Question: Hoping to learn how to control crop

> For a sales promotion, the manufacturer places winning symbols under the caps of 10% of all Pepsi bottles. You buy a six-pack. What is the probability that you win something?

> You purchased a five-pack of new light bulbs that were recalled because 6% of the lights did not work. What is the probability that at least one of your lights is defective?

> Census reports for a city indicate that 62% of residents classify themselves as Christian, 12% as Jewish, and 16% as members of other religions (Muslims, Buddhists, etc.). The remaining residents classify themselves as nonreligious. A polling organizatio

> Suppose that in your city 37% of the voters are registered as Democrats, 29% as Republicans, and 11% as members of other parties (Liberal, Right to Life, Green, etc.). Voters not aligned with any official party are termed Independent. You are conducting

> To get to work, a commuter must cross train tracks. The time the train arrives varies slightly from day to day, but the commuter estimates he’ll get stopped on about 15% of work days. During a certain 5-day work week, what is the probability that he 1. g

> A certain bowler can bowl a strike 70% of the time. If the bowls are independent, what the probability that she 1. goes three consecutive frames without a strike? 2. makes her first strike in the third frame? 3. has at least one strike in the first three

> A survey was conducted in the United States and 10 countries of Western Europe to determine the percentage of teenagers who had used marijuana and other drugs. The results are summarized in the following table. 1. Create a scatterplot. 2. What is the cor

> A slot machine has three wheels that spin independently. Each has 10 equally likely symbols: 4 bars, 3 lemons, 2 cherries, and a bell. If you play, what is the probability that 1. you get 3 lemons? 2. you get no fruit symbols? 3. you get 3 bells (the jac

> You roll a fair die three times. What is the probability that 1. you roll all 6? 2. you roll all odd numbers? 3. none of your rolls gets a number divisible by 3? 4. you roll at least one 5? 5. the numbers you roll are not all 5?

> In Exercise 40, you calculated probabilities involving various blood types. Some of your answers depended on the assumption that the outcomes described were disjoint; that is, they could not both happen at the same time. Other answers depended on the ass

> In Exercise 39, you calculated probabilities of getting various M&M. Some of your answers depended on the assumption that the outcomes described were disjoint; that is, they could not both happen at the same time. Other answers depended on the assumption

> The American Red Cross says that about 45% of the U.S. population has Type O blood, 40% Type A, 11% Type B, and the rest Type AB. 1. Someone volunteers to give blood. What is the probability that this donor 1. has Type AB blood? 2. has Type A or Type B?

> The Mars company says that before the introduction of purple, yellow candies made up 20% of their plain M&M, red another 20%, and orange, blue, and green each made up 10%. The rest were brown. 1. If you pick an M&M at random, what is the probability that

> According to Pew Research, the contact rate (probability of contacting a selected household) was 90% in 1997 and 62% in 2012. However, the cooperation rate (probability of someone at the contacted household agreeing to be interviewed) was 43% in 1997 and

> As mentioned in the chapter, opinion-polling organizations contact their respondents by sampling random telephone numbers. Although interviewers can reach about 62% of U.S. households, the percentage of those contacted who agree to cooperate with the sur

> Consider again the results of the poll about fathering discussed in Exercise 34. If we select two people at random from this sample, 1. what is the probability that both think that being a father is easier today? 2. what is the probability that neither t

> Exercise 33 shows the results of a Gallup Poll about energy. Suppose we select three people at random from this sample. 1. What is the probability that all three responded Develop wind and solar? 2. What is the probability that none responded Equally imp

> Here are engine size (displacement, in liters) and gas mileage (estimated combined city and highway) for a random sample of 35 2016 model cars (taken from Fuel economy 2016 and identified in the data with Sample=Yes) 1. Make a scatterplot fo

> A Pew Research poll in 2011 asked 2005 U.S. adults whether being a father today is harder than it was a generation ago. Here how they responded: If we select a respondent at random from this sample of 2005 adults, 1. what is the probability that the sele

> A Gallup Poll (www.gallup.com/poll/161729/americans-divided-energy-environment-trade-off.aspx) in March 2013 asked 529 U.S. adults whether increasing oil, gas, and coal production or developing alternative energy sources such as wind and solar power shou

> You used the Multiplication Rule to calculate probabilities about the calculus background of your statistics groupmates in Exercise 30. 1. What must be true about the groups in order to make that approach valid? 2. Do you think this assumption is reasona

> You used the Multiplication Rule to calculate repair probabilities for your cars in Exercise 29. 1. What must be true about your cars in order to make that approach valid? 2. Do you think this assumption is reasonable? Explain.

