Many investment advisors argue that after stocks have declined in value for 2 consecutive years, people should invest heavily because the market rarely declines 3 years in a row. 1. Since the stock market began in 1872, there have been two consecutive losing years eight times. In six of those cases, the market rose during the following year. Does this confirm the advice? 2. Overall, stocks have risen in value during 95 of the 130 years since the market began in 1872. How is this fact relevant in assessing the statistical reasoning of the advisors?
> The Centers for Disease Control and Prevention reports that 9.3% of surveyed high school students reported in 2015 that they had smoked cigarettes in the past 30 days. A college has 522 students in its freshman class. How likely is it that more than 10%
> The 2014 U.S. Religious Landscape Study interviewed more than 35,000 Americans from all 50 states about their beliefs and the role of religion in their lives. The fastest-growing group is the 22.8% who are Nones those who are not affiliated with any orga
> Neurological research has shown that in about 80% of people language abilities reside in the brain left side. Another 10% display right-brain language centers, and the remaining 10% have two-sided language control. (The latter two groups are mainly left-
> A Rutgers University study found that many high school students cheat on tests. The researchers surveyed a random sample of 4500 high school students nationwide; 74% of them said they had cheated at least once. 1. Create a 90% confidence interval for the
> Here are the summary statistics for the weekly payroll of a small company: lowest salary=$300, mean salary=$700, median=$500, range=$1200, IQR=$600, first quartile=$350, standard deviation=$400. 1. Do you think the distribution of salaries is symmetric,
> Organizers of a fishing tournament believe that the lake holds a sizable population of largemouth bass. They assume that the weights of these fish have a model that is skewed to the right with a mean of 3.5 pounds and a standard deviation of 2.2 pounds.
> One of the important issues for poultry farmers is the production rate the percentage of days on which a given hen actually lays an egg. Ideally, that would be 100% (an egg every day), but realistically, hens tend to lay eggs on about 3 of every 4 days.
> A newspaper article that reported the results of an election poll included the following explanation: The Associated Press poll on the 2016 presidential campaign is based on telephone interviews with 798 randomly selected registered voters from all state
> According to the U.S. American Community Survey (ACS), by 2014, for the first time in the history of the ACS, more U.S. 18- to 34-year-olds reported living with a parent than were living independently in their own homes. The survey found that 32.1% were
> The 2016 State of Women-Owned Businesses Report commissioned by American Express (www.womenable.com/70/the-state-of-women-owned-businesses-in-the-u.s.:-2016) says that, excluding large, publicly traded firms, women-owned firms make up 38% of the privatel
> The National Perinatal Statistics Unit of the Sydney Children Hospital reports that the mean birth weight of all babies born in birth centers in Australia in a recent year was 3564 grams about 7.86 pounds. A Missouri hospital reports that the average wei
> A group of 5 women became pregnant while undergoing fertility treatments with the drug Clomid, discussed in Exercise 7 . What the probability that 1. none will have twins? 2. exactly 1 will have twins? 3. at least 3 will have twins?
> A car owner may buy insurance that will pay the full price of repairing the car after an at-fault accident, or save $12 a year by getting a policy with a $500 deductible. Her insurance company says that about 0.5% of drivers in her area have an at-fault
> In the United States, the probability of having twins (usually about 1 in 90 births) rises to about 1 in 10 for women who have been taking the fertility drug Clomid. Among a group of 10 pregnant women, what the probability that 1. at least one will have
> Safety engineers must determine whether industrial workers can operate a machine emergency shutoff device. Among a group of test subjects, 66% were successful with their left hands, 82% with their right hands, and 51% with both hands. 1. What percent of
> The mean price of pizza in Baltimore was $2.85, $0.23 higher than the mean price of $2.62 in Dallas. To see if that difference was real, or due to chance, we took the 156 prices from Baltimore and Dallas and mixed those 312 prices together. Then we rando
> To play a game, you must pay $5 for each play. There is a 10% chance you will win $5, a 40% chance you will win $7, and a 50% chance you will win only $3. 1. What are the mean and standard deviation of your net winnings? 2. You play twice. Assuming the p
> You are among 100 people attending a charity fundraiser at which a large-screen TV will be given away as a door prize. To determine who wins, 99 white balls and 1 red ball have been placed in a box and thoroughly mixed. The guests will line up and, one a
> Suppose that 70% of the women who suspect they may be pregnant and purchase an in-home pregnancy test are actually pregnant. Further suppose that the test is 98% accurate. What the probability that a woman whose test indicates that she is pregnant actual
> In a car rental company fleet, 70% of the cars are American brands, 20% are Japanese, and the rest are German. The company notes that manufacturers recalls seem to affect 2% of the American cars, but only 1% of the others. 1. What the probability that a
> In 1961 astronomer Frank Drake developed an equation to try to estimate the number of extraterrestrial civilizations in our galaxy that might be able to communicate with us via radio transmissions. Now largely accepted by the scientific community, the Dr
> A coin is to be tossed 36 times. 1. What are the mean and standard deviation of the number of heads? 2. Suppose the resulting number of heads is unusual, two standard deviations above the mean. How many extra heads were observed? 3. If the coin were toss
> Psychiatrists estimate that about 1 in 100 adults suffers from bipolar disorder. What the probability that in a city of 10,000 there are more than 200 people with this condition? Be sure to verify that a Normal model can be used here.
