According to a Pew Research poll conducted in 2016, 55% of men and 43% of women support the death penalty in cases of murder. Suppose these are accurate percentages. Now suppose a random man and a random woman meet. a. What is the probability that both support the death penalty? b. What is the probability that neither support the death penalty? c. What is the probability that only one of them supports the death penalty? d. What is the probability that at least one of them supports the death penalty?
> The graph shows the rates of visits to the emergency room (ER) for injuries by gender and by age. Note that we are concerned with the rate per 100 people of that age and gender in the population. (Source: National Safety Council 2004) a. Why does the Nat
> One of the authors wanted to determine the effect of changing answers on multiple-choice tests. She had advised her students that if they had changed their minds about a previous answer, they should replace their first choice with their new choice. By lo
> Patients with Alzheimer’s disease are randomly divided into two groups. One group is given a new drug, and the other is given a placebo. After six months they are given a memory test to see whether the new drug fights Alzheimer’s better than a placebo.
> Can mindful yoga have a beneficial impact on alcohol use in high-risk adolescents? Read excerpts from the research published in The Journal of Child and Family Studies and answer the questions that follow. (Source: Fishbein et al., “Behavioral and psycho
> A researcher is interested in the effect of music on memory. She randomly divides a group of students into three groups: those who will listen to quiet music, those who will listen to loud music, and those who will not listen to music. After the appropri
> Patients with multiple sclerosis are randomly assigned a new drug or a placebo and are then given a test of coordination after six months.
> Patients with high blood pressure are asked to keep food diaries recording all items they eat for a one-week period. Researchers analyze the food diary data for trends.
> The September 2017 issue of Alzheimer’s and Dementia reported on a study that found an association between drinking sugary drinks and lower brain volume. Is this likely to be a conclusion from observational studies or randomized experiments? Can we concl
> The Harvard Heart Letter reported on a study that examined the diets of 1226 older women over 15 years. They discovered that the more vegetables the women consumed, the lower their risk of dying of cardiovascular disease. From this study can we conclude
> A study was conducted to see whether participants would ignore a sign that said, “Elevator may stick between floors. Use the stairs.” The study was done at a university dorm on the ground floor of a three-level building. Those who used the stairs were sa
> An article in the journal BMC Medicine reported on a study designed to study the effect of diet on depression. Subjects suffering from moderate to severe depression were randomly assigned to one of two groups: a diet intervention group and a social suppo
> An article by Wakefield et al. in the British medical journal Lancet claimed that autism was caused by the measles, mumps, and rubella (MMR) vaccine. This vaccine is typically given to children twice, at about the age of 1 and again at about 4 years of a
> Cartilage is a smooth, rubber-like padding that protects the long bones in the body at the joints. A study by Lu et. al. in Arthritis Care & Research found that women who drank one glass of milk daily had 32% thicker, healthier cartilage than women who d
> An article in the Journal of the Academy of Nutrition and Dietetics reported on a study of diet in subjects with moderate to severe acne. Read the excerpts from the abstract and answer the questions that follow. (Source: Burris et al., “Differences in di
> People who have had strokes are often put on “blood thinners” such as aspirin or Coumadin to help prevent a second stroke. Describe the design of a controlled experiment to determine whether aspirin or Coumadin works better in preventing second strokes.
> The New England Journal of Medicine reported on a study of fish oil consumption in pregnant mothers and the subsequent development of asthma in their children. Read the excerpts from the abstract and answer the questions that follow: (Source: Bisgaard et
> A study reported by Griffin et al. compared the rate of pneumonia between 1997 and 1999 before pneumonia vaccine (PCV7) was introduced and between 2007 and 2009 after pneumonia vaccine was introduced. Read the excerpts from the abstract, and answer the q
> In a 2017 study designed to investigate the effects of exercise on second language learning, 40 subjects were randomly assigned to one of two conditions: an experimental group that engaged in simultaneous physical activity while learning vocabulary in a
> A doctor who believes strongly that antidepressants work better than “talk therapy” tests depressed patients by treating half of them with antidepressants and the other half with talk therapy. After six months the patients are evaluated on a scale of 1 t
> A group of educators want to determine how effective tutoring is in raising students’ grades in a math class, so they arrange free tutoring for those who want it. Then they compare final exam grades for the group that took advantage of the tutoring and t
> You can find many testimonials on the Internet that drinking aloe vera juice helps with digestive ailments. From these testimonials can we conclude that aloe vera juice causes digestive problems to go away? Why or why not?
