 Women 260 250 240 230 Men 220
You are the manager of a large department store. Over the years, you’ve found a strong correlation between your September sales and the number of employees you’ll need to hire for peak efficiency during the holiday season; the correlation coefficient is 0.950. This year your September sales are
Political scientists are interested in knowing what factors affect voter turnout in elections. One such factor is the unemployment rate. Data collected in presidential election years since 1964 show a very weak negative correlation between voter turnout and the unemployment rate, with a correlation
You’ve been hired by your college’s alumni association to research how past contributions were associated with alumni income and years that have passed since graduation. It is found that R2 = 0.36. What does that result tell us?
What do we mean when we say that “the probability of getting 20 babies of the same gender when 20 random babies are born is 1/524,288? Is such an event unusual? Why or why not?
Use subjective judgment to estimate the probability that the next time you ride an elevator, it gets stuck between floors.
When randomly selecting a day of the week, it is certain that you will select a day containing the letter y, so P(y) = 1.For Exercises 5–10, decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly; not all of these have
Because it is impossible for Thanksgiving to fall on Tuesday, the probability of Thanksgiving falling on Tuesday is 0.For Exercises 5–10, decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly; not all of these have definitive
If there is a 0.9 probability that it will rain sometime today, then there is a probability of 0.1 that it will not rain sometime today.For Exercises 5–10, decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly; not all of these
An insurance company states that the probability that a particular car will be involved in a car crash this year is 0.6 and the probability that the car will not be involved in a car crash this year is 0.3.For Exercises 5–10, decide whether the statement makes sense (or is clearly true) or does
Jack estimates that the subjective probability of his being struck by lightning sometime next year is 1/2.For Exercises 5–10, decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly; not all of these have definitive answers, so
Jill estimates that the subjective probability of her being struck by lightning sometime next year is 1/1,000,000.For Exercises 5–10, decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly; not all of these have definitive
Rolling a die and getting an outcome that is greater than 2.For Exercises 11–18, use the theoretical method to determine the probability of the given outcome or event. State any assumptions that you need to make.
Getting an outcome of a red slot when a roulette wheel is spun (A roulette wheel has slots of 0, 00, 1, 2, 3, . . . , 36, and 18 of those slots are red.).For Exercises 11–18, use the theoretical method to determine the probability of the given outcome or event. State any assumptions that you need
Finding that the next baby born in Alaska is a girl.For Exercises 11–18, use the theoretical method to determine the probability of the given outcome or event. State any assumptions that you need to make.
Rolling a pair of dice and getting an outcome (sum) of 12.For Exercises 11–18, use the theoretical method to determine the probability of the given outcome or event. State any assumptions that you need to make.
What is the probability of rolling a fair die and not getting an outcome less than 7?Exercises 19–26 involve complementary events. In each exercise, find the probability of the given event. State any assumptions that you use.
What is the probability of rolling a fair die and not getting an outcome that is greater than 6?Exercises 19–26 involve complementary events. In each exercise, find the probability of the given event. State any assumptions that you use.
What is the probability of randomly selecting a day of the week and not getting Monday?Exercises 19–26 involve complementary events. In each exercise, find the probability of the given event. State any assumptions that you use.
What is the probability that a 55% free-throw shooter will miss her next free throw?Exercises 19–26 involve complementary events. In each exercise, find the probability of the given event. State any assumptions that you use.
What is the probability that a 0.280 hitter in baseball will not get a hit on his next at-bat?Exercises 19–26 involve complementary events. In each exercise, find the probability of the given event. State any assumptions that you use.
What is the probability of not getting a defective fuse when one fuse is randomly selected from an assembly line and 1% of the fuses are defective?Exercises 19–26 involve complementary events. In each exercise, find the probability of the given event. State any assumptions that you use.
A bag contains 10 red M&Ms, 15 blue M&Ms, and 20 yellow M&Ms. What is the probability of drawing a red M&M? A blue M&M? A yellow M&M? Something besides a yellow M&M?For Exercises 27–30, use the theoretical method to determine the probability of the given outcome or event. State any assumptions
After recording the forecasts of your local weatherman for 30 days, you conclude that he gave a correct forecast 18 times. What is the probability that his next forecast will be correct?Use the relative frequency method to estimate the probabilities in Exercises 31–34.
Halfway through the season, a basketball player has hit 86% of her free throws. What is the probability that her next free throw will be successful?Use the relative frequency method to estimate the probabilities in Exercises 31–34.
In a clinical trial of 73 carpal tunnel syndrome patients treated with surgery, 67 had successful treatments (based on data from “Splinting vs. Surgery in the Treatment of Carpal Tunnel Syndrome” by Gerritsen et al., Journal of the American Medical Association, Vol. 288, No. 10). What is the
The four major blood groups are designated A, B, AB, and O. Within each group there are two Rh types: positive and negative. Using library resources or the Internet, find data on the relative frequency of blood groups, including the Rh types. Construct a table showing the probability of meeting
In your own words, describe the gambler’s fallacy.
