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business
business statistics in practice

Questions and Answers of Business Statistics In Practice

Larger sample Suppose that the blood cholesterol level of all men aged 20 to 34 follows the Normal distribution with mean m = 188 milligrams per deciliter(mg/dl) and standard deviation s = 41
Dead battery? A car company has found that the lifetime of its batteries varies from car to car according to a Normal distribution with mean m = 48 months and standard deviation s = 8.2 months. The
Bottling cola A bottling company uses a filling machine to fill plastic bottles with cola. The bottles are supposed to contain 300 milliliters (ml). In fact, the contents vary according to a Normal
Cereal A company’s cereal boxes advertise 9.65 ounces of cereal. In fact, the amount of cereal in a randomly selected box follows a Normal distribution with mean m = 9.70 ounces and standard
What does the CLT say? Asked what the central limit theorem says, a student replies, “As you take larger and larger samples from a population, the histogram of the sample values looks more and more
What does the CLT say? Asked what the central limit theorem says, a student replies, “As you take larger and larger samples from a population, the spread of the sampling distribution of the sample
Songs on an iPod Refer to Exercise 49.(a) Explain why you cannot safely calculate the probability that the mean play time x– is more than 4 minutes (240 seconds) for an SRS of 10 songs.(b) Suppose
Lightning strikes The number of lightning strikes on a square kilometer of open ground in a year has mean 6 and standard deviation 2.4. The National Lightning Detection Network (NLDN) uses automatic
Airline passengers get heavier In response to the increasing weight of airline passengers, the Federal Aviation Administration (FAA) told airlines to assume that passengers average 190 pounds in the
How many people in a car? A study of rush-hour traffic in San Francisco counts the number of people in each car entering a freeway at a suburban interchange.Suppose that this count has mean 1.5 and
More on insurance An insurance company claims that in the entire population of homeowners, the mean annual loss from fire is m = $250 and the standard deviation of the loss is s = $1000. The
Bad carpet The number of flaws per square yard in a type of carpet material varies with mean 1.6 flaws per square yard and standard deviation 1.2 flaws per square yard. The population distribution
Scores on the mathematics part of the SAT exam in a recent year were roughly Normal with mean 515 and standard deviation 114. You choose an SRS of 100 students and average their SAT Math
Why is it important to check the 10% condition before calculating probabilities involving x–?(a) To reduce the variability of the sampling distribution of x–.(b) To ensure that the distribution
A newborn baby has extremely low birth weight(ELBW) if it weighs less than 1000 grams. A study of the health of such children in later years examined a random sample of 219 children. Their mean
The number of hours a lightbulb burns before failing varies from bulb to bulb. The population distribution of burnout times is strongly skewed to the right. The central limit theorem says that (a) as
Unemployment (1.1) Find the unemployment rate for people with each level of education. How does the unemployment rate change with education?
Unemployment (5.1) What is the probability that a randomly chosen person 25 years of age or older is in the labor force? Show your work.
Unemployment (5.3) If you know that a randomly chosen person 25 years of age or older is a college graduate, what is the probability that he or she is in the labor force? Show your work.
Unemployment (5.3) Are the events “in the labor force” and “college graduate” independent? Justify your answer.