> You are assigned to be part of a group of three students from the intro stats class described in Exercise 28. What is the probability that of your other two groupmates, 1. neither has studied calculus? 2. both have studied at least one semester of calcul

> Consider again the auto repair rates described in Exercise 27. If you own two cars, what is the probability that 1. neither will need repair? 2. both will need repair? 3. at least one car will need repair?

> In a large introductory statistics lecture hall, the professor reports that 55% of the students enrolled have never taken a calculus course, 32% have taken only one semester of calculus, and the rest have taken two or more semesters of calculus. The prof

> A consumer organization estimates that over a 1-year period 17% of cars will need to be repaired only once, 7% will need repairs exactly twice, and 4% will require three or more repairs. What is the probability that a car chosen at random will need 1. no

> In Exercise 25, we saw that in 2013 Harvard accepted about 5.8% of its applicants, Dartmouth 10%, and Penn 12.1%. Jorge has applied to all three. He figures that his chances of getting into at least one of the three must be about 27.9%. 1. How has he arr

> For high school students graduating in 2013, college admissions to the nation most selective schools were the most competitive in memory. Harvard accepted about 5.8% of its applicants, Dartmouth 10%, and Penn 12.1%. Jorge has applied to all three. Assumi

> Since 1985, average mortgage interest rates have fluctuated from a low of nearly 3% to a high of over 14%. Is there a relationship between the amount of money people borrow and the interest rate that offered? Here is a scatterplot of Mortgage Loan Amount

> The following data relate traffic Density (measured as number of cars per mile) and the average Speed of traffic (in mph) on city highways. The data were collected at the same location at 10 different times randomly selected within a span of 3 months. 1.

> Although it hard to be definitive in classifying people as right- or left-handed, some studies suggest that about 14% of people are left-handed. Since 0.14—0.14=0.0196, the Multiplication Rule might suggest that there about a 2% chance that a brother and

> Traffic checks on a certain section of highway suggest that 60% of drivers are speeding there. Since 0.6—0.6=0.36, the Multiplication Rule might suggest that there a 36% chance that two vehicles in a row are both speeding. What wrong with that reasoning?

> Funding for many schools comes from taxes based on assessed values of local properties. People homes are assessed higher if they have extra features such as garages and swimming pools. Assessment records in a certain school district indicate that 37% of

> Suppose that 46% of families living in a certain county own a computer and 18% own an HDTV. The Addition Rule might suggest, then, that 64% of families own either a computer or an HDTV. What wrong with that reasoning?

> Many stores run secret sales : Shoppers receive cards that determine how large a discount they get, but the percentage is revealed by scratching off that black stuff (what is that?) only after the purchase has been totaled at the cash register. The store

> The plastic arrow on a spinner for a child game stops rotating to point at a color that will determine what happens next. Which of the following probability assignments are legitimate?

> On February 11, 2009, the AP news wire released the following story: (LAS VEGAS, Nev.) A man in town to watch the NCAA basketball tournament hit a $38.7 million jackpot on Friday, the biggest slot machine payout ever. The 25-year-old software engineer fr

> Insurance companies collect annual payments from drivers in exchange for paying for the cost of accidents. 1. Why should you be reluctant to accept a $1500 payment from your neighbor to cover his automobile accidents in the next year? 2. Why can the insu

> Commercial airplanes have an excellent safety record. Nevertheless, there are crashes occasionally, with the loss of many lives. In the weeks following a crash, airlines often report a drop in the number of passengers, probably because people are afraid

> A basketball player missed 8 of 11 shots in the final portion of a game. When talking to reporters afterward, he says that he not worried about his next game because he due to make a lot of shots. Comment on his reasoning.

