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Statistics Concepts And Controversies 7th Edition David S Moore, William I Notz - Solutions
Searching for ESP. A researcher looking for evidence of extrasensory perception (ESP) tests 200 subjects. Only one of these subjects does significantly better (P < 0.01) than random guessing.(a) Do the results of this study provide strong evidence that this person has ESP? Explain your answer.(b)
How far do rich parents take us? How much education children get is strongly associated with the wealth and social status of their parents. In social science jargon, this is “socioeconomic status,” or SES. But the SES of parents has little influence on whether children who have graduated from
Who will win? A Gallup Poll taken in early March 2008 found that 48% of Democratic and Democratic-leaning voters supported Hillary Clinton for the Democratic presidential candidate. The poll had a margin of sampling error of plus or minus three percentage points at 95%confidence. A political
Ages of presidents. Joe is writing a report on the backgrounds of American presidents. He looks up the ages of all 43 presidents when they entered office. Because Joe took a statistics course, he uses these 43 numbers to get a 95% confidence interval for the mean age of all men who have been
A television poll. A television news program conducts a call-in poll about immigration. Of the 2372 callers, 1921 believe that the level of immigration in the United States should be decreased. The station, following 516 CHAPTER 23 Use and Abuse of Statistical Inference recommended practice, makes
Take me out to the ball game. A researcher compared a random sample of recently divorced men in a large city with a random sample of men from the same city who had been married at least 10 years and had never been divorced. The researcher measured 122 variables on each man and compared the two
Weight loss. A weight-loss program conducted a randomized experiment to determine whether people lost weight after eight weeks on the program. The researchers report that, on average, the subjects in the study lost weight and that the weight loss was statistically significant with a P-value of
Web-based exercise. Choose a major journal in your field of study.Use aWeb search engine to find itsWeb site—just search on the journal’s name. Find a paper that uses a phrase like “significant (P = 0.01).”
Will they charge more? A bank wonders whether omitting the annual credit card fee for customers who charge at least $3000 in a year will increase the amount charged on its credit cards. The bank makes this offer to an SRS of 400 of its credit card customers. It then compares how much these
Testing a random number generator. Our statistical software has a“random number generator” that is supposed to produce numbers scattered at random between 0 and 1. If this is true, the numbers generated come from a population with μ = 0.5. A command to generate 100 random numbers gives
Response time. Last year, your company’s service technicians took an average of 2.5 hours to respond to trouble calls from business customers who had purchased service contracts. Do this year’s data show a significantly different average response time? What null and alternative hypotheses
Mice in a maze. Experiments on learning in animals sometimes measure how long it takes mice to find their way through a maze. The mean time is 19 seconds for one particular maze. A researcher thinks that a loud noise will cause the mice to complete the maze faster. She measures how long each of
Student attitudes. The Survey of Study Habits and Attitudes (SSHA)is a psychological test that measures students’ study habits and attitude toward school. Scores range from 0 to 200. The mean score for U.S. college students is about 115, and the standard deviation is about 30. A teacher suspects
Speeding. It often appears that most drivers on the road are driving faster than the posted speed limit. Situations differ, of course, but here is one set of data. Researchers studied the behavior of drivers on a rural interstate highway in Maryland where the speed limit was 55 miles per hour.They
Do chemists have more girls? Some people think that chemists are more likely than other parents to have female children. (Perhaps chemists are exposed to something in their laboratories that affects the sex of their children.)The Washington State Department of Health lists the parents’
Side effects. An experiment on the side effects of pain relievers assigned arthritis patients to one of several over-the-counter pain medications.Of the 420 patients who took one brand of pain reliever, 21 suffered some “adverse symptom.”(a) If 10% of all patients suffer adverse symptoms, what
Teens and their TV sets. The New York Times and CBS News conducted a nationwide poll of 1048 randomly selected 13- to 17-yearolds.Of these teenagers, 692 had a television in their room. We can act as if the sample were an SRS. Is there good evidence that more than half of all teenagers have a TV in
Using the Internet. Return to the study in Exercise 22.16, which found that 130 of 200 first-year students said that they used the Internet frequently for research or homework. Carry out the hypothesis test described in Exercise 22.16 and compute the P-value. How does your value compare with the
Finding a P-value by simulation. A classic experiment to detect extra-sensory perception (ESP) uses a shuffled deck of cards containing five suits (waves, stars, circles, squares, and crosses). As the experimenter turns over each card and concentrates on it, the subject guesses the suit of the
Finding a P-value by simulation. Is a new method of teaching reading to first-graders (Method B) more effective than the method now in use(Method A)? You design a matched pairs experiment to answer this question.You form 20 pairs of first-graders, with the two children in each pair carefully
Significance means what? Asked to explain the meaning of “statistically significant at the α = 0.05 level,” a student says: “This means that the probability that the null hypothesis is true is less than 0.05.” Is this explanation correct? Why or why not?
