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business statistics in practice

The Practice Of Statistics 5th Edition Daren S. Starnes, Josh Tabor - Solutions

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 mg/dl.(a) Choose an SRS of 100 men from this population.Describe the sampling distribution of x–.(b) Find
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 company installs a new brand of battery on an SRS of 8 cars.(a) If the new brand has the same
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 distribution with mean m = 298 ml and standard deviation s = 3 ml.(a) What is the probability that a
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 deviation s = 0.03 ounces.(a) What is the probability that a randomly selected box of the cereal contains
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 Normal.” Is the student right? Explain your answer.
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 mean decreases.”Is the student right? Explain your answer.
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 we take an SRS of 36 songs instead. Explain how the central limit theorem allows us to find the
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 sensors to watch for lightning in a random sample of 10 one-square-kilometer plots of land.(a) What
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 summer, including clothes and carry-on baggage.But passengers vary, and the FAA did not specify a
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 standard deviation 0.75 in the population of all cars that enter at this interchange during rush
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 distribution of losses is strongly right-skewed: many policies have $0 loss, but a few have large losses. An
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 cannot be Normal, because a count takes only whole-number values. An inspector studies a random sample
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 scores.Suppose that you do this many, many times. Which of the following are the mean and standard deviation of
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 of x– is approximately Normal.(c) To ensure that we can generalize the results to a larger
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 weight at birth was x– = 810 grams. This sample mean is an unbiased estimator of the mean weight m in
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 we look at more and more bulbs, their average burnout time gets ever closer to the mean m for all
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 reports that 9 of these eggs had salmonella contamination.Unknown to the producer, 3% of all eggs
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 graph above, there is a dot at approximately 2750. Explain what this value represents.
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 sampling distribution of the sample range.
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 sampling distribution of p^ ?Justify your answer.(b) Find the standard deviation of the sampling
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 want to be sure that passengers do not bring illegal items into the country. But they do not have time
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 standard deviation 15.(a) What is the probability that a randomly chosen individual has a WAIS score
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 is inspected, the number of moths in each trap is recorded, and the mean number of moths is
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 election.Which of the following statements is true about the boldface numbers?(a) 72% is a
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 of voters who favor a new law banning smoking in public buildings. The effect of this increase is
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 Normal approximation to the sampling distribution of p^ ?(a) 0.01 (b) 0.09 (c) 0.85 (d) 0.975 (e)
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 any population).(b) if the population is Normally distributed and the sample size is reasonably
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 3%of the undergraduates is taken. Each sample is used to estimate the proportion p of all students at
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 sampling distribution of the sample mean would be multiplied by(a) !2. (b) 1•!2. (c) 2. (d) 1/2. (e)
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. Suppose that(unknown to you) 55% of all undergraduates favor eliminating the carnival. If you took a very
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 increases.(b) The standard deviation of the sampling distribution is a measure of the variability of the sample
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 deviation 0.1 ounce. Assume that the machine is working properly. If four bottles are randomly
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 week is $80. If it comes up tails, your pay for the week is $40. You work for the library for 100
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 histogram.Which statistic would provide the best estimate of the parameter?Justify your answer. A B C
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 households pay a base rate for low-speed access, but some pay much more for faster connections. A
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 of 300 children. Find the probability that more than 20% of the sample are from poverty-level
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 any existed), what would be the maximum possible length of the right-side “whisker”?(a) 33 (b) 35
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 least one tail in four tosses of a coin is(a) 0.2500. (c) 0.6875. (e) 0.0625.(b) 0.3125. (d) 0.9375.
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 population for a market research study. The distribution of the sample mean of IQ scores is(a)
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 determine the number of correct answers that Jason gets. One correct way to use a table of random
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 entries 95592 94007 69769 33547 72450 16632 81194 14873 The first three students in your sample have
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 that a certain number of the bags will be underfilled, so the company will replace for free the 5%
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 commercial.Each subject will be shown one of the three versions and then asked about her attitude
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 infection and failure occur together 1% of the time. What is the probability that the operation is
