Question: Stereograms appear to be composed entirely of

> 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

> 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 lo

> 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

> 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

> Tests of gene therapy on laboratory rats have raised hopes of stopping the degeneration of tissue that characterizes chronic heart failure. Researchers at the University of California, San Diego, used hamsters with cardiac disease, randomly assigning 30

> An artisan wants to create pottery that has the appearance of age. He prepares several samples of clay with four different glazes and test fires them in a kiln at three different temperature settings.

> Widely used antidepressants may reduce ominous brain plaques associated with Alzheimer disease. In the study, mice genetically engineered to have large amounts of brain plaque were given a class of antidepressants that boost serotonin in the brain. After

> Students were asked how many songs they had in their digital music libraries. Here a display of the responses: 1. What aspect of this distribution makes it difficult to summarize, or to discuss, center and spread? 2. What would you suggest doing with the

> Some doctors have expressed concern that men who have vasectomies seemed more likely to develop prostate cancer. Medical researchers used a national cancer registry to identify 923 men who had had prostate cancer and 1224 men of similar ages who had not.

> Researchers identified 242 children in the Cleveland area who had been born prematurely (at about 29 weeks). They examined these children at age 8 and again at age 20, comparing them to another group of 233 children not born prematurely. Their report, pu

> Exercise R2.7 examined the correlation between BCI and pH in streams sampled in the Adirondack Mountains. Here is the corresponding regression model: Response variable is: BCI R-squared = 27.1% s = 140.4 1. Write the regression model. 2. What is the inte

> Marine biologists warn that the growing number of powerboats registered in Florida threatens the existence of manatees. The data in the table come from the Florida Fish and Wildlife Conservation Commission (myfwc.com/research/manatee/) and the U.S. Coast

> Biologists studying the effects of acid rain on wildlife collected data from 163 streams in the Adirondack Mountains. They recorded the pH (acidity) of the water and the BCI, a measure of biological diversity, and they calculated R2=27%. Here a scatterpl

> The Dow Jones stock index measures the performance of the stocks of America largest companies (finance.yahoo.com). A regression of the Dow prices on years 1972–2015 looks like this: Dependent variable is:

> In January 2012, the New York Times published a story called Twin Births in the U.S., Like Never Before, in which they reported a 76 percent increase in the rate of twin births from 1980 to 2009. Here are the numbers of twin births each year (per 1000 li

> How are a company profits related to its sales? Let examine data from 71 large U.S. corporations. All amounts are in millions of dollars. 1. Histograms of Profits and Sales and histograms of the logarithms of Profits and Sales are seen below. Why are the

> The Minnesota Department of Transportation hoped that they could measure the weights of big trucks without actually stopping the vehicles by using a newly developed weigh-in-motion scale. After installation of the scale, a study was conducted to find out

> Here are the average weights of the football team for the University of Texas for various years in the 20th century. 1. Fit a straight line to the relationship of Weight by Year for Texas football players. 2. According to these models, in what year will

> Here is a histogram of the assets (in millions of dollars) of 79 companies chosen from the Forbes list of the nation top corporations: (Data in Companies) 1. What aspect of this distribution makes it difficult to summarize, or to discuss, center and spre

> Find the predicted value of y, using each model for x=10. 1. y^=2+0.8 ln x 2. log y^=50.23x 3. 1y^=17.1 1.66x

> The Sears Cup was established in 1993 to honor institutions that maintain a broad-based athletic program, achieving success in many sports, both men and women. In the years following its Division III inception in 1995, the cup was won by Williams College

> Instead of Age, perhaps the Size of the vineyard (in acres) is associated with the price of the wines. Look at the scatterplot: 1. Do you see any evidence of an association? 2. What concern do you have about this scatterplot? 3. If the red + data point i

> Are people who use tobacco products more likely to consume alcohol? Here are data on household spending (in pounds) taken by the British government on 11 regions in Great Britain. Do tobacco and alcohol spending appear to be related? What questions do yo

> Since clean-air regulations have dictated the use of unleaded gasoline, the supply of leaded gas in New York state has diminished. The following table was given on the August 2001 New York State Math B exam, a statewide achievement test for high school s

> Does how long toddlers sit at the lunch table help predict how much they eat? The table and graph show the number of minutes the kids stayed at the table and the number of calories they consumed. Create and interpret a model for these data.