Bad eggs Sale of eggs that are contaminated with salmonella can cause food poisoning in consumers.A large egg producer takes an SRS of 200 eggs from all the eggs shipped in one day. The laboratory
Birth weights(a) Sketch a graph that displays the distribution of birth weights for this population.(b) Sketch a possible graph of the distribution of birth weights for an SRS of size 5.(c) In the
Birth weights(a) Is the sample range an unbiased estimator of the population range? Give evidence from the graph above to support your answer.(b) Explain how we could decrease the variability of the
Do you jog? The Gallup Poll once asked a random sample of 1540 adults, “Do you happen to jog?”Suppose that the true proportion of all adults who jog is p = 0.15.(a) What is the mean of the
Bag check Thousands of travelers pass through the airport in Guadalajara, Mexico, each day.Before leaving the airport, each passenger must pass through the Customs inspection area. Customs agents
IQ tests The Wechsler Adult Intelligence Scale(WAIS) is a common “IQ test” for adults. The distribution of WAIS scores for persons over 16 years of age is approximately Normal with mean 100 and
Detecting gypsy moths The gypsy moth is a serious threat to oak and aspen trees. A state agriculture department places traps throughout the state to detect the moths. Each month, an SRS of 50 traps
A study of voting chose 663 registered voters at random shortly after an election. Of these, 72% said they had voted in the election. Election records show that only 56% of registered voters voted in
The Gallup Poll has decided to increase the size of its random sample of voters from about 1500 people to about 4000 people right before an election. The poll is designed to estimate the proportion
Suppose we select an SRS of size n = 100 from a large population having proportion p of successes.Let p^ be the proportion of successes in the sample.For which value of p would it be safe to use the
The central limit theorem is important in statistics because it allows us to use the Normal distribution to find probabilities involving the sample mean(a) if the sample size is reasonably large (for
The number of undergraduates at Johns Hopkins University is approximately 2000, while the number at Ohio State University is approximately 60,000. At both schools, a simple random sample of about
A researcher initially plans to take an SRS of size n from a population that has mean 80 and standard deviation 20. If he were to double his sample size (to 2n), the standard deviation of the
The student newspaper at a large university asks an SRS of 250 undergraduates, “Do you favor eliminating the carnival from the term-end celebration?”All in all, 150 of the 250 are in favor.
Which of the following statements about the sampling distribution of the sample mean is incorrect?(a) The standard deviation of the sampling distribution will decrease as the sample size
A machine is designed to fill 16-ounce bottles of shampoo. When the machine is working properly, the amount poured into the bottles follows a Normal distribution with mean 16.05 ounces and standard
Suppose that you are a student aide in the library and agree to be paid according to the“random pay” system. Each week, the librarian flips a coin. If the coin comes up heads, your pay for the
Below are histograms of the values taken by three sample statistics in several hundred samples from the same population. The true value of the population parameter is marked with an arrow on each
The amount that households pay service providers for access to the Internet varies quite a bit, but the mean monthly fee is $38 and the standard deviation is $10. The distribution is not Normal: many
According to government data, 22% of American children under the age of six live in households with incomes less than the official poverty level.A study of learning in early childhood chooses an SRS
The five-number summary for a data set is given by min = 5, Q1 = 18, median = 20, Q3 = 40, max = 75. If you wanted to construct a boxplot for the data set (that is, one that would show outliers, if
The probability distribution for the number of heads in four tosses of a coin is given by Number of heads: 0 1 2 3 4 Probability: 0.0625 0.2500 0.3750 0.2500 0.0625 The probability of getting at
In a certain large population of adults, the distribution of IQ scores is strongly left-skewed with a mean of 122 and a standard deviation of 5. Suppose 200 adults are randomly selected from this
A 10-question multiple-choice exam offers 5 choices for each question. Jason just guesses the answers, so he has probability 1/5 of getting any one answer correct. You want to perform a simulation to
Suppose we roll a fair die four times. The probability that a 6 occurs on exactly one of the rolls is(a) 4a 16 b3 a5 6b 1(c) 4a 16 b1 a5 6b 3(e) 6a 16 b1 a5 6b 3(b) a 16 b3 a5 6b 1(d) a 16 b1 a5 6b 3
You want to take an SRS of 50 of the 816 students who live in a dormitory on a college campus. You label the students 001 to 816 in alphabetical order.In the table of random digits, you read the
The number of unbroken charcoal briquets in a 20-pound bag filled at the factory follows a Normal distribution with a mean of 450 briquets and a standard deviation of 20 briquets. The company expects
You work for an advertising agency that is preparing a new television commercial to appeal to women. You have been asked to design an experiment to compare the effectiveness of three versions of the
Suppose that you have torn a tendon and are facing surgery to repair it. The orthopedic surgeon explains the risks to you. Infection occurs in 3% of such operations, the repair fails in 14%, and both
Social scientists are interested in the association between high school graduation rate (HSGR, measured as a percent) and the percent of U.S.families living in poverty (POV). Data were collected from
The overall shape of this distribution is(a) clearly skewed to the right.(b) clearly skewed to the left.(c) roughly symmetric.(d) uniform.(e) There is no clear shape.