Significant at what level? Explain in plain language why a result that is significant at the 1% level must always be significant at the 5% level. If a result is significant at the 5% level, what can you say about its significance at the 1% level?
Using the Internet. Is the result of Exercise 22.16 statistically significant at the 5% level? At the 1% level?
Do our athletes graduate? Is the result of Exercise 22.15 statistically significant at the 10% level? At the 5% level?
Using the Internet. In 2006, 75.9% of first-year college students responding to a national survey said that they used the Internet frequently for research or homework. A state university finds that 130 of an SRS of 200 of its first-year students said that they used the Internet frequently for
Do our athletes graduate? The National Collegiate Athletic Association(NCAA) requires colleges to report the graduation rates of their athletes.At one large university, 71% of all students who entered in 2000 graduated within six years. Seventy-three of the 117 students who entered with athletic
First-year students. A UCLA survey of college freshmen in the 2006–2007 academic year found that 28.6% of all first-year college students identify themselves as politically liberal. You wonder if this percentage is different at your school, but you have no idea whether it is higher or lower. You
Unemployment. The national unemployment rate in a recent month was 4.9%. You think the rate may be different in your city, so you plan a sample survey that will ask the same questions as the Current Population Survey.To see if the local rate differs significantly from 4.9%, what hypotheses will you
Body temperature. We have all heard that 98.6 degrees Fahrenheit(or 37 degrees Celsius) is “normal body temperature.” In fact, there is evidence that most people have a slightly lower body temperature. You plan to measure the body temperature of a random sample of people very accurately. You
Attending church. A 2006 Gallup Poll found that 40% of American adults say they attended religious services last week. This is almost certainly not true.(a) Why might we expect answers to a poll to overstate true church attendance?(b) You suspect strongly that the true percentage attending church
What’s a gift worth? Do people value gifts from others more highly than they value the money it would take to buy the gift?We would like to think so, because we hope that “the thought counts.” A survey of 209 adults asked them to list three recent gifts and then asked, “Aside from any
Ancient Egypt. Settlements in Egypt before the time of the pharaohs are dated by measuring the presence of forms of carbon that decay over time. The first datings of settlements in the Nagada region used hair that had been excavated 60 years earlier. Now researchers have used newer methods and more
Pigs and prestige in ancient China. It appears that pigs in Stone Age China were not just a source of food. Owning pigs was also a display of wealth.Evidence for this comes from examining burial sites. If the skulls of sacrificed pigs tend to appear along with expensive ornaments, that suggests
Diet and bowel cancer. It has long been thought that eating a healthier diet reduces the risk of bowel cancer. A large study cast doubt on this advice.The subjects were 2079 people who had polyps removed from their bowels in the past six months. Such polyps may lead to cancer. The subjects were
Diet and diabetes. Does eating more fiber reduce the blood cholesterol level of patients with diabetes? A randomized clinical trial compared normal and high-fiber diets. Here is part of the researchers’ conclusion: “The high-fiber diet reduced plasma total cholesterol concentrations by 6.7
Students’ earnings. The financial aid office of a university asks a sample of students about their employment and earnings. The report says, “For academic year earnings, a significant difference (P = 0.028) was found between the sexes, with men earning more on the average. No difference (P =
Ethnocentrism. A social psychologist reports, “In our sample, ethnocentrism was significantly higher (P < 0.05) among church attenders than among nonattenders.” Explain to someone who knows no statistics what this means.