> In your sock drawer you have 4 blue socks, 5 gray socks, and 3 black ones. Half asleep one morning, you grab 2 socks at random and put them on. Find the probability you end up wearing 1. 2 blue socks. 2. no gray socks. 3. at least 1 black sock. 4. a gree
> Almost every year, there is some incidence of volcanic activity on the island of Japan. In 2005 there were 5 volcanic episodes, defined as either eruptions or sizable seismic activity. Suppose the mean number of episodes is 2.4 per year. Let X be the num
> Failures of O-rings on the space shuttle are fairly rare, but often disastrous, events. If we are testing O-rings, suppose that the probability of a failure of any one O-ring is 0.01. Let X be the number of failures in the next 10 O-rings tested. 1. What
> The company that sells frozen pizza to stores in four markets in the United States (Denver, Baltimore, Dallas, and Chicago) wants to examine the prices that the stores charge for pizza slices. Here are boxplots comparing data from a sample of stores in e
> A census by the county dog control officer found that 18% of homes kept one dog as a pet, 4% had two dogs, and 1% had three or more. If a salesman visits two homes selected at random, what the probability he encounters 1. no dogs? 2. some dogs? 3. dogs i
> Every 5 years the Conference Board of the Mathematical Sciences surveys college math departments. In 2000 the board reported that 51% of all undergraduates taking Calculus I were in classes that used graphing calculators and 31% were in classes that used
> Here another attempt at developing a good strategy for the dice game in Exercise 33 . Instead of stopping after a certain number of rolls, you could decide to stop when your score reaches a certain number of points. 1. How many points would you expect a
> When to stop In Exercise 27 of the Review Exercises for Part III, we posed this question: You play a game that involves rolling a die. You can roll as many times as you want, and your score is the total for all the rolls. But if you roll a 6, your score
> A Statistics professor comes home to find that all four of his children got white team shirts from soccer camp this year. He concludes that this year, unlike other years, the camp must not be using a variety of colors. But then he finds out that in each
> The 2013 State of Women-Owned Businesses Report commissioned by American Express (www.womenable.com/content/userfiles/2013_State_of_WomenOwned_Businesses_Report_FINAL.pdf) says that, excluding large, publicly traded firms, women-owned firms make up 30% o
> The first store in Exercise 28 sells watermelons for 32 cents a pound. The second store is having a sale on watermelons only 25 cents a pound. Find the mean and standard deviation of the difference in the price you may pay for melons randomly selected at
> Each year a company must send 3 officials to a meeting in China and 5 officials to a meeting in France. Airline ticket prices vary from time to time, but the company purchases all tickets for a country at the same price. Past experience has shown that ti
> According to the 2000 Census, 66% of U.S. households own the home they live in. A mayoral candidate conducts a survey of 820 randomly selected homes in your city and finds only 523 owned by the current residents. The candidate then attacks the incumbent
> Two stores sell watermelons. At the first store the melons weigh an average of 22 pounds, with a standard deviation of 2.5 pounds. At the second store the melons are smaller, with a mean of 18 pounds and a standard deviation of 2 pounds. You select a mel
> From Exercise 50 it appeared that the mean log fusion time for the VV group was greater than that of the NV group. Could the difference be due to chance? The histogram below shows the difference in the means of the log fusion times by randomly selecting
> Your pocket copy of Kyrgyzstan on 4237±360 Som a Day claims that you can expect to spend about 4237 som each day with a standard deviation of 360 som. How well can you estimate your expenses for the trip? 1. Your budget allows you to spend 90,000 som. To
> A college student on a seven-day meal plan reports that the amount of money he spends daily on food varies with a mean of $13.50 and a standard deviation of $7. 1. What are the mean and standard deviation of the amount he might spend in two consecutive d
> According to a recent Gallup survey, 93% of teens use the Internet, but there are differences in how teen boys and girls say they use computers. The telephone poll found that 77% of boys had played computer games in the past week, compared with 65% of gi
> Explain why the facts you know about variances of independent random variables might encourage two small insurance companies to merge. (Hint: Think about the expected amount and potential variability in payouts for the separate and the merged companies.)
> Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of each of these variables: 1. X+50 2. 10Y 3. X+0.5Y 4. XY 5. X+Y
> Suppose that, as reported by the Centers for Disease Control, about 18% of high school students smoke tobacco. You randomly select 120 high school students to survey them on their attitudes toward scenes of smoking in the movies. 1. What the expected num
> Molly college offers two sections of Statistics 101. From what she has heard about the two professors listed, Molly estimates that her chances of passing the course are 0.80 if she gets Professor Scedastic and 0.60 if she gets Professor Kurtosis. The reg
> The Centers for Disease Control and Prevention say that about 18% of high-school students smoke tobacco (down from a high of 38% in 1997). Suppose you randomly select high-school students to survey them on their attitudes toward scenes of smoking in the
> A company human resources officer reports a breakdown of employees by job type and sex shown in the table. 1. What the probability that a worker selected at random is 1. female? 2. female or a production worker? 3. female, if the person works in producti
> A 65-year-old woman takes out a $100,000 term life insurance policy. The company charges an annual premium of $520. Estimate the company expected profit on such policies if mortality tables indicate that only 2.6% of women age 65 die within a year.
> From Exercise 16 it appeared that the mean cost of a cappuccino was slightly higher than the mean cost of a dozen eggs. Given the variation among the prices, could that difference be due just to chance? To examine that further, we took 1000 random sample
> A multiple choice test has 50 questions, with 4 answer choices each. You must get at least 30 correct to pass the test, and the questions are very difficult. 1. Are you likely to be able to pass by guessing on every question? Explain. 2. Suppose, after s
> Since the stock market began in 1872, stock prices have risen in about 73% of the years. Assuming that market performance is independent from year to year, what the probability that 1. the market will rise for 3 consecutive years? 2. the market will rise
> In some cities tall people who want to meet and socialize with other tall people can join Beanstalk Clubs. To qualify, a man must be over 6²2³ tall, and a woman over 5²10³. According to the National Health Survey, heights of adults may have a Normal mode
> If you land in a penalty zone on the game board described in Exercise 12 , your move will be determined by subtracting the roll of the die from the result on the spinner. Now what are the mean and standard deviation of the number of spots you may move?