Steve learns that for a $$5$ bet on a number in roulette, the expected return is $$4.74,$ but for a $$5$ bet on the pass line in the game of craps, the expected return is $$4.93,$ so it is better to play this particular craps bet than the roulette bet.For Exercises 5–8, decide whether the
Kelly studies the Wisconsin Pick 3 lottery and finds that for a $$1$ bet, the expected return is 50¢, so she reasons that this is bad bet and she does not play.For Exercises 5–8, decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain
When considering the chances of winning a lottery, Kim reasons that the number combination of 1, 2, 3, 4, 5, and 6 is less likely to occur because of the obvious pattern.For Exercises 5–8, decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false).
Describe a situation in which you or someone you know has fallen victim to the gambler’s fallacy. How could the situation have been dealt with correctly?
Because people are not expected to live longer than 90 years, a 100-year-old person has a negative life expectancy.For Exercises 5–8, decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly. Not all of these have definitive
Your life expectancy increases as your age increases.For Exercises 5–8, decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly. Not all of these have definitive answers, so your explanation is more important than your chosen
As you become older, your expected age at death increases.For Exercises 5–8, decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly. Not all of these have definitive answers, so your explanation is more important than your
In a recent year, the total numbers of deaths in the United States due to either accidents or pneumonia were approximately equal. Therefore, the risks of death by accident and pneumonia per 100,000 people are approximately equal.For Exercises 5–8, decide whether the statement makes sense (or is
How many years is a randomly selected 19-year-old expected to live beyond his or her 19th birthday?For Exercises 13–16, use the data in the following table for people in the United States between the ages of 16 and 21 years. Probability of dying during Number surviving to the Expected remaining
How many years is a randomly selected 17-year-old expected to live beyond his or her 17th birthday?For Exercises 13–16, use the data in the following table for people in the United States between the ages of 16 and 21 years. Probability of dying during Number surviving to the Expected remaining
Find the death rate per 10,000 for people during their 17th year (age 16–17).For Exercises 13–16, use the data in the following table for people in the United States between the ages of 16 and 21 years. Probability of dying during Number surviving to the Expected remaining life- Number of
In your own words, state what it means for two events to be non-overlapping.
The professor in a class of 25 students randomly selects a student and then randomly selects a second student. If all 25 students are available for the second selection, is this sampling with replacement or sampling without replacement? Is the second outcome independent of the first?
Let A denote some event. Are events A and A non-overlapping? Why or why not?
The numbers 5, 17, 18, 27, 36, and 41 were drawn in the last lottery; they should not be bet on in the next lottery because they are now less likely to occur.For Exercises 5–8, decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain
Either/Or Probability. P(A) = 0.5 and P(A or B) = 0.8.For Exercises 5–8, decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly; not all of these have definitive answers, so your explanation is more important than your chosen
The probability of your winning the state lottery this week is not affected by whether you won that same lottery last week.For Exercises 5–8, decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly; not all of these have
a. A detective in Detroit finds that 25 of the 62 guns used in crimes during the past week were sold by the same gun shop. This finding is statistically significant. Because there are many gun shops in the Detroit area, having 25 out of 62 guns come from the same shop seems unlikely to have
A researcher conducts a double-blind experiment that tests whether a new herbal formula is effective in preventing colds. During a 3-month period, the 100 randomly selected people in a treatment group take the herbal formula while the 100 randomly selected people in a control group take a placebo.
In the test of the Salk polio vaccine, 33 of the 200,000 children in the treatment group got paralytic polio, while 115 of the 200,000 in the control group got paralytic polio. Calculations show that the probability of this difference between the groups occurring by chance is less than 0.01.
You select a person at random from a large group at a conference. What is the probability that the person selected has a birthday in July? Assume 365 days in a year.
a. How many outcomes are there if you roll two fair dice?b. What is the probability of rolling two 1’s (snake eyes) when two fair dice are rolled?
What is the probability that a randomly selected family with three children has two girls and one boy? Assume that births of boys and girls are equally likely.
Geological records indicate that a river has crested above a particular high flood level four times in the past 2,000 years. What is the relative frequency probability that the river will crest above the high flood level next year?
Identify the method that resulted in the following statements.a. The chance that you’ll get married in the next year is zero.b. Based on government data, the chance of dying in an automobile accident is about 1 in 8,000 (per year).c. The chance of rolling a 7 with a 12-sided die is 1/12.
In a study of checkout scanning systems, samples of purchases were used to compare the scanned prices to the posted prices. Table 1 summarizes results for a sample of 819 items. Based on these data, what is the probability that a regular-priced item has a scanning error? What is the probability
Make a probability distribution for the sum of the dice when two dice are rolled.