IQ scores. The mean IQ for the entire population in any age group is supposed to be 100. Suppose the IQ scores of 31 seventh-grade girls in a Midwest school district are measured and the sample mean is found to be 105.8 and the sample standard deviation is 14.3.Treat the scores as if they were an
Coin tossing. Refer to Exercise 22.1 (page 488). We tossed a coin only 50 times and got 22 heads, so the proportion of heads is^p= 22 50= 0.44 This is less than one-half. Is this evidence that our coin was not balanced?For the hypotheses you formulated in Exercise 22.1, find the P-value based on
Coin tossing. We do not have the patience of Count Buffon, so we tossed a coin only 50 times. We got 22 heads.The proportion of heads is^p= 22 50= 0.44 This is less than one-half. Is this evidence that our coin was not balanced?Formulate the hypotheses for an appropriate significance test and
Rolling dice. Suppose you roll two casino dice, as in Example 2. What is the probability that the sum of the spots on the up-faces is 7? 11? 7 or 11?
Web-based exercise. Search the Web for a recent poll in which the sample statistic is a proportion, for example, the proportion in the sample responding “Yes” to a question. Calculate a 95% confidence interval for the population proportion (assume that the sample is a random sample). Describe
Web-based exercise. Results from the Behavioral Risk Factor Surveillance System (BRFSS) can be found at apps.nccd.cdc.gov/brfss/.Find the sample proportion of college graduates in your state who engaged in binge drinking for the most recent year reported at theWeb site.Construct a 95% confidence
Web-based exercise. If you go to the Centers for Disease Control and PreventionWeb site, you will find that the proportion of college graduates in California who engaged in binge drinking in 2006 is reported as 15.2%. Go to the Web site at apps.nccd.cdc.gov/brfss/. Why is the percentage reported at
A sampling distribution, continued. Exercise 21.33 presents 50 sample means x from 50 random samples of size 100. Using a calculator, find the mean and standard deviation of these 50 values. Then answer these questions.(a) The mean of the population from which the 50 samples were drawn isμ = 0.5
Will they charge more? In Exercise 21.32, you carried out the calculations for a confidence interval based on a bank’s experiment in changing the rules for its credit cards. You ought to ask some questions about this study.(a) The distribution of the amount charged is skewed to the right, but
A sampling distribution. Exercise 21.31 concerns the mean of the random numbers generated by a computer program. The mean is supposed to be 0.5 because the numbers are supposed to be spread at random between 0 and 1. We asked the software to generate samples of 100 random numbers repeatedly. Here
Will they charge more? A bank wonders whether omitting the annual credit card fee for customers who charge at least $2500 in a year will increase the amount charged on its credit cards. The bank makes this offer to an SRS of 200 of its credit card customers. It then compares how much these
Testing a random number generator. Our statistical software has a “random number generator” that is supposed to produce numbers scattered at random between 0 to 1. If this is true, the numbers generated come from a population with μ = 0.5. A command to generate 100 random numbers gives
Blood pressure. A randomized comparative experiment studied the effect of diet on blood pressure. Researchers divided 54 healthy white males at random into two groups. One group received a calcium supplement; the other, a placebo. At the beginning of the study, the researchers measured many
Averages versus individuals. Scores on the ACT college entrance examination vary Normally with mean μ = 18 and standard deviation σ = 6. The range of reported scores is 1 to 36.(a) What range contains the middle 95% of all individual scores?(b) If the ACT scores of 25 randomly selected students
IQ test scores. Here are the IQ test scores of 31 seventh-grade girls in a Midwest school district:114 100 104 89 102 91 114 114 103 105 108 130 120 132 111 128 118 119 86 72 111 103 74 112 107 103 98 96 112 112 93(a) We expect the distribution of IQ scores to be close to Normal. Make a histogram
The idea of a sampling distribution. Figure 21.1 (page 458) shows the idea of the sampling distribution of a sample proportion ^p in picture form.Draw a similar picture that shows the idea of the sampling distribution of a sample mean x.
