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fundamentals of statistics
Questions and Answers of
Fundamentals Of Statistics
2 How do discrete and continuous random variables differ?
1 What is a random variable?
Refer to Example 2 . A second random variable of interest is the amount x of pesticide (in milligrams per liter) found in the monthly sample of discharge waters from the same chemical company. What
Suppose the Environmental Protection Agency (EPA)takes readings once a month on the amount of pesticide in the discharge water of a chemical company. If the amount of pesticide exceeds the maximum
A panel of 10 experts for the Wine Spectator (a national publication) is asked to taste a new white wine and assign it a rating of 0, 1, 2, or 3. A score is then obtained by adding together the
Refer to the reaction data presented in Table 1 . Consider the straight-line model E1y2 = b0 + b1x, where y = reaction time (in seconds) and x = percent of drug received.a. Use the method of least
Use a random-number table or random-number generator to generate a random sample of 30 distinct values from the set of integers 1 to
Focus Problem: Fireflies Suppose you are conducting a study to compare firefly populations exposed to normal daylight/darkness conditions with firefly populations exposed to continuous light (24
Census: Web Site Census and You, a publication of the Census Bureau, indicates that “Wherever your Web journey ends up, it should start at the Census Bureau’s site.” Visit the Brase/Brase
Student Life: Data Collection Project Make a statistical profile of your own statistics class. Items of interest might be(a) Height, age, gender, pulse, number of siblings, marital status(b) Number
General: Experiment How would you use a completely randomized experiment in each of the following settings? Is a placebo being used or not? Be specific and give details.(a) A charitable nonprofit
General: Gathering Data Which technique for gathering data (observational study or experiment) do you think was used in the following studies? Explain.(a) The U.S. Census Bureau tracks population
General: Type of Sampling Categorize the type of sampling (simple random, stratified, systematic, cluster, or convenience) used in each of the following situations.(a) To conduct a preelection
Simulation: TV Habits One cable station knows that approximately 30% of its viewers have TIVO and can easily skip over advertising breaks. You are to design a simulation of how a random sample of
Statistical Literacy You are conducting a study of students doing work-study jobs on your campus. Among the questions on the survey instrument are:A. How many hours are you scheduled to work each
Instructions for doing this using the TI-84Plus/TI-83Plus/TI-nspire (with TI-84 Plus keypad), Excel 2007, Minitab, or SPSS are given in Using Technology at the end of this chapter. Generate five such
What does it mean to say that we are going to use a sample to draw an inference about a population? Why is a random sample so important for this process? If we wanted a random sample of students in
In your own words, explain the differences among the following sampling techniques:simple random sample, stratified sample, systematic sample, cluster sample, multistage sample, and convenience
Critical Thinking Sudoku is a puzzle consisting of squares arranged in 9 rows and 9 columns. The 81 squares are further divided into nine square boxes.The object is to fill in the squares with
Simulate the results of tossing a fair die 18 times.Repeat the simulation. Are the results the same? Did you expect them to be the same? Why or why not?Do there appear to be equal numbers of outcomes
Critical Thinking Alisha wants to do a statistical study to determine how long it takes people to complete a Sudoku puzzle (see Problem 1 for a description of the puzzle). Her plan is as
A college has 5000 students, and the registrar wishes to use a random sample of 50 students to examine credit hour enrollment for this semester. Write a brief description of how a random sample can
Suppose you are working for the regional water commissioner.You have been asked to submit a brief report about the pH level in ground water in the west Texas region. Write such a report and include
Look at the stem-and-leaf plot. Are there any unusually high or low pH levels in this sample of wells?How many wells are neutral (pH of 7)? LO.1
Look at the ogive. What percent of the wells have a pH less than 8.15? Suppose a certain crop can tolerate irrigation water with a pH between 7.35 and 8.55.What percent of the wells could be used for
Look at the histogram. Is the pH distribution for these wells symmetric or skewed? Are lower or higher values more common? LO.1
Make a box-and-whisker plot. Find the interquartile range.Interpretation Wow! In Problems 5–13 you constructed a lot of information regarding the pH of west Texas ground water based on sample data.
