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business
business statistics

Questions and Answers of Business Statistics

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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.”
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
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
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
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
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
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
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
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 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
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%
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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%
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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
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)
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
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
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
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

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