> The Office of Federal Housing Enterprise Oversight (www.fhfa.gov) collects data on various aspects of housing costs around the United States. Here is a scatterplot of the Housing Cost Index versus the Median Family Income for each of the 50 states. The c

> After an unusually dry autumn, a radio announcer is heard to say, Watch out! We’ll pay for these sunny days later on this winter. Explain what he trying to say, and comment on the validity of his reasoning.

> Comment on the following quotation: What I think is our best determination is it will be a colder than normal winter, said Pamela Naber Knox, a Wisconsin state climatologist. I’m basing that on a couple of different things. First, in looking at the past

> The weather reporter on TV makes predictions such as a 25% chance of rain. What do you think is the meaning of such a phrase?

> A casino claims that its roulette wheel is truly random. What should that claim mean?

> A humor piece published in the British Medical Journal (Parachute Use to Prevent Death and Major Trauma Related to Gravitational Challenge: Systematic Review of Randomized Control Trials, Gordon, Smith, and Pell, BMJ, 2003:327) notes that we can’t tell f

> A consumer group wants to test the effectiveness of a new organic laundry detergent and make recommendations to customers about how to best use the product. They intentionally stain 30 white T-shirts with grass in order to see how well the detergent will

> An industrial machine requires an emergency shutoff switch that must be designed so that it can be easily operated with either hand. Design an experiment to find out whether workers will be able to deactivate the machine as quickly with their left hands

> Can special study courses actually help raise SAT scores? One organization says that the 30 students they tutored achieved an average gain of 60 points when they retook the test. 1. Explain why this does not necessarily prove that the special course caus

> A research doctor has discovered a new ointment that she believes will be more effective than the current medication in the treatment of shingles (a painful skin rash). Eight patients have volunteered to participate in the initial trials of this ointment

> A polling organization is checking its database to see if the data sources it used sampled the same ZIP codes. The variable Datasource=1 if the data source is MetroMedia, 2 if the data source is DataQwest, and 3 if it RollingPoll. The organization finds

> A study published in the New England Journal of Medicine (Aug. 2001) suggests that it dangerous to enter a hospital on a weekend. During a 10-year period, researchers tracked over 4 million emergency admissions to hospitals in Ontario, Canada. Their find

> Do cars get better gas mileage with premium instead of regular unleaded gasoline? It might be possible to test some engines in a laboratory, but we’d rather use real cars and real drivers in real day-to-day driving, so we get 20 volunteers. Design the ex

> Some schools teach reading using phonics (the sounds made by letters) and others using whole language (word recognition). Suppose a school district wants to know which method works better. Suggest a design for an appropriate experiment.

> A medical researcher suspects that giving post-surgical patients large doses of vitamin E will speed their recovery times by helping their incisions heal more quickly. Design an experiment to test this conjecture. Be sure to identify the factors, levels,

> Before drilling for water, many rural homeowners hire a dowser (a person who claims to be able to sense the presence of underground water using a forked stick). Suppose we wish to set up an experiment to test one dowser ability. We get 20 identical conta

> Recently, a group of adults who swim regularly for exercise were evaluated for depression. It turned out that these swimmers were less likely to be depressed than the general population. The researchers said the difference was statistically significant.

> A Danish study published in the Archives of Internal Medicine casts significant doubt on suggestions that adults who drink wine have higher levels of good cholesterol and fewer heart attacks. These researchers followed a group of individuals born at a Co

> Contrast bath treatments use the immersion of an injured limb alternately in water of two contrasting temperatures. Those who use the method claim that it can reduce swelling. Researchers compared three treatments: (1) contrast baths and exercise, (2)

> Will listening to a Mozart piano sonata make you smarter? In a study published in the journal Psychological Science, Rauscher, Shaw, and Ky reported that when students were given a spatial reasoning section of a standard IQ test, those who listened to Mo

> An experiment showed that subjects fed the DASH diet were able to lower their blood pressure by an average of 6.7 points compared to a group fed a control diet. All meals were prepared by dieticians. 1. Why were the subjects randomly assigned to the diet