> The blog NHS Choices ( February 10, 2014) noted that “there has been increasing anecdotal evidence that vitamin C may still be useful as an anticancer medicine if used in high concentrations and given directly into the vein (intravenously).” Explain what
> A local public school encourages, but does not require, students to wear uniforms. The principal of the school compares the grade point averages (GPAs) of students at this school who wear uniforms with the GPAs of those who do not wear uniforms to deter
> A group of boys is randomly divided into two groups. One group watches violent cartoons for one hour, and the other group watches cartoons without violence for one hour. The boys are then observed to see how many violent actions they take in the next two
> a. A statistics class is made up of 15 men and 23 women. What percentage of the class is male? b. A different class has 234 students, and 64.1% of them are men. How many men are in the class? c. A different class is made up of 40% women and has 20 women
> Describe the design of a controlled experiment to determine whether the use of vitamin D supplements reduces the chance of broken bones in women with osteoporosis (weak bones). Assume you have 200 women with osteoporosis to work with. Your description sh
> A survey was done of men’s and women’s hands to see if the ring finger appeared longer than the index finger or not. Yes means the ring finger is longer, and No means the ring finger appears shorter or the same length
> A survey was done of men’s and women’s hands to see if the ring finger appeared longer than the index finger or not. Yes means the ring finger is longer, and No means the ring finger appears shorter or the same length
> In 2015, the National Highway Traffic Safety Administration reported the number of pedestrian fatalities in San Francisco County was 24 and that the number in Los Angeles County was 209. Can we conclude that pedestrians are safer in San Francisco than in
> Two sections of statistics are offered, the first at 8 a.m. and the second at 10 a.m. The 8 a.m. section has 25 women, and the 10 a.m. section has 15 women. A student claims this is evidence that women prefer earlier statistics classes than men do. What
> The marriage and divorce rates are given per 1000 people in various years. Find the divorce rate as a percentage of the marriage rate and comment on the trend over time. (Source: https://www.cdc.gov/nchs)
> A recent study found that highly experienced teachers may be associated with higher student achievement. Suppose fourth-grade students at an elementary school are randomly assigned to one of eight teachers. Teachers Nagle, Crouse, Warren, Tejada, and Tra
> A medical practice group consists of seven doctors, four women and three men. The women are Drs. Town, Wu, Hein, and Lee. The men are Drs. Marland, Penner, and Holmes. Sup-pose new patients are randomly assigned to one of the doctors in the group. a. Lis
> A bag of candy contains 3 red candies and 7 brown candies. A friend says the probability of reaching the bag without looking and pulling out a red candy is 30% because 3 out of 10 candies are red. Is this an example of an empirical probability or a theor
> A student flips a coin 10 times and sees that it landed on tails 4 times. Based on this, the student says that the probability of getting a tail is 40%. Is the student referring to an empirical probability or a theoretical probability? Explain.
> The projected U.S. population is given for different decades. The projected number of people 65 years of age or older is also given. Find the percentage of people 65 or over and comment on the trend over time. Numbers are in millions of people (Source: 2
> A person was trying to figure out the probability of getting two heads when flipping two coins. He flipped two coins 10 times, and in 2 of these 10 times, both coins landed heads. On the basis of this outcome, he claims that the probability of two heads
> A Monopoly player claims that the probability of getting a 4 when rolling a six-sided die is 1/6 because the die is equally likely to land on any of the six sides. Is this an example of an empirical probability or a theoretical probability? Explain.
