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Understandable Statistics Concepts And Methods 13th Edition Charles Henry Brase, Corrinne Pellillo Brase - Solutions

Stocks: Retail and Utility How profitable are different sectors of the stock market? One way to answer such a question is to examine profit as a percentage of stockholder equity. A random sample of 32 retail stocks was studied for x1, profit as a percentage of stockholder equity. The result was x1
Wildlife: Wolves A random sample of 17 wolf litters in Ontario, Canada, gave an average of x1 5 4.9 wolf pups per litter, with estimated sample standard deviation s1 51.0. Another random sample of 6 wolf litters in Finland gave an average of x2 5 2.8 wolf pups per litter, with sample standard
Survey Response: Validity A study was conducted to determine accuracy of answers to questions from surveys. In the study, the question “Are you a registered voter?” was considered. Accuracy of response was confirmed by a check of city voting records. Two methods of survey were used: a
Survey Response: Validity From public records, individuals were identified as having been charged with drunken driving not less than 6 months or more than 12 months from the starting date of the study.Two random samples from this group were studied.In the first sample of 30 individuals, the
Expand Your Knowledge: Two Confidence Intervals What happens if we want several confidence intervals to hold at the same time (concurrently)? Do we still have the same level of confidence we had for each individual interval?(a) Suppose we have two independent random variables x1 and x2 with
Compute the sample size to be used for estimating a proportion p when we have no estimate for p.AppendixLO1
Compute the sample size to be used for estimating a proportion p when we have an estimate for p.AppendixLO1
Compute and interpret confidence intervals for p.AppendixLO1
Compute the maximal margin of error for proportions using a given level of confidence.AppendixLO1
Expand Your Knowledge: Alternate Method for Confidence Intervals When s is unknown and the sample is of size n $ 30, there are two methods for computing confidence intervals for m.Method 1: Use the Student’s t distribution with d.f.5n 2 1.This is the method used in the text. It is widely employed
Baseball: Home Run Percentage The home run percentage is the number of home runs per 100 times at bat in a baseball game. A random sample of 43 professional baseball players gave the following data for home run percentages (Reference: The Baseball Encyclopedia, Macmillan).1.6 2.4 1.2 6.6 2.3 0.0
Examine the confidence intervals in parts (b) and (c). How would you describe these stocks at the time the sample was taken?(e) Check Requirements In previous problems, we assumed the x distribution was normal or approximately normal. Do we need to make such an assumption in this problem? Why or
Finance: P/E Ratio The price of a share of stock divided by a company’s estimated future earnings per share is called the P/E ratio. High P/E ratios usually indicate “growth” stocks, or maybe stocks that are simply overpriced. Low P/E ratios indicate “value’’stocks or bargain stocks. A
Crime Rate: Denver The following data represent crime rates per 1000 population for a random sample of 46 Denver neighborhoods (Reference: The Piton Foundation, Denver, Colorado).63.2 36.3 26.2 53.2 65.3 32.0 65.0 66.3 68.9 35.2 25.1 32.5 54.0 42.4 77.5 123.2 66.3 92.7 56.9 77.1 27.5 69.2 73.8 71.5
Hospitals: Charity Care What percentage of hospitals provide at least some charity care? The following problem is based on information taken from State Health Care Data: Utilization, Spending, and Characteristics (American Medical Association).Based on a random sample of hospital reports from
Diagnostic Tests: Total Calcium Over the past several months, an adult patient has been treated for tetany (severe muscle spasms). This condition is associated with an average total calcium level below 6 mg/dl (Reference: Manual of Laboratory and Diagnostic Tests by F. Fischbach). Recently, the
Franchise: Candy Store Do you want to own your own candy store? With some interest in running your own business and a decent credit rating, you can probably get a bank loan on startup costs for franchises such as Candy Express, The Fudge Company, Karmel Corn, and Rocky Mountain Chocolate Factory.