> Neurological research has shown that in about 80% of people, language abilities reside in the brain left side. Another 10% display right-brain language centers, and the remaining 10% have two-sided language control. (The latter two groups are mainly left
> In a board game you determine the number of spaces you may move by spinning a spinner and rolling a die. The spinner has three regions: Half of the spinner is marked 5, and the other half is equally divided between 10 and 20. The six faces of the die sho
> At a large fertility clinic, 152 women became pregnant while taking Clomid. (See Exercise 7 .) 1. What are the mean and standard deviation of the number of twin births we might expect? 2. Can we use a Normal model in this situation? Explain. 3. What the
> The car insurance company in Exercise 8 believes that about 0.5% of drivers have an at-fault accident during a given year. Suppose the company insures 1355 drivers in that city. 1. What are the mean and standard deviation of the number who may have at-fa
> A consumer organization estimates that 29% of new cars have a cosmetic defect, such as a scratch or a dent, when they are delivered to car dealers. This same organization believes that 7% have a functional defect something that does not work properly and
> Because of the skewness of the distributions of fusion times described in Exercise 49, we might consider a re-expression. Here are the boxplots of the log of fusion times. Is it better to analyze the original fusion times or the log fusion times? Explain
> Does keeping a child lunch in an insulated bag, even with ice packs, protect the food from warming to temperatures where germs can proliferate? Researchers used an electric temperature gun on 235 lunches at preschools 90 minutes before they were to be ea
> People who read the last page of a mystery novel first generally like stories better. Researchers recruited 819 college students to read short stories, and for one story, they were given a spoiler paragraph beforehand. On the second and third story, the
> Fireworks manufacturers face a dilemma. They must be sure that the rockets work properly, but test-firing a rocket essentially destroys it. On the other hand, not testing the product leaves open the danger that they sell a bunch of duds, leading to unhap
> In the journal Science, a research team reported that plants in southern England are flowering earlier in the spring. Records of the first flowering dates for 385 species over a period of 47 years indicate that flowering has advanced an average of 15 day
> Data were collected over a decade from 1021 men and women with a recent history of precancerous colon polyps. Participants were randomly assigned to receive folic acid (a B vitamin) or a placebo, and the study concluded that those receiving the folic aci
> Carsten, Matt, and Rainer designed an experiment to see how different environments affect the Internet speed around campus. They used their own Mac computer and a PC belonging to the school and tested each in two different libraries, the main and the sci
> There are 20 first-class passengers and 120 coach passengers scheduled on a flight. In addition to the usual security screening, 10% of the passengers will be subjected to a more complete search. 1. Describe a sampling strategy to randomly select those t
> Wayne Collier designed an experiment to measure the fuel efficiency of his family car under different tire pressures. For each run, he set the tire pressure to either 28 or 32 psi and then measured the miles driven on a highway (I-95 between Mills River
> The radioactive gas radon, found in some homes, poses a health risk to residents. To assess the level of contamination in their area, a county health department wants to test a few homes. If the risk seems high, they will publicize the results to emphasi
> Research reported in 2008 brings to light the effectiveness of treating chronic lower back pain with different methods. One-third of nearly 1200 volunteers were administered conventional treatment (drugs, physical therapy, and exercise). The remaining pa
> Stereograms appear to be composed entirely of random dots. However, they contain separate images that a viewer can fuse into a three-dimensional (3D) image by staring at the dots while defocusing the eyes. An experiment was performed to determine whether
> It generally believed that baseball players can hit the ball farther with aluminum bats than with the traditional wooden ones. Is that true? And, if so, how much farther? Players on your local high school baseball team have agreed to help you find out. D
> Vineyard owners have problems with birds that like to eat the ripening grapes. Some vineyards use scarecrows to try to keep birds away. Others use netting that covers the plants. Owners really would like to know if either method works and, if so, which o
> Political analyst Michael Barone has written that conservatives are more likely than others to refuse to respond to polls, particularly those polls taken by media outlets that conservatives consider biased (The Weekly Standard, March 10, 1997). The Pew R
> The Pew Research Center collected data from national exits polls conducted by NBC News after the 2008 presidential election. The following table shows information regarding voter age and party preference: 1. What sampling strategy do you think the pollst
> In England, a Leeds University researcher said that the local watering hole welcoming atmosphere helps men get rid of the stresses of modern life and is vital for their psychological well-being. Author of the report, Dr. Colin Gill, said rather than comp
> Does the content of a television program affect viewers memory of the products advertised in commercials? Design an experiment to compare the ability of viewers to recall brand names of items featured in commercials during programs with violent content,
> A researcher wants to compare the performance of three types of antacid in volunteers suffering from acid reflux disease. Because men and women may react differently to this medication, the subjects are split into two groups, by sex. Subjects in each gro
> Medical studies indicate that smokers are less likely to develop Alzheimer disease than people who never smoked. 1. Does this prove that smoking may offer some protection against Alzheimer? Explain. 2. Offer an alternative explanation for this associatio
> Readers Digest (April 2002, p. 152) reported results of several surveys that asked graduate students to examine photographs of men and women and try to guess their ages. Researchers compared these guesses with the number of times the people in the pictur
> Researchers at the Purina Pet Institute studied Labrador retrievers for evidence of a relationship between diet and longevity. At 8 weeks of age, 2 puppies of the same sex and weight were randomly assigned to one of two groups a total of 48 dogs in all.