> Suppose you are carrying out a randomized experiment to test if there is a difference in the amount of information remembered between students who take notes using a computer versus those who take notes by hand using pen and paper. You have 20 college st
> If we flip a coin 10 times, what percentage of the time will the coin land on heads? A first step to answering this question is to simulate 10 flips. Use the random number table in Appendix A to simulate flipping a coin 10 times. Let the digits 0, 1,
> A 2018 Marist poll found that interest in baseball has been declining recently in the United States. A random sample of U.S. adults were asked how much baseball they intended to watch this season. The results are shown in the following table. a. What pe
> In 2016 the Pew Research Center asked a sample of American adults which of the following they had done in the previous 12 months: read a book in any format, read a print book, read an e-book, and listened to an audio book. The percent-ages of who had eng
> In 2017 the Pew Research Center asked young adults aged 18 to 29 about their media habits. When asked, “What is the primary way you watch television?” 61% said online streaming service, 31% said cable/satellite subscription, and 5% said digital antenna.
> In California, about 92% of teens who take the written driver’s exam fail the first time they take it (www.teendrivingcourse.com). Suppose that Sam and Maria are randomly selected teenagers taking the test for the first time. a. What is the probability t
> Suppose all the days of the week are equally likely as birthdays. Alicia and David are two randomly selected, unrelated people. a. What is the probability that they were both born on Monday? b. What is the probability that Alicia OR David was born on Mon
> A 2016 Pew Research poll reported that 80% of Americans shop online. Assume the percentage is accurate. a. If two Americans are randomly selected, what is the probability that both shop online? b. If the two Americans selected are a married couple, expla
> The accompanying table gives the number of cable television subscribers (in millions) and the number of households with televisions (in millions) in the United States. Find the percentage of TV owners with cable subscriptions for each year and comment on
> A 2016 Pew Research poll reported that 27% of young adults aged 18 to 24 had used an online dating site. Assume the percentage is accurate. a. If two young adults are randomly selected, what is the probability that both have used an online dating site? b
> A 2017 Pew Research poll asked people if they agreed with this statement: The United States hasn’t gone far enough when it comes to giving women equal rights with men. 42% of men agreed with the statement and 57% of women agreed with the statement. Suppo
> Use your general knowledge to label the following pairs of variables as independent or associated. Explain. a. The outcome on flips of two separate, fair coins. b. Breed of dog and weight of dog for dogs at a dog show.
> Use your general knowledge to label the following pairs of variables as independent or associated. Explain. a. For a sample of adults, gender and shoe size b. For a sample of football teams, win/loss record for the coin toss at the beginning of the game
> According to a Gallup poll conducted in 2017, 723 out of 1018 Americans surveyed said they believed global warming is occurring. If an American is selected at random, what is the probability that the person believes that global warming is occurring?
> According to a Gallup poll conducted in 2016, 627 out of 1012 Americans surveyed said they were dissatisfied with the country’s current gun laws. If an American is selected at random, what is the probability that the person is dissatisfied with the curre
> a. Explain how you could use a random number table to simulate rolling a fair six-sided die 20 times. Assume you wish to find the probability of rolling a 1. Then report a line or two of the random number table (or numbers generated by a computer or calc
> a. Explain how you could use a random number table (or the random numbers generated by software or a calculator) to simulate rolling a fair four-sided die 20 times. Assume you are interested in the probability of rolling a 1. Then report a line or two of
> Some estimates say that 10% of the population is left-handed. We wish to design a simulation to find an empirical probability that if five babies are born on a single day, one or more will be left-handed. Suppose we decide that the even digits (0, 2, 4,
> The accompanying table gives the population (in hundred thousands) and number of people not covered by health insurance (in hundred thousands) for the United States. Find the percentage of people not covered by health insurance for each of the given year
> A jury is supposed to represent the population. We wish to perform a simulation to determine an empirical probability that a jury of 12 people has 5 or fewer women. Assume that about 50% of the population is female, so the probability that a person who i
> The graph shows the average when a six-sided die is rolled repeatedly. For example, if the first two rolls resulted in a 6 and a 2, the average would be 4. If the next trial resulted in a 1, the new average would be (6 + 2 + 1)/3 = 3. Explain how the gra
> If you flip a fair coin repeatedly and the first four results are tails, are you more likely to get heads on the next flip, more likely to get tails again, or equally likely to get heads or tails?