Wildlife: Mountain Lions How much do wild mountain lions weigh? The 77th Annual Report of the New Mexico Department of Game and Fish, edited by Bill Montoya, gave the following information. Adult wild mountain lions (18 months or older) captured and released for the first time in the San Andres
Camping: Cost of a Sleeping Bag How much does a sleeping bag cost? Let’s say you want a sleeping bag that should keep you warm in temperatures from 208F to 458F. A random sample of prices ($) for sleeping bags in this temperature range was taken from Backpacker Magazine: Gear Guide (Vol. 25,
Archaeology: Tree Rings At Burnt Mesa Pueblo, the method of tree-ring dating gave the following years a.d. for an archaeological excavation site (Bandelier Archaeological Excavation Project: Summer 1990 Excavations at Burnt Mesa Pueblo, edited by Kohler, Washington State University):1189 1271 1267
Basic Computation: Confidence Interval A random sample of size 81 has sample mean 20 and sample standard deviation 3.(a) Check Requirements Is it appropriate to use a Student’s t distribution to compute a confidence interval for the population mean m? Explain.(b) Find a 95% confidence interval
Basic Computation: Confidence Interval Suppose x has a mound-shaped symmetric distribution. A random sample of size 16 has sample mean 10 and sample standard deviation 2.(a) Check Requirements Is it appropriate to use a Student’s t distribution to compute a confidence interval for the population
Critical Thinking Cleo and Phillipe each gathered a random sample of 100 individuals to compute a 95%confidence interval for the average hourly income of citizens in their city. Suppose Cleo’s data has a sample standard deviation of $1.20 and Phillipe’s data has a sample standard deviation of
Critical Thinking Cleo and Phillipe each gathered a random sample of 100 individuals to compute a 95%confidence interval for the average hourly income of citizens in their city. Cleo ended up with a margin of error of $0.75 for their computation. Do you expect Phillipe to have the same margin of
Critical Thinking Lorraine was in a hurry when she computed a confidence interval for m. Because s was not known, she used a Student’s t distribution.However, she accidentally used degrees of freedom n instead of n 21. Was her confidence interval longer or shorter than one found using the correct
Critical Thinking Lorraine computed a confidence interval for m based on a sample of size 41. Since she did not know s , she used s in her calculations. Lorraine used the normal distribution for the confidence interval instead of a Student’s t distribution. Was her interval longer or shorter than
Critical Thinking Consider a 90% confidence interval for m. Assume s is not known. For which sample size, n 510 or n 5 20, is the confidence interval longer?AppendixLO1
Critical Thinking Consider a 90% confidence interval for m. Assume s is not known. For which sample size, n 510 or n 5 20, is the critical value tc larger?AppendixLO1
Statistical Literacy As the degrees of freedom increase, what distribution does the Student’s t distribution become more like?AppendixLO1
Statistical Literacy Student’s t distributions are symmetric about a value of t. What is that t value?AppendixLO1
Use Table 6 of Appendix II to find tc for a 0.95 confidence level when the sample size is 12.AppendixLO1
Use Table 6 of Appendix II to find tc for a 0.90 confidence level when the sample size is 22.AppendixLO1
Use Table 6 of Appendix II to find tc for a 0.99 confidence level when the sample size is 4.AppendixLO1
Use Table 6 of Appendix II to find tc for a 0.95 confidence level when the sample size is 18.AppendixLO1
Compute and interpret confidence intervals for m when s is unknown.AppendixLO1
Find critical values using degrees of freedom and confidence levels.AppendixLO1
Explain degrees of freedom and Student’s t distributions.AppendixLO1
Ballooning: Air Temperature How hot is the air in the top (crown) of a hot air balloon? Information from Ballooning: The Complete Guide to Riding the Winds by Wirth and Young (Random House) claims that the air in the crown should be an average of 1008C for a balloon to be in a state of equilibrium.
Profits: Retail Jobs and productivity! How do retail stores rate? One way to answer this question is to examine annual profits per employee. The following data give annual profits per employee (in units of one thousand dollars per employee) for companies in retail sales. (See reference in Problem
Profits: Banks Jobs and productivity! How do banks rate? One way to answer this question is to examine annual profits per employee. Forbes Top Companies, edited by J. T. Davis (John Wiley &Sons), gave the following data about annual profits per employee (in units of one thousand dollars per
Ecology: Sand Dunes At wind speeds above 1000 centimeters per second (cm/sec), significant sandmoving events begin to occur. Wind speeds below 1000 cm/sec deposit sand, and wind speeds above 1000 cm/sec move sand to new locations. The cyclic nature of wind and moving sand determines the shape and
Confidence Intervals: Sample Size A random sample is drawn from a population with s 512. The sample mean is 30.(a) Compute a 95% confidence interval for m based on a sample of size 49. What is the value of the margin of error?(b) Compute a 95% confidence interval for m based on a sample of size
Confidence Intervals: Values of s A random sample of size 36 is drawn from an x distribution. The sample mean is 100.(a) Suppose the x distribution has s 5 30. Compute a 90% confidence interval for m. What is the value of the margin of error?(b) Suppose the x distribution has s 5 20. Compute a 90%
FBI Report: Larceny Thirty small communities in Connecticut (population near 10,000 each) gave an average of x 5138.5 reported cases of larceny per year. Assume that s is known to be 42.6 cases per year(Reference: Crime in the United States, Federal Bureau of Investigation).(a) Find a 90%
Agriculture: Watermelon What price do farmers get for their watermelon crops? In the third week of July, a random sample of 40 farming regions gave a sample mean of x 5$6.88 per 100 pounds of watermelon.Assume that s is known to be $1.92 per 100 pounds(Reference: Agricultural Statistics, U.S.