> Medical researchers followed 1435 middle-aged men for a period of 5 years, measuring the amount of Baldness present (none=1,little=2,some=3,much=4,extreme=5) and presence of Heart Disease (No=0,Yes=1). They found a correlation of 0.089 between the two va

> Exercise 33 discussed an experiment to see if the time it took athletes with hamstring injuries to be able to return to sports was different depending on which of two exercise programs they engaged in. 1. Explain why it was important to assign the athlet

> A running-shoe manufacturer wants to test the effect of its new sprinting shoe on 100-meter dash times. The company sponsors 5 athletes who are running the 100-meter dash in the 2012 Summer Olympic games. To test the shoe, it has all 5 runners run the 10

> Describe a strategy to randomly split 24 tomato plants into the three groups for the completely randomized single-factor experiment of Exercise 4.

> Exercise 33 describes an experiment that studies hamstring injuries. Describe a strategy to randomly assign injured athletes to the two exercise programs. What should be done if one of the athletes says he’d prefer the other program?

> Exercises 24, 36, and 38 describe an experiment investigating the effectiveness of exercise in combating insomnia. Suppose some of the 40 subjects had maintained a healthy weight, but others were quite overweight. Why might researchers choose to block th

> Exercises 21, 35, and 37 describe an experiment investigating the effectiveness of omega-3 fats in treating bipolar disorder. Suppose some of the 30 subjects were very active people who walked a lot or got vigorous exercise several times a week, while ot

> Exercises 24 and 36 describe an experiment investigating the effectiveness of exercise in combating insomnia. Researchers randomly assigned half of the 40 volunteers to an exercise program. 1. Why was it important to randomize in deciding who would exerc

> Exercises 21 and 35 describe an experiment investigating a dietary approach to treating bipolar disorder. Researchers randomly assigned 30 subjects to two treatment groups, one group taking a high dose of omega-3 fats and the other a placebo. 1. Why was

> Exercise 24 describes an experiment showing that exercise helped people sleep better. The experiment involved other groups of subjects who didn’t exercise. Why didn’t the experimenters just have everyone exercise and see if their ability to sleep improve

> The correlation between Fuel Efficiency (as measured by miles per gallon) and Price of 150 cars at a large dealership is r=0.34. Explain whether or not each of these possible conclusions is justified: 1. The more you pay, the lower the fuel efficiency of

> Exercise 21 describes an experiment that showed that high doses of omega-3 fats might be of benefit to people with bipolar disorder. The experiment involved a control group of subjects who received a placebo. Why didn’t the experimenters just give everyo

> Pew Research compared respondents to an ordinary 5-day telephone survey with respondents to a 4-month-long rigorous survey designed to generate the highest possible response rate. They were especially interested in identifying any variables for which tho

> Athletes who had suffered hamstring injuries were randomly assigned to one of two exercise programs. Those who engaged in static stretching returned to sports activity in a mean of 15.2 days faster than those assigned to a program of agility and trunk st

> A dog food company wants to compare a new lower-calorie food with their standard dog food to see if it effective in helping inactive dogs maintain a healthy weight. They have found several dog owners willing to participate in the trial. The dogs have bee

> Some people claim they can get relief from migraine headache pain by drinking a large glass of ice water. Researchers plan to enlist several people who suffer from migraines in a test. When a participant experiences a migraine headache, he or she will ta

> Some people who race greyhounds give the dogs large doses of vitamin C in the belief that the dogs will run faster. Investigators at the University of Florida tried three different diets in random order on each of five racing greyhounds. They were surpri

> The May 4, 2000, issue of Science News reported that, contrary to popular belief, depressed individuals cry no more often in response to sad situations than non-depressed people. Researchers studied 23 men and 48 women with major depression and 9 men and

> Scientists at a major pharmaceutical firm investigated the effectiveness of an herbal compound to treat the common cold. They exposed each subject to a cold virus, then gave him or her either the herbal compound or a sugar solution known to have no effec