> Consider two pairs of grandparents. The first pair has 4 grandchildren, and the second pair has 32 grand-children. Which of the two pairs is more likely to have between 40% and 60% boys as grandchildren, assuming that boys and girls are equally likely as
> Betty and Jane are gambling. They are cutting cards (picking a random place in the deck to see a card). Whoever has the higher card wins the bet. If the cards have the same value (for example, they are both eights), they try again. Betty and Jane do this
> Refer to the following figure. a. After a large number of flips, the overall proportion of heads “settles down” to nearly what value? b. Approximately how many coin flips does it take before the proportion of heads set
> Imagine flipping a fair coin many times. Explain what should happen to the proportion of heads as the number of coin flips increases.
> The table shows the results of rolling a fair six-sided die. Using the table, find the empirical probability of rolling a 1 for 20, 100, and 1000 trials. Report the theoretical probability of rolling a 1 with a fair six-sided die. Compare the empirical
> Refer to Histograms A, B, and C, which show the relative frequencies from experiments in which a fair six-sided die was rolled. One histogram shows the results for 20 rolls, one the results for 100 rolls, and another the results for 10,000 rolls. Which h
> a. Explain how you could use digits from a random number table to simulate rolling a fair six-sided die. b. Carry out your simulation beginning with line 3 of the random number table in Appendix A. Repeat your simulation 5 times. c. Use your simulation t
> The accompanying table gives the 2018 population and area (in square kilometers) of five U.S. cities. See page 39 for guidance. (Source: www.citymayors.com). a. Determine and report the ranking of the population density (people per square kilometer) by
> a. Use the line of random numbers below to simulate flipping a coin 20 times. Use the digits 0, 1, 2, 3, 4 to represent heads and the digits 5, 6, 7, 8, 9 to represent tails. 11164 … 36318 … 75061 … 37674 b. Based on these 20 trials, what is the simulate
> A true/false test has 20 questions. Each question has two choices (true or false), and only one choice is correct. Which of the following methods is a valid simulation of a student who guesses randomly on each question. Explain. (Note: there might be mor
> A multiple-choice test has 30 questions. Each question has three choices, but only one choice is correct. Using a random number table, which of the following methods is a valid simulation of a student who circles his or her choices randomly? Explain. (No
> What’s the probability of rolling two numbers whose sum is 7 when you roll two dice? The table below shows the outcome of ten trials in which two dice were rolled. a. List the trials that had a sum of 7. b. Based on these data, what&aci
> What’s the probability of getting at least one six when you roll two dice? The table below shows the outcome of five trials in which two dice were rolled. a. List the trials that had at least one 6. b. Based on these data, whatâ&#
> About 8 women in 100,000 have cervical cancer (C), so P(C) = 0.00008 and P(no C) = 0.99992. The chance that a Pap smear will incorrectly indicate that a woman without cervical cancer has cervical cancer is 0.03. Therefore, P (test pos | no C) = 0.03 Wha
> According to a study published in Scientific American, about 8 women in 100,000 have cervical cancer (which we’ll call event C), so P(C) = 0.00008. Suppose the chance that a Pap smear will detect cervical cancer when it is present is 0.84. Therefore, P (
> According to the National Center for Health Statistics, 52% of U.S. households no longer have a landline and instead only have cell phone service. Suppose three U.S. households are selected at random. a. What is the probability that all three have only c
> According to a recent Gallup poll, 62% of Americans took a vacation away from home in 2017. Suppose two Americans are randomly selected. a. What is the probability that both took a vacation away from home in 2017? b. What is the probability that neither
> Assume that babies born are equally likely to be boys (B) or girls (G). Assume a woman has six children, none of whom are twins. Which sequence is more likely? Explain. Sequence A: GGGGGG Sequence B: GGGBBB
> The table gives the prison population and total population for a sample of states in 2014–15. (Source: The 2017 World Almanac and Book of Facts) Find the number of people in prison per thousand residents in each state and rank each sta
> College students who were drivers were asked if they had ever driven a car 100 mph or more (yes or no). The results are shown in the table, along with gender. a. There are two variables in the table, state what they are and whether each is categorical or
> Roll a fair six-sided die five times, and record the number of spots on top. Which sequence is more likely? Explain. Sequence A: 66666 Sequence B: 16643
> Imagine rolling a fair six-sided die three times. a. What is the theoretical probability that all three rolls of the die show a 1 on top? b. What is the theoretical probability that the first roll of the die shows a 6 AND the next two rolls both show a 1
> Imagine flipping three fair coins. a. What is the theoretical probability that all three come up heads? b. What is the theoretical probability that the first toss is tails AND the next two are heads?