Compute a 75% Chebyshev interval centered on the mean. LO.1
(a) Verify that and .(b) Compute the sample variance, sample standard deviation, and coefficient of variation for the given data. Is the sample standard deviation small relative to the mean pH? LO.1
Compute the range, mean, median, and mode for the given data. LO.1
Make an ogive using five classes. LO.1
Make a frequency table, histogram, and relativefrequency histogram using five classes. Recall that for decimal data, we “clear the decimal” to determine classes for whole-number data and then
Make a stem-and-leaf display. Use five lines per stem so that leaf values 0 and 1 are on one line, 2 and 3 are on the next line, 4 and 5 are on the next, 6 and 7 are on the next, and 8 and 9 are on
Is the given data nominal, ordinal, interval, or ratio?Explain. LO.1
Write a brief description in which you outline how you would obtain a random sample of 102 west Texas water wells. Explain how random numbers would be used in the selection process. LO.1
What is Chebyshev’s theorem? Suppose you have a friend who knows very little about statistics. Write a paragraph or two in which you describe Chebyshev’s theorem for your friend. Keep the
Why is the coefficient of variation important? What do we mean when we say that the coefficient of variation has no units? What advantage can there be in having no units? Why is relative size
Why do we need to study the variation of a collection of data? Why isn’t the average by itself adequate? We have studied three ways to measure variation.The range, the standard deviation, and, to a
An average is an attempt to summarize a collection of data into just one number.Discuss how the mean, median, and mode all represent averages in this context.Also discuss the differences among these
Auto Insurance: Interpret Graphs Consumer Reports rated automobile insurance companies and listed annual premiums for top-rated companies in several states. Figure 3-9 shows box-and-whisker plots for
Sociology: High School Dropouts What percentage of the general U.S. population are high school dropouts? The Statistical Abstract of the United States, 120th Edition, gives the percentage of high
Sociology: College Graduates What percentage of the general U.S. population have bachelor’s degrees? The Statistical Abstract of the United States, 120th Edition, gives the percentage of
Discuss the locations of the medians, the locations of the middle halves of the data banks, and the distances from Q1 and Q3 to the extreme values. LO.1
Health Care: Staff Another survey was done at Center Hospital to determine how long (in months) clerical staff had been in their current positions. The responses (in months) of 20 clerical staff
Health Care: Nurses At Center Hospital there is some concern about the high turnover of nurses. A survey was done to determine how long (in months) nurses had been in their current positions. The
Basic Computation: Five-Number Summary, Interquartile Range Consider the following ordered data:(a) Find the low, Q1, median, Q3 high.(b) Find the interquartile range.(c) Make a box-and-whisker
Basic Computation: Five-Number Summary, Interquartile Range Consider the following ordered data:(a) Find the low, Q1, median, Q3, high.(b) Find the interquartile range.(c) Make a box-and-whisker
Critical Thinking Clayton and Timothy took different sections of Introduction to Economics. Each section had a different final exam. Timothy scored 83 out of 100 and had a percentile rank in his
Critical Thinking The town of Butler, Nebraska, decided to give a teachercompetency exam and defined the passing scores to be those in the 70th percentile or higher. The raw test scores ranged from 0
Statistical Literacy One standard for admission to Redfield College is that the student rank in the upper quartile of his or her graduating high school class.What is the minimal percentile rank of a
Statistical Literacy Angela took a general aptitude test and scored in the 82nd percentile for aptitude in accounting. What percentage of the scores were at or below her score? What percentage were
Archaeology: Ireland The Hill of Tara in Ireland is a place of great archaeological importance. This region has been occupied by people for more than 4000 years. Geomagnetic surveys detect subsurface
Space Shuttle: Epoxy Kevlar epoxy is a material used on the NASA space shuttles.Strands of this epoxy were tested at the 90% breaking strength. The following data represent time to failure (in hours)
Investing: Stocks and Bonds Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for Vanguard Total Stock Index (all stocks). Let
Basic Computation: Coefficient of Variation, Chebyshev Interval Consider population data with and .(a) Compute the coefficient of variation.(b) Compute an 88.9% Chebyshev interval around the
Basic Computation: Coefficient of Variation, Chebyshev Interval Consider sample data with and .(a) Compute the coefficient of variation.(b) Compute a 75% Chebyshev interval around the sample mean.
Basic Computation: Variance, Standard Deviation Given the sample data x: 23 17 15 30 25(a) Find the range.(b) Verify that and .(c) Use the results of part (b) and appropriate computation formulas to
Critical Thinking: Outliers One indicator of an outlier is that an observation is more than 2.5 standard deviations from the mean. Consider the data value 80.(a) If a data set has mean 70 and
Critical Thinking: Data Transformation In this problem, we explore the effect on the standard deviation of multiplying each data value in a data set by the same constant. Consider the data set 5, 9,
Critical Thinking: Data Transformation In this problem, we explore the effect on the standard deviation of adding the same constant to each data value in a data set. Consider the data set 5, 9, 10,
Critical Thinking Each of the following data sets has a mean of .(i) 8 9 10 11 12 (ii) 7 9 10 11 13 (iii) 7 8 10 12 13(a) Without doing any computations, order the data sets according to increasing
Critical Thinking Consider two data sets with equal sample standard deviations.The first data set has 20 data values that are not all equal, and the second has 50 data values that are not all equal.