Diagnostic Tests: Plasma Volume Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. (Reference: See Problem 21.)Suppose
Diagnostic Tests: Uric Acid Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advance indication of illness such as gout, leukemia, or lymphoma(Reference: Manual of Laboratory and Diagnostic Tests by F. Fischbach). Over a period of months, an adult male
Zoology: Hummingbirds Allen’s hummingbird(Selasphorus sasin) has been studied by zoologist Bill Alther (Reference: Hummingbirds by K. Long and W.Alther). A small group of 15 Allen’s hummingbirds has been under study in Arizona. The average weight for these birds is x 5 3.15 grams. Based on
Basic Computation: Sample Size Suppose x has a normal distribution with s 51.2.(a) Find the minimal sample size required so that for a 90% confidence interval, the maximal margin of error is E 5 0.5.(b) Check Requirements Based on this sample size and the x distribution, can we assume that the x
Basic Computation: Sample Size Suppose x has a mound-shaped distribution with s 5 3.(a) Find the minimal sample size required so that for a 95% confidence interval, the maximal margin of error is E 5 0.4.(b) Check Requirements Based on this sample size, can we assume that the x distribution is
Basic Computation: Confidence Interval Suppose x has a mound-shaped distribution with s 5 9. A random sample of size 36 has sample mean 20.(a) Check Requirements Is it appropriate to use a normal distribution to compute a confidence interval for the population mean m? Explain.(b) Find a 95%
Basic Computation: Confidence Interval Suppose x has a normal distribution with s 5 6. A random sample of size 16 has sample mean 50.(a) Check Requirements Is it appropriate to use a normal distribution to compute a confidence interval for the population mean m? Explain.(b) Find a 90% confidence
Critical Thinking Shawna computed a 90%confidence interval for the average weight (in lbs)of adult citizens in their country, using a known population standard deviation s . The confidence interval was 124 , m , 167. Suppose Shawna decided to increase the sample size. What do you think would happen
Critical Thinking Shawna computed a 90%confidence interval for the average weight (in lbs) of adult citizens in their country. The confidence interval was 124 , m , 167. If Shawna instead decided to compute a 95% confidence interval, what would happen to the confidence interval? Explain.AppendixLO1
Critical Thinking Chance wants to compute a confidence interval for the average income of people in the United States. Unfortunately, the survey they distributed only produced a random sample of 20 individuals. Historically, the distribution of income amongst citizens in the United States is known
Critical Thinking Kalia computed a 90% confidence interval for m from a specific random sample of weights for newborn infants. The confidence interval was 5 , m , 10. They claim that a newborn infant has a 90% chance of being within the weight of 5 to 10 lbs.What is wrong with the claim?AppendixLO1
Critical Thinking Kalia computed a 90% confidence interval for m from a specific random sample of weights for newborn infants. The confidence interval was 5 , m , 10. They claim that the probability that the sample mean x is in this interval is 0.90. What is wrong with the claim?AppendixLO1
Critical Thinking Sam computed a 90% confidence interval for m from a specific random sample of size n. He claims that at the 90% confidence level, his confidence interval contains m. Is his claim correct?Explain.AppendixLO1
Critical Thinking Sam computed a 95% confidence interval for m from a specific random sample. His confidence interval was 10.1 , m , 12.2. He claims that the probability that m is in this interval is 0.95.What is wrong with his claim?AppendixLO1
Statistical Literacy For the same random sample, when the confidence level c is reduced, the confidence interval for m becomes shorter.AppendixLO1
Statistical Literacy If the sample mean x of a random sample from an x distribution is relatively small, then the confidence interval for m will be relatively short.AppendixLO1
Statistical Literacy If the original x distribution has a relatively small standard deviation, the confidence interval for m will be relatively short.AppendixLO1
Statistical Literacy A larger sample size produces a longer confidence interval for m.AppendixLO1
Statistical Literacy Every random sample of the same size from a given population will produce exactly the same confidence interval for m.AppendixLO1
Statistical Literacy Consider a random sample of size n from an x distribution. For such a sample, the margin of error for estimating m is the magnitude of the difference between x and m.AppendixLO1
Statistical Literacy The point estimate for the population mean m of an x distribution is x , computed from a random sample of the x distribution.AppendixLO1
Statistical Literacy The value zc is a value from the standard normal distribution such that P(2zc , x , zc ) 5c.AppendixLO1
Compute the sample size to be used for estimating a mean m.AppendixLO1
Compute and interpret the results of confidence intervals for m when s is known.AppendixLO1
Find the critical value corresponding to a given confidence level.AppendixLO1
Explain the meanings of confidence level, error of estimate, and critical value.AppendixLO1