> Using the table in exercise 5.53, determine whether being female is independent of choice of local TV. Explain your answer in the context of this problem.
> A 2018 Pew Research Center report asked people who got their news from television which television sector they relied on primarily for their news: local TV, network TV, or cable TV. The results were used to generate the data in the table below. a. Inclu
> When two dice are rolled, is the event “the first die shows a 1 on top” independent of the event “the second die shows a 1 on top”?
> When people fold their hands together with interlocking fingers, most people are more comfortable with one of two ways. In one way, the right thumb ends up on top, and in the other way, the left thumb is on top. The table shows the data from one group of
> Assume a person is selected randomly from the group of people represented in the table in exercise 5.41. The probability the person says “Hasn’t Gone Far Enough” given that the person is a woman is 57/100 or 57%. The probability that person is a woman gi
> Refer to the table in Exercise 5.41. Suppose a person is randomly selected from this group. Is being female independent of answering “Hasn’t Gone Far Enough”?
> Ring sizes typically range from about 3 to about 14. Based on what you know about gender differences, if we randomly select a person, are the event that the ring size is smaller than 5 and the event that the person is a male independent or associated? Ex
> The 2017 World Almanac and Book of Facts reported that in 2016, M&Ms had sales of approximately $3.48 million and that this accounted for 12.95% of the total chocolate candy sales. What was the total amount of chocolate candy sales?
> Suppose a person is chosen at random. Use your knowledge about the world to decide whether the event that the person has brown eyes and the event that the person is female are independent or associated. Explain.
> About 12% of men and 10% of women are left-handed. If we select a person at random, are the event that the person is male and the event that the person is left-handed independent or associated?
> Suppose a person is chosen at random. Use your understanding about the world of basketball to decide whether the event that the person is taller than 6 feet and the event that the person plays professional basketball are independent or associated. Explai
> Use the data in exercise 5.43 for this problem. Note: Your answers to each of these three questions should not be the same. a. Find the probability that a randomly selected person did not have a child under 18 years old, given that they said No. b. Find
> A Gallup poll asked people with and without children under 18 years old if they frequently experienced stress. The results are shown in the table below. (Source: Gallup.com) a. Find the probability that a randomly chosen person from this group said &aci
> A driving exam consists of 30 multiple-choice questions. Each of the answers is either right or wrong. Suppose that the probability of making fewer than 7 mistakes is 0.23 and the probability of making from 7 to 15 mistakes is 0.41. Find the probability
> An exam consists of 12 multiple-choice questions. Each of the 12 answers is either right or wrong. Suppose the probability a student makes fewer than 3 mistakes on the exam is 0.48 and the probability that a student makes from 3 to 8 (inclusive) mistakes
> When a certain type of thumbtack is tossed, the probability that it lands tip up is 60%, and the probability that it lands tip down is 40%. All possible outcomes when two thumbtacks are tossed are listed. U means the tip is Up, and D means the tip is Dow
> When a certain type of thumbtack is tossed, the probability that it lands tip up is 60%. All possible outcomes when two thumbtacks are tossed are listed. U means the tip is up, and D means the tip is down. UU … UD … DU … DD a. What is the probability of