The mean of this distribution (don’t try to find it)will be(a) very close to the median.(b) greater than the median.(c) less than the median.(d) You can’t say, because distribution isn’t
Based on the shape of this distribution, what measures of center and spread would be most appropriate to report?(a) The mean and standard deviation(b) The mean and the interquartile range(c) The
The correlation between the age and height of children under the age of 12 is found to be r = 0.60. Suppose we use the age x of a child to predict the height y of the child. What can we conclude?(a)
An agronomist wants to test three different types of fertilizer (A, B, and C) on the yield of a new variety of wheat. The yield will be measured in bushels per acre. Six 1-acre plots of land were
According to the U.S. Census, the proportion of adults in a certain county who owned their own home was 0.71. An SRS of 100 adults in a certain section of the county found that 65 owned their home.
Which one of the following would be a correct interpretation if you have a z-score of +2.0 on an exam?(a) It means that you missed two questions on the exam.(b) It means that you got twice as many
Records from a random sample of dairy farms yielded the information below on the number of male and female calves born at various times of the day.Day Evening Night Total Males 129 15 117 261 Females
When people order books from a popular online source, they are shipped in standard-sized boxes.Suppose that the mean weight of the boxes is 1.5 pounds with a standard deviation of 0.3 pounds, the
A grocery chain runs a prize game by giving each customer a ticket that may win a prize when the box is scratched off. Printed on the ticket is a dollar value ($500, $100, $25) or the
A large company is interested in improving the efficiency of its customer service and decides to examine the length of the business phone calls made to clients by its sales staff. A cumulative
A health worker is interested in determining if omega-3 fish oil can help reduce cholesterol in adults. She obtains permission to examine the health records of 200 people in a large medical clinic
There are four major blood types in humans: O, A, B, and AB. In a study conducted using blood specimens from the Blood Bank of Hawaii, individuals were classified according to blood type and ethnic
Every 17 years, swarms of cicadas emerge from the ground in the eastern United States, live for about six weeks, and then die. (There are several different “broods,” so we experience cicada
In a city library, the mean number of pages in a novel is 525 with a standard deviation of 200.Approximately 30% of the novels have fewer than 400 pages. Suppose that you randomly select 50 novels
Protecting wood How can we help wood surfaces resist weathering, especially when restoring historic wooden buildings? In a study of this question, researchers prepared wooden panels and then exposed
Medical study variables Data from a medical study contain values of many variables for each of the people who were the subjects of the study. Here are some of the variables recorded: gender (female
A class survey Here is a small part of the data set that describes the students in an AP® Statistics class. The data come from anonymous responses to a questionnaire filled out on the first day of
Coaster craze Many people like to ride roller coasters.Amusement parks try to increase attendance by building exciting new coasters. The following table displays data on several roller coasters that
Ranking colleges Popular magazines rank colleges and universities on their “academic quality” in serving undergraduate students. Describe two categorical variables and two quantitative variables
Students and TV You are preparing to study the television-viewing habits of high school students. Describe two categorical variables and two quantitative variables that you might record for each
The individuals in this data set are(a) households.(b) people.(c) adults.(d) 120 variables.(e) columns.
This data set contains(a) 7 variables, 2 of which are categorical.(b) 7 variables, 1 of which is categorical.(c) 6 variables, 2 of which are categorical.(d) 6 variables, 1 of which is categorical.(e)
Display categorical data with a bar graph. Decide if it would be appropriate to make a pie chart.