Critical Thinking For a given data set in which not all data values are equal, which value is smaller, s or s? Explain. LO.1
Basic Computation: Range, Standard Deviation Consider the data set 1 2 3 4 5(a) Find the range.(b) Use the defining formula to compute the sample standard deviation s.(c) Use the defining formula to
Basic Computation: Range, Standard Deviation Consider the data set 2 3 4 5 6(a) Find the range.(b) Use the defining formula to compute the sample standard deviation s.(c) Use the defining formula to
Statistical Literacy What symbol is used for the standard deviation when it is a sample statistic? What symbol is used for the standard deviation when it is a population parameter? LO.1
Statistical Literacy When computing the standard deviation, does it matter whether the data are sample data or data comprising the entire population?Explain. LO.1
Statistical Literacy What is the relationship between the variance and the standard deviation for a sample data set? LO.1
Statistical Literacy Which average—mean, median, or mode—is associated with the standard deviation? LO.1
Expand Your Knowledge: Geometric Mean When data consist of percentages, ratios, growth rates, or other rates of change, the geometric mean is a useful measure of central tendency. For n data values,
Expand Your Knowledge: Harmonic Mean When data consist of rates of change, such as speeds, the harmonic mean is an appropriate measure of central tendency. For n data values, Suppose you drive 60
EPA: Wetlands Where does all the water go? According to the Environmental Protection Agency (EPA), in a typical wetland environment, 38% of the water is outflow; 47% is seepage; 7% evaporates; and 8%
Merit Pay Scale: Weighted Average At General Hospital, nurses are given performance evaluations to determine eligibility for merit pay raises. The supervisor rates the nurses on a scale of 1 to 10
Grades: Weighted Average In your biology class, your final grade is based on several things: a lab score, scores on two major tests, and your score on the final exam. There are 100 points available
Basic Computation: Weighted Average Find the weighted average of a data set where LO.1
Basic Computation: Weighted Average Find the weighted average of a data set where LO.1
Leisure: Maui Vacation How expensive is Maui? If you want a vacation rental condominium (up to four people), visit the Brase/Brase statistics site at http://www.cengage.com/statistics/brase, find the
Football: Age of Professional Players How old are professional football players?The 11th Edition of The Pro Football Encyclopedia gave the following information.Random sample of pro football player
Medical: Injuries The Grand Canyon and the Colorado River are beautiful, rugged, and sometimes dangerous. Thomas Myers is a physician at the park clinic in Grand Canyon Village. Dr. Myers has
Ecology: Wolf Packs How large is a wolf pack? The following information is from a random sample of winter wolf packs in regions of Alaska, Minnesota, Michigan, Wisconsin, Canada, and Finland (Source:
Environmental Studies: Death Valley How hot does it get in Death Valley? The following data are taken from a study conducted by the National Park System, of which Death Valley is a unit. The ground
Critical Thinking Consider a data set of 15 distinct measurements with mean A and median B.(a) If the highest number were increased, what would be the effect on the median and mean? Explain.(b) If
Compute the mode, median, and mean.(c) Compare the results of parts (a) and (b). In general, how do you think the mode, median, and mean are affected when each data value in a set is multiplied by
Critical Thinking: Data Transformation In this problem, we explore the effect on the mean, median, and mode of multiplying each data value by the same number. Consider the data set 2, 2, 3, 6, 10.(a)
Critical Thinking: Data Transformation In this problem, we explore the effect on the mean, median, and mode of adding the same number to each data value.Consider the data set 2, 2, 3, 6, 10.(a)
Interpretation A job-performance evaluation form has these categories:Based on 15 client reviews, one employee had The employee was pleased that most clients had rated her as excellent. The
Critical Thinking Consider two data sets.(a) Suppose the number 20 is included as an additional data value in Set A.Compute for the new data set. Hint: . To compute for the new data set, add 20 to of
Critical Thinking Consider the numbers 2 3 4 5 5(a) Compute the mode, median, and mean.(b) If the numbers represent codes for the colors of T-shirts ordered from a catalog, which average(s) would
Critical Thinking Consider the following types of data that were obtained from a random sample of 49 credit card accounts. Identify all the averages (mean, median, or mode) that can be used to
Critical Thinking When a distribution is mound-shaped symmetrical, what is the general relationship among the values of the mean, median, and mode? LO.1
Critical Thinking If a data set has an even number of data, is it true or false that the median is never equal to a value in the data set? Explain. LO.1
Basic Computations Mean. Median, Mode Find the mean, median, and mode of the data set LO.1
Basic Computation: Mean, Median, Mode Find the mean, median, and mode of the data set LO.1
Basic Computation: Mean, Median, Mode Find the mean, median, and mode of the data set LO.1
Statistical Literacy What symbol is used for the arithmetic mean when it is a sample statistic? What symbol is used when the arithmetic mean is a population parameter? LO.1
Statistical Literacy Consider the mode, median, and mean. Which average represents the middle value of a data distribution? Which average represents the most frequent value of a distribution? Which
Use the software or method of your choice to make stem-and-leaf displays for each set of scores. If your software does not make stem-and-leaf displays, sort the data first and then make a
Use the same class boundaries for histograms of men’s and of women’s scores. How do the scores for the two groups compare? What general shape do the histograms follow? LO.1
Use the software or method of your choice to construct separate histograms for the men’s and women’s winning scores. Try 5, 7, and 10 classes for each. Which number of classes seems to be the
Go to the library and pick up a current issue of The Wall Street Journal, Newsweek, Time, USA Today, or other news medium. Examine each newspaper or magazine for graphs of the types discussed in this
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