Safe margin of error. The margin of error z∗^p(1−^p)/n is 0 when^p is 0 or 1 and is largest when ^p is 1/2. To see this, calculate ^p(1 − ^p) for^p= 0, 0.1, 0.2, . . . , 0.9, and 1. Plot your results vertically against the values of ^p horizontally. Draw a curve through the points. You have
Estimating unemployment. The Bureau of Labor Statistics (BLS)uses 90% confidence in presenting unemployment results from the monthly Current Population Survey (CPS). The January 2008 survey interviewed 134,163 people. Of these, 65,481 were employed and 3293 were unemployed.The CPS is not an SRS,
Unhappy HMO patients. How likely are patients who file complaints with a health maintenance organization (HMO) to leave the HMO? In one year, 639 of the more than 400,000 members of a large New England HMO filed complaints. Fifty-four of the complainers left the HMO voluntarily. (That is, they were
The effect of confidence level. An October 2007 Los Angeles Times Poll found that 52% of its sample of 1209 adults preferred social spending to cutting taxes. Use this poll result and Table 21.1 to give 70%, 80%, 90%, and 99% confidence intervals for the proportion of all adults who feel this way.
Illegal immigrants. Exercise 21.8 reports a New York Times Poll that found that 776 in a random sample of 1125 American adults said they believe illegal immigrants should “be prosecuted and deported for being in the U.S. illegally.”Give a 99% confidence interval for the proportion of all
Gun safety. Exercise 21.7 reports a Gallup Poll in which 425 of a random sample of 1012 adults thought that having a gun in the house makes it a safer place. Give a 90% confidence interval for the proportion of all adults who feel this way. How does your interval compare with the 95% confidence
Simulating confidence intervals. In Exercise 21.19, you found the recipe for a 68% confidence interval for a population proportion p. Suppose that (unknown to anyone) 60% of the voters in her district favor the reelection of Congresswoman Caucus.(a) How would you simulate the votes of an SRS of 25
68% confidence. We used the 95 part of the 68–95–99.7 rule to give a recipe for a 95% confidence interval for a population proportion p.(a) Use the 68 part of the rule to give a recipe for a 68% confidence interval.(b) Explain in simple language what “68% confidence” means.(c) Use the
The quick method. The quick method of Chapter 3 (pages 42–43) uses^p± 1/√n as a rough recipe for a 95% confidence interval for a population proportion.The margin of error from the quick method is a bit larger than needed.It differs most from the more accurate method of this chapter when ^p is
Do you jog? Suppose that 10% of all adults jog. An opinion poll asks an SRS of 400 adults if they jog.(a) What is the sampling distribution of the proportion ^p in the sample who jog?(b) According to the 68–95–99.7 rule, what is the probability that the sample proportion who jog will be 7.3% or
Harley motorcycles. Harley-Davidson motorcycles make up 14% of all the motorcycles registered in the United States. You plan to interview an SRS of 600 motorcycle owners.(a) What is the sampling distribution of the proportion of your sample who own Harleys?(b) How likely is your sample to contain
Teens and their TV sets. The New York Times and CBS News conducted a nationwide poll of 1048 randomly selected 13- to 17-yearolds.Of these teenagers, 692 had a television in their room. Also, of the 1048 teens surveyed, 189 named Fox as their favorite television network. We can consider the sample
Count Buffon’s coin. The 18th-century French naturalist Count Buffon tossed a coin 4040 times. He got 2048 heads. Give a 95% confidence interval for the probability that Buffon’s coin lands heads up. Are you confident that this probability is not 1/2? Why?