Identify what makes some graphs of categorical data deceptive.
Calculate and display the marginal distribution of a categorical variable from a two-way table.
Calculate and display the conditional distribution of a categorical variable for a particular value of the other categorical variable in a two-way table.
Describe the association between two categorical variables by comparing appropriate conditional distributions.
Cool car colors The most popular colors for cars and light trucks change over time. Silver passed green in 2000 to become the most popular color worldwide, then gave way to shades of white in
Spam Email spam is the curse of the Internet. Here is a compilation of the most common types of spam:9 Type of spam Percent Adult 19 Financial 20 Health 7 Internet 7 Leisure 6 Products 25 Scams 9
Birth days Births are not evenly distributed across the days of the week. Here are the average numbers of babies born on each day of the week in the United States in a recent year:10 Day Births
Deaths among young people Among persons aged 15 to 24 years in the United States, the leading causes of death and number of deaths in a recent year were as follows: accidents, 12,015; homicide, 4651;
Hispanic origins Below is a pie chart prepared by the Census Bureau to show the origin of the more than 50 million Hispanics in the United States in 2010.12 About what percent of Hispanics are
Which major? About 1.6 million first-year students enroll in colleges and universities each year. What do they plan to study? The pie chart displays data on the percents of first-year students who
Buying music online Young people are more likely than older folk to buy music online. Here are the percents of people in several age groups who bought music online in a recent year:14 Age group
The audience for movies Here are data on the percent of people in several age groups who attended a movie in the past 12 months:15 Age group Movie attendance 18 to 24 years 83%25 to 34 years 73%35 to
Going to school Students in a high school statistics class were given data about the main method of transportation to school for a group of 30 students. They produced the pictograph shown.Walk Bus
Oatmeal and cholesterol Does eating oatmeal reduce cholesterol? An advertisement included the following graph as evidence that the answer is “Yes.”210 208 206 204 202 200 198 196 Cholesterol Week
Attitudes toward recycled products Recycling is supposed to save resources. Some people think recycled products are lower in quality than other products, a fact that makes recycling less practical.
Smoking by students and parents Here are data from a survey conducted at eight high schools on smoking among students and their parents:17 Neither parent smokes One parent smokes Both parents smoke
Attitudes toward recycled products Exercise 19 gives data on the opinions of people who have and have not bought coffee filters made from recycled paper. To see the relationship between opinion and
Smoking by students and parents Refer to Exercise 20. Calculate three conditional distributions of students’ smoking behavior: one for each of the three parental smoking categories. Describe the
Popular colors—here and there Favorite vehicle colors may differ among countries. The side-by-side bar graph shows data on the most popular colors of cars in a recent year for the United States and
Comparing car colors Favorite vehicle colors may differ among types of vehicle. Here are data on the most popular colors in a recent year for luxury cars and for SUVs, trucks, and vans.Color Luxury
Snowmobiles in the park Yellowstone National Park surveyed a random sample of 1526 winter visitors to the park. They asked each person whether they owned, rented, or had never used a snowmobile.
Angry people and heart disease People who get angry easily tend to have more heart disease. That’s the conclusion of a study that followed a random sample of 12,986 people from three locations for
The percent of females among the respondents was(a) 2625. (c) about 46%. (e) None of these.(b) 4877. (d) about 54%.28. Your percent from the previous exercise is part of(a) the marginal distribution
What percent of females thought that they were almost certain to be married in the next ten years?(a) About 16% (c) About 40% (e) About 61%(b) About 24% (d) About 45%30. Your percent from the
In the 2010–2011 season, the Dallas Mavericks won the NBA championship. The two-way table below displays the relationship between the outcome of each game in the regular season and whether the
The following partially complete two-way table shows the marginal distributions of gender and handedness for a sample of 100 high school students.Male Female Total Right x 90 Left 10 Total 40 60 100

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