> In 2002, the journal Science reported that a study of women in Finland indicated that having sons shortened the life spans of mothers by about 34 weeks per son, but that daughters helped to lengthen the mother lives. The data came from church records fro

> Researchers have linked an increase in the incidence of breast cancer in Italy to dioxin released by an industrial accident in 1976. The study identified 981 women who lived near the site of the accident and were under age 40 at the time. Fifteen of the

> The correlation between Age and Income as measured on 100 people is r=0.75. Explain whether or not each of these possible conclusions is justified: 1. When Age increases, Income increases as well. 2. The form of the relationship between Age and Income is

> After menopause, some women take supplemental estrogen. There is some concern that if these women also drink alcohol, their estrogen levels will rise too high. Twelve volunteers who were receiving supplemental estrogen were randomly divided into two grou

> Is diet or exercise effective in combating insomnia? Some believe that cutting out desserts can help alleviate the problem, while others recommend exercise. Forty volunteers suffering from insomnia agreed to participate in a month-long test. Half were ra

> In a test of roughly 200 men and women, those with moderately high blood pressure (averaging 164/89 mm Hg) did worse on tests of memory and reaction time than those with normal blood pressure. (Hypertension 36 [2000]: 1079)

> Among a group of disabled women aged 65 and older who were tracked for several years, those who had a vitamin B12 deficiency were twice as likely to suffer severe depression as those who did not. (American Journal of Psychiatry 157 [2000]: 715)

> Over a 4-month period, among 30 people with bipolar disorder, patients who were given a high dose (10 g/day) of omega-3 fats from fish oil improved more than those given a placebo. (Archives of General Psychiatry 56 [1999]: 407)

> Coffee stations in offices often just ask users to leave money in a tray to pay for their coffee, but many people cheat. Researchers at Newcastle University replaced the picture of flowers on the wall behind the coffee station with a picture of staring e

> Researchers studied the herb black cohosh as a treatment for hot flashes caused by menopause. They randomly assigned 351 women aged 45 to 55 who reported at least two hot flashes a day to one of five groups: (1) black cohosh, (2) a multiherb supplement

> When spending large amounts to purchase advertising time, companies want to know what audience they’ll reach. In January 2011, a poll asked 1008 American adults whether they planned to watch the upcoming Super Bowl. Men and women were asked separately wh

> Multiple sclerosis (MS) is an autoimmune disease that strikes more often the farther people live from the equator. Could vitamin D which most people get from the sun ultraviolet rays be a factor? Researchers compared vitamin D levels in blood samples fro

> Researchers who examined health records of thousands of males found that men who died of myocardial infarction (heart attack) tended to be shorter than men who did not. 1. Is this an experiment? If not, what kind of study is it? 2. Is it correct to concl

> A survey of the world nations in 2014 shows a strong positive correlation between percentage of the country using smartphones and life expectancy in years at birth. 1. Does this mean that smartphones are good for your health? 2. What might explain the st

> For his statistics class experiment, researcher J. Gilbert decided to study how parents income affects children performance on standardized tests like the SAT. He proposed to collect information from a random sample of test takers and examine the relatio

> Consider each of these situations. Do you think the proposed sampling method is appropriate? Explain. 1. We want to know if there is neighborhood support to turn a vacant lot into a playground. We spend a Saturday afternoon going door-to-door in the neig

> Consider each of these situations. Do you think the proposed sampling method is appropriate? Explain. 1. We want to know what percentage of local doctors accept Medicaid patients. We call the offices of 50 doctors randomly selected from local Yellow Page

> In recent years, beaches around the world have seen fish washing up on shore in large numbers. One group of scientists thought that leakage from the damaged Fukushima nuclear power plant in Japan might be a cause. They propose to measure the mean amount

> Concerned about reports of discolored scales on fish caught downstream from a newly sited chemical plant, scientists set up a field station in a shoreline public park. For one week, they asked fishermen there to bring any fish they caught to the field st

> Sammy Salsa, a small local company, produces 20 cases of salsa a day. Each case contains 12 jars and is imprinted with a code indicating the date and batch number. To help maintain consistency, at the end of each day, Sammy selects three jars of salsa, w