Don’t forget the basics. The Behavioral Risk Factor Surveillance System(BRFSS) survey found that 279 individuals in its 2006 random sample of 2166 college graduates in California said they had engaged in binge drinking 474 CHAPTER 21 What Is a Confidence Interval?in the past year. We used this
Tossing a thumbtack. If you toss a thumbtack on a hard surface, what is the probability that it will land point up? Estimate this probability p by tossing a thumbtack 100 times. The 100 tosses are an SRS of size 100 from the population of all tosses. The proportion of these 100 tosses that land
Random digits. We know that the proportion of 0s among a large set of random digits is p = 0.1 because all 10 possible digits are equally probable.The entries in a table of random digits are a sample from the population of all random digits. To get an SRS of 200 random digits, look at the first
The effect of sample size. An October 2007 Los Angeles Times Poll found that 52% of its sample preferred social spending to cutting taxes. Give a 95% confidence interval for the proportion of all adults who feel this way, assuming that the result ^p = 0.52 comes from a sample of size(a) n = 750(b)
Gun safety. In Exercise 21.7, you gave a 95% confidence interval based on a random sample of n = 1012 adults. How large a sample would be needed to get a margin of error half as large as the one in Exercise 21.7?
Illegal immigrants. A May 2007 New York Times Poll on illegal immigrants interviewed 1125 randomly selected American adults.Of those in the sample, 776 said they believe illegal immigrants should“be prosecuted and deported for being in the U.S. illegally.” Although the samples in national polls
Gun safety. An October 2004 Gallup Poll asked a sample of 1012 adults whether they thought that having a gun in the house makes it a safer place to be or a more dangerous place to be. The number who thought having a gun in the house makes it a safer place was 425. Although the samples in national
The schools’ most serious problem. Results from a Gallup Youth Survey reveal that teens most often mention “violence, fighting, and school safety” when asked to name the biggest problem their schools must deal with. The report of this sample survey of 600 teens found that, with 95%
Fire the coach? A college president says, “99% of the alumni support my firing of Coach Boggs.” You contact an SRS of 200 of the college’s 15,000 living alumni and find that 66 of them support firing the coach.(a) What population does inference concern here?(b) Explain clearly what the
A student survey. Tonya wants to estimate what proportion of the students in her dormitory like the dorm food. She interviews an SRS of 50 of the 175 students living in the dormitory. She finds that 14 think the dorm food is good.(a) What population does Tonya want to draw conclusions about?(b) In
Blood pressure of executives. The medical director of a large company looks at the medical records of 72 executives between the ages of 35 and 44 years. He finds that the mean systolic blood pressure in this sample is x = 126.1 and the standard deviation is s = 15.2.Assuming the sample is a random
Gambling on sports. A December 2007 Gallup Poll consisting of a random sample of 1027 adult Americans found that 17% had gambled on sports in the last 12 months. Find a 99% confidence interval for the proportion of all adult Americans who gambled on sports in this time period. How would you
Gambling on sports. A December 2007 Gallup Poll consisting of a random sample of 1027 adult Americans found that 17% had gambled on sports in the last 12 months. Find a 95% confidence interval for the proportion of all adult Americans who gambled on sports in this time period. How would you
Web-based exercise. Oddsmakers often list the odds for certain sporting events on the Web. For example, one can find the current odds of winning the next Super Bowl for each NFL team. We found a list of such odds at www.vegas.com/gaming/futures/superbowl.html. When an oddsmaker says the odds are A
Generating a sampling distribution. Let us illustrate the idea of a sampling distribution in the case of a very small sample from a very small Notes and Data Sources 409 population. The population is the scores of 10 students on an exam:Student: 0 1 2 3 4 5 6 7 8 9 Score: 82 62 80 58 72 73 65 66 74
Applying to college. You ask an SRS of 1500 college students whether they applied for admission to any other college. Suppose that in fact 35% of all college students applied to colleges besides the one they are attending. (That’s close to the truth.) The sampling distribution of the proportion
Do you jog? An opinion poll asks an SRS of 1500 adults, “Do you happen to jog?” Suppose (as is approximately correct) that the population proportion who jog is p = 0.15. In a large number of samples, the proportion ^p who answer“Yes” will be approximately Normally distributed with mean 0.15
Airplane safety (optional). In the setting of Exercise 18.16, what is the probability of getting a sample in which fewer than 60% think that airplanes would be safer if pilots carried guns? (Use Table B.)