How can you use confidence intervals to estimate differences between population parameters?AppendixLO1
How do you estimate the proportion p of successes in a binomial experiment? How does the normal approximation fit into this process?AppendixLO1
How can you use confidence intervals to construct estimates from sample data? (SECTION 7.2)AppendixLO1
How do you determine an appropriate sample size at the beginning stage of a statistical project? (SECTION 7.1)AppendixLO1
How do you calculate the level confidence when estimating a population parameter? (SECTION 7.1)AppendixLO1
What assumptions are necessary to ensure the results of confidence interval are valid? (SECTION 7.1)AppendixLO1
How do you estimate the expected value of a random variable using a confidence interval? (SECTION 7.1)AppendixLO1
Law: Corporation Lawsuits Many people say the civil justice system is overburdened. Many cases center on suits involving businesses. The following data are based on a Wall Street Journal report. Researchers conducted a study of lawsuits involving 1908 businesses ranked in the Fortune 1000 over a
Agriculture: Apple Trees The following data represent trunk circumferences (in mm) for a random sample of 60 4-year-old apple trees at East Malling Agriculture Research Station in England (Reference:S. C. Pearce, University of Kent at Canterbury). Note:These data are also available for download at
Law Enforcement: DUI Driving under the influence of alcohol (DUI) is a serious offense. The following data give the ages of a random sample of 50 drivers arrested while driving under the influence of alcohol.This distribution is based on the age distribution of DUI arrests given in the Statistical
IRS: Tax Returns Almost everyone files (or will someday file) a federal income tax return. A research poll for TurboTax (a computer software package to aid in tax-return preparation) asked what aspect of filing a return people thought to be the most difficult.The results showed that 43% of the
Focus Problem: Pandemic Graphs Solve the focus problem at the beginning of this chapter.AppendixLO1
Expand Your Knowledge How are dotplots and stemand-leaf displays similar? How are they different?AppendixLO1
Critical Thinking Describe how data outliers might be revealed in histograms and stem-and-leaf plots.AppendixLO1
Critical Thinking A consumer interest group is tracking the percentage of household income spent on gasoline over the past 30 years. Which graphical display would be more useful, a histogram or a timeseries graph? Why?AppendixLO1
Critical Thinking Consider these types of graphs:histogram, bar graph, Pareto chart, pie chart, stem-andleaf display.(a) Which are suitable for qualitative data?(b) Which are suitable for quantitative data?AppendixLO1
Health: Cigarette Smoke Use the data in Table 2-16 to make a stem-and-leaf display for milligrams of nicotine per cigarette smoked. In this case, truncate the measurements at the tenths position and use two lines per stem (see Problem 7, part a).AppendixLO1
Health: Cigarette Smoke Use the data in Table 2-16 to make a stem-and-leaf display for milligrams of carbon monoxide per cigarette smoked. Are there any outliers?AppendixLO1
Health: Cigarette Smoke Use the data in Table 2-16 to make a stem-and-leaf display for milligrams of tar per cigarette smoked. Are there any outliers?AppendixLO1
Expand Your Knowledge: Split Stem The Boston Marathon is the oldest and best-known U.S. marathon.It covers a route from Hopkinton, Massachusetts, to downtown Boston. The distance is approximately 26 miles. The Boston Marathon web site has a wealth of information about the history of the race. In
Health Care: Hospitals Using the number of hospitals per state listed in the table in Problem 5, make a stem-and-leaf display for the number of community hospitals per state. Which states have an unusually high number of hospitals?AppendixLO1
Ecology: Habitat Wetlands offer a diversity of benefits. They provide a habitat for wildlife, spawning grounds for U.S. commercial fish, and renewable timber resources. In the last 200 years, the United States has lost more than half its wetlands.Environmental Almanac gives the percentage of
Cowboys: Longevity How long did real cowboys live? One answer may be found in the book The Last Cowboys by Connie Brooks (University of New Mexico Press). This delightful book presents a thoughtful sociological study of cowboys in west Texas and southeastern New Mexico around the year 1890.A sample
Texting: Messages With the age of cellphones, adults have relied on the use of text messages as a fast and efficient way to communicate. This has led many researchers to believe that more adults spend their time sending text messages rather than talking on their phone. A sample of 22 random adults
Movies: Reviews Recently, people have a tendency to check a movie’s review online before deciding whether watching the movie is worth the time and money. One of the most prominent web sites for movie reviews is Rotten Tomatoes, which is well-known for scoring movies by collecting information from
Compare a stem-and-leaf display to a histogram.AppendixLO1
Visualize a data distribution using a stem-and-leaf display.AppendixLO1
Construct a stem-and-leaf display from raw data.AppendixLO1
feel safer with the technologies;AppendixLO1

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