> The table lists the amounts of rainfall (in acre-feet) from the 26 clouds seeded with silver iodide discussed in Exercise 40. (Data in Cloud seeding) 1. Why is acre-feet a good way to measure the amount of precipitation produced by cloud seeding? 2. Plot
> A study examined brain size (measured as pixels counted in a digitized magnetic resonance image [MRI] of a cross section of the brain) and IQ (4 performance scales of the Wechsler IQ test) for college students. The scatterplot shows the Performance IQ sc
> A college statistics class conducted a survey concerning community attitudes about the college large homecoming celebration. That survey drew its sample in the following manner: Telephone numbers were generated at random by selecting one of the local tel
> Mary Beth, Nigel, and Molly want to design an experiment to find the recipe for the best chocolate chip cookies. They will try to keep the size of the cookies the same, but use cooking times of 10 and 15 minutes. They will use three different temperature
> Sofie, Ryan, and Alessandra wanted to design an experiment to find out how distraction affects our ability to judge time. The experiment consisted of starting a clock (out of view of the subject) and then asking the subject to tell them when they thought
> An experiment to test a new laundry detergent, SparkleKleen, is being conducted by a consumer advocate group. They would like to compare its performance with that of a laboratory standard detergent they have used in previous experiments. They can stain 1
> In August 2011, a Sodahead.com voluntary response poll asked site visitors, Obama is on Vacation Again: Does He Have the Worst Timing Ever? 56% of the 629 votes were for Yes. During the week of the poll, a 5.8 earthquake struck near Washington, D.C., and
> In another experiment to see if getting candy after a meal would induce customers to leave a bigger tip, a waitress randomly decided what to do with 80 dining parties. Some parties received no candy, some just one piece, and some two pieces. Others initi
> In restaurants, servers rely on tips as a major source of income. Does serving candy after the meal produce larger tips? To find out, two waiters determined randomly whether or not to give candy to 92 dining parties. They recorded the sizes of the tips a
> Researchers at the Washington University School of Medicine randomly placed 480 rats into one of three chambers containing radio antennas. One group was exposed to digital cell phone radio waves, the second to analog cell phone waves, and the third group
> A paper published in 2017 in JAMA Internal Medicine (jamanetwork.com/journals/jamainternalmedicine/fullarticle/2623528) reported on a study of alternate-day fasting as a weight-loss method. One hundred obese persons were assigned at random to one of thre
> Use the statistics package of your choice or the simple sample tool at astools.datadesk.com to draw samples of the conditions from the New York bridges 2016 data file. Draw a sample of 50, a sample of 100, a sample of 200, and a sample of 500. Compare th
> Here are the same data you saw in Exercise 45 after re-expressions as the square root of assets (in $M) and the logarithm of assets (in $M): 1. Which re-expression do you prefer? Why? 2. In the square root re-expression, what does the value 50 actually i
> The journal Circulation reported that among 1900 people who had heart attacks, those who drank an average of 19 cups of tea a week were 44% more likely than nondrinkers to survive at least 3 years after the attack.
> The data file Commuter sample holds a sample drawn from the Population commute times data set. Using your statistics program make histograms of the sample and the population. Discuss how they are similar and how they differ.
> Does the use of computer software in introductory statistics classes lead to better understanding of the concepts? A professor teaching two sections of statistics decides to investigate. She teaches both sections using the same lectures and assignments,
> Older Americans with a college education are significantly more likely to be emotionally well-off than are people in this age group with less education. Among those aged 65 and older, 35% scored 90 or above on the Emotional Health Index, but for those wi
> A soft-drink manufacturer must be sure the bottle caps on the soda are fully sealed and will not come off easily. Inspectors pull a few bottles off the production line at regular intervals and test the caps. If they detect any problems, they will stop th
> An orange-juice processing plant will accept a shipment of fruit only after several hundred oranges selected from various locations within the truck are carefully inspected. If too many show signs of unsuitability for juice (bruised, rotten, unripe, etc.
> People aged 50 to 71 were initially contacted in the mid-1990s to participate in a study about smoking and bladder cancer. Data were collected from more than 280,000 men and 186,000 women from eight states who answered questions about their health, smoki