Immigration (optional). In the setting of Exercise 18.15, what is the probability of getting a sample in which more than 51% of those sampled think that the level of immigration to this country should be decreased?(Use Table B.)
Airplane safety. Suppose that 62% of all adults think that airplanes would be safer places if pilots carried guns. An opinion poll plans to ask an SRS of 1009 adults about airplane safety. The proportion of the sample who think that airplanes would be safer if pilots carried guns will vary if we
Immigration. Suppose that 55% of all adult American think that the level of immigration to this country should be decreased. An opinion poll interviews 1007 randomly chosen Americans and records the sample proportion who feel that the level of immigration to this country should be decreased.This
Legitimate probabilities? In each of the following situations, state whether or not the given assignment of probabilities to individual outcomes is legitimate, that is, satisfies the rules of probability. If not, give specific reasons for your answer.(a) When a coin is spun, P(H) = 0.55 and P(T) =
Colors of M&M’s. If you draw an M&M candy at random from a bag of the candies, the candy you draw will have one of six colors. The probability of drawing each color depends on the proportion of each color among all candies made.(a) Here are the probabilities of each color for a randomly chosen
Roulette. A roulette wheel has 38 slots, numbered 0, 00, and 1 to 36.The slots 0 and 00 are colored green, 18 of the others are red, and 18 are black.The dealer spins the wheel and at the same time rolls a small ball along the wheel in the opposite direction. The wheel is carefully balanced so that
More tetrahedral dice. Tetrahedral dice are described in Exercise 18.9.Give a probability model for rolling two such dice. That is, write down all possible outcomes and give a probability to each. (Example 2 and Figure 18.1 may help you.) What is the probability that the sum of the down-faces is 5?
Birth order. A couple plan to have three children. There are 8 possible arrangements of girls and boys. For example, GGB means the first two children are girls and the third child is a boy. All 8 arrangements are (approximately)equally likely.(a) Write down all 8 arrangements of the sexes of three
High school academic rank. Select a first-year college student at random and ask what his or her academic rank was in high school. Here are the probabilities, based on proportions from a large sample survey of first-year students:Rank: Top 20% Second 20% Third 20% Fourth 20% Lowest 20%Probability:
Our next president? A Gallup Poll on Presidents Day 2008 interviewed a random sample of 1007 adult Americans. Those in the sample were asked which former president they would like to bring back as the next president if they could. Here are the results:Outcome Probability John F. Kennedy 0.23 Ronald
Land in Canada. Choose an acre of land in Canada at random. The probability is 0.45 that it is forest and 0.03 that it is pasture.(a) What is the probability that the acre chosen is not forested?(b) What is the probability that it is either forest or pasture?(c) What is the probability that a
Causes of death. Government data assign a single cause for each death that occurs in the United States. The data show that the probability is 0.27 that a randomly chosen death was due to heart disease, and 0.23 that it was due to cancer. What is the probability that a death was due either to heart
Moving up. A sociologist studying social mobility in Denmark finds that the probability that the son of a lower-class father remains in the lower class is 0.46. What is the probability that the son moves to one of the higher classes?
Teen opinion poll. Refer to Example 4. Using the 68–95–99.7 rule, what is the probability that more than 54.4%say “Yes”?
Selling cars. Bill sells new cars for a living. On a weekday afternoon, he will deal with 1 customer with probability 0.2, 2 customers with probability 0.5, and 3 customers with probability 0.3. Each customer has probability 0.2 of buying a car. Customers buy independently of each other.Describe
Predicting the winner. There are 11 teams in the Big Ten athletic conference. Here’s one set of personal probabilities for next year’s basketball Part III Projects 451 champion: Michigan State has probability 0.3 of winning. Iowa, Michigan, Illinois, Northwestern, and Penn State have no chance.
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