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 all 50 states and the District of Columbia, and a regression analysis was conducted.The resulting
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 symmetric.(e) You can’t say, because the distribution isn’t Normal.
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 median and the standard deviation(d) The median and the interquartile range(e) The mean and the range
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) The height is generally 60% of a child’s weight.(b) About 60% of the time, age will accurately
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 randomly assigned to each of the three fertilizers.The treatment, experimental unit, and response
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 represents the approximate probability of obtaining a sample of 100 adults
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 questions correct as the average student.(c) It means that your grade was 2 points higher than the
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 118 18 116 252 Total 247 33 233 513 What is the probability that a randomly selected calf was born
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 mean weight of the packing material is 0.5 pounds with a standard deviation of 0.1 pounds, and the mean
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 statement“This ticket is not a winner.” Monetary prizes can be redeemed for groceries at the store. Here is 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 relative frequency graph is shown below from data collected over the past year. According to the graph,
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 and classifies them according to whether or not they take omega-3 fish oil. She also obtains their
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 group. The ethnic groups were Hawaiian, Hawaiian-White, Hawaiian-Chinese, and White.Suppose that a
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 eruptions more often than every 17 years.) There are so many cicadas that their dead bodies can serve as
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 from the library.(a) What is the probability that the total number of pages is fewer than 25,000? Show
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 them to the weather. Here are some of the variables recorded: type of wood (yellow poplar, pine,
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 or male); age(years); race (Asian, black, white, or other); smoker(yes or no); systolic blood
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 class.Gender Hand Height (in.)Homework time (min)Favorite music Pocket change (cents)F L 65 200
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 were opened in a recent year Roller coaster Type Height (ft) Design Speed (mph)Duration (s)Wild
Ranking colleges Popular magazines rank colleges and universities on their “academic quality” in serving undergraduate students. Describe two categorical variables and two quantitative variables that you might record for each institution.
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 student.At the Census Bureau Web site www.census.gov, you can view detailed data collected by the
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) None of these.At the Census Bureau Web site www.census.gov, you can view detailed data collected by
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 2007.Here is the distribution of colors for vehicles sold in North America in 2011.8 Color Percent of
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 Other ??(a) What percent of spam would fall in the “Other”category?(b) Display these data in a bar
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 Sunday 7374 Monday 11,704 Tuesday 13,169 Wednesday 13,038 Thursday 13,013 Friday 12,664 Saturday 8459(a)
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; suicide, 4559; cancer, 1594; heart disease, 984; congenital defects, 401.11(a) Make a bar graph to
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 Mexican? Puerto Rican?Percent Distribution of Hispanics by Type: 2010 Mexican Puerto Rican Cuban Central
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 plan to major in several discipline areas.13 About what percent of first-year students plan to major
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 Bought music online 12 to 17 years 24%18 to 24 years 21%25 to 34 years 20%35 to 44 years 16%45 to 54
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 44 years 68%45 to 54 years 60%55 to 64 years 47%65 to 74 years 32%75 years and over 20%(a) Display
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 Car Cycle Mode of transport STATE COLLEGE BUS SERVICE STATE COLLEGE BUS SERVICE Key:= 1 Cycler= 2
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 1 Week 2 Week 3 Week 4 Representative cholesterol point drop(a) How is this graph misleading?(b)
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. People who use a recycled product may have different opinions from those who don’t use it. Here are
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 Student does not smoke 1168 1823 1380 Student smokes 188 416 400(a) How many students are described
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 experience with the product, find the conditional distributions of opinion (the response variable)
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 relationship between the smoking behaviors of students and their parents in a few sentences.
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 Europe. Write a few sentences comparing the two distributions.White/pearl 30 25 20 15 10 50 Percent
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 cars (%) SUVs, trucks, vans (%)Black 22 13 Silver 16 16 White pearl 14 1 Gray 12 13 White 11 25 Blue
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. Respondents were also asked whether they belonged to an environmental organization (like the Sierra
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 about four years. All subjects were free of heart disease at the beginning of the study. The
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 of females.(b) the marginal distribution of gender.(c) the marginal distribution of opinion about
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 previous exercise is part of(a) the marginal distribution of gender.(b) the marginal distribution of
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 Mavericks scored at least 100 points.100 or more points Fewer than 100 points Total Win 43 14 57 Loss 4
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 If there is no association between gender and handedness for the members of the sample, which of the

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