A roulette wheel has 38 numbers: 18 black numbers, 18 red numbers, and the numbers 0 and 00 in green. (Assume that all outcomes––the 38 numbers––have equal probability.)a. What is the probability of getting a red number on any spin?b. If patrons in a casino spin the wheel 100,000 times, how
Suppose that $$1$ lottery tickets have the following probabilities: 1 in 5 to win a free ticket (worth $$1)$, 1 in 100 to win $$5,$ 1 in 100,000 to win $$1,000$, and 1 in 10 million to win $$1$ million. What is the expected value of a lottery ticket? Discuss the implications. (Note:
You are playing the coin-toss game in which you win $$1$ for heads and lose $$1$ for tails. After 100 tosses, you are $$10$ in the hole because you have 45 heads and 55 tails. You continue playing until you’ve tossed the coin 1,000 times, at which point you’ve gotten 480 heads and 520
A farmer knows that at this time of year in his part of the country, the probability of rain on a given day is 0.5. It hasn’t rained in 10 days, and he needs to decide whether to start irrigating. Is he justified in postponing irrigation because he is due for a rainy day?
Figure 9 shows the number of automobile fatalities and the total number of miles driven (among all Americans) for each year over a period of more than four decades. In terms of death rate per mile driven, how has the risk of driving changed? Deaths 40,000 30,000 20,000 10,000 0 + + + 3.6 60,000
For the period 1990 through 2010, the average (mean) number of deaths in commercial airplane accidents in the United States was roughly 60 per year. (The actual number varies significantly from year to year.) As of 2010, airplane passengers in the United States travel a total of about 8 billion
Assuming an approximate U.S. population of 300 million, find and compare risks per person and per 100,000 people for pneumonia (and influenza) and cancer.
Using Figure 10b, find the life expectancy of a 20-year-old person and of a 60-year-old person. Are the numbers consistent? Explain. TABLE 10 And probability: Summary of Combining Probabilities independent events P(A and B) = P(A) X P(B) And probability: dependent events P(A and B) = P(A) XP(B
Suppose you toss three fair coins. What is the probability of getting three tails?
The game of bingo involves drawing labeled buttons from a bin at random, without replacement. There are 75 buttons, 15 for each of the letters B, I, N, G, and O. What is the probability of drawing two B buttons in the first two selections?
A polling organization has a list of 1,000 people for a telephone survey. The pollsters know that 433 people out of the 1,000 are members of the Democratic Party. Assuming that a person cannot be called more than once, what is the probability that the first two people called will be members of the
Suppose you roll a single die. What is the probability of rolling either a 2 or a 3?
Suppose that the town of Pine Creek has 2,350 citizens, of which 1,950 are white and 400 are nonwhite. Further suppose that 11% of the white citizens, or 215 people, live below the poverty level, while 28% of the nonwhite citizens, or 112 people, live below the poverty level. If you visit Pine
In the context of correlation, what does r measure, and what is it called?
Does it follow that there is no relationship between the two variables? Why or why not?
Two studies both found a correlation between low birth weight and weakened immune systems. The second study had a much larger sample size, so the correlation it found must be stronger.For Exercises 5–8, decide whether the statement makes sense (or is clearly true) or does not make sense (or is
In investigating correlations between many different pairs of variables, in each case the correlation coefficient r must fall between -1 and 1.
The weights and costs of 50 different bags of apples.Exercises 9–16, list pairs of variables. For each pair, state whether you believe the two variables are correlated. If you believe they are correlated, state whether the correlation is positive or negative. Explain your reasoning.
The IQ scores and hat sizes of randomly selected adults.Exercises 9–16, list pairs of variables. For each pair, state whether you believe the two variables are correlated. If you believe they are correlated, state whether the correlation is positive or negative. Explain your reasoning.
The total weights of airliners flying from New York to San Francisco and the total amounts of fuel that they consume.Exercises 9–16, list pairs of variables. For each pair, state whether you believe the two variables are correlated. If you believe they are correlated, state whether the
The total number of points scored in Super Bowl football games and the changes in the Dow Jones Industrial stock index in the years following those games Exercises 9–16, list pairs of variables. For each pair, state whether you believe the two variables are correlated. If you believe they are
The outside air temperature and the altitude of aircraft.Exercises 9–16, list pairs of variables. For each pair, state whether you believe the two variables are correlated. If you believe they are correlated, state whether the correlation is positive or negative. Explain your reasoning.
The heights and SAT scores of randomly selected subjects who take the SAT.Exercises 9–16, list pairs of variables. For each pair, state whether you believe the two variables are correlated. If you believe they are correlated, state whether the correlation is positive or negative. Explain your
Golf scores and prize money won by professional golfers.Exercises 9–16, list pairs of variables. For each pair, state whether you believe the two variables are correlated. If you believe they are correlated, state whether the correlation is positive or negative. Explain your reasoning.
One classic application of correlation involves the association between the temperature and the number of times a cricket chirps in a minute. The scatterplot in Figure 7 shows the relationship for eight different pairs of temperature/chirps data. Estimate the correlation coefficient and determine
Use the Bureau of Labor Statistics Web page to find monthly unemployment rates and inflation rates over the past year. Construct a scatter-plot for the data. Do you see any trends?

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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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