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Understanding Basic Statistics 7th Edition Charles Henry Brase, Corrinne Pellillo Brase - Solutions

Statistical Literacy In order to fi nd the median of a data set, what do we do fi rst with the data?
Basic Computation: Mean, Median, Mode Find the mean, median, and mode of the data set 8 2 7 2 6
Basic Computation: Mean, Median, Mode Find the mean, median, and mode of the data set 10 12 20 15 20
Basic Computations Mean, Median, Mode Find the mean, median, and mode of the data set 8 2 7 2 6 5
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.
Critical Thinking When a distribution is mound-shaped symmetrical, what is the general relationship among the values of the mean, median, and mode?
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 make sense?(c) If the numbers represent one-way mileages for trails to different lakes, which
Critical Thinking Consider two data sets.Set A: n 5 5; x 5 10 Set B: n 5 50; x 5 10(a) Suppose the number 20 is included as an additional data value in Set A.Compute x for the new data set. Hint: x 5 nx. To compute x for the new data set, add 20 to x of the original data set and divide by 6.(b)
Interpretation A job-performance evaluation form has these categories:1 5 excellent; 2 5 good; 3 5 satisfactory; 4 5 poor; 5 5 unacceptable Based on 15 client reviews, one employee had median rating of 4; mode rating of 1 The employee was pleased that most clients had rated her as excellent. The
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 Service, of which Death Valley is a unit. The ground temperatures (F) were taken from May to November in the vicinity of Furnace Creek.146 152 168 174
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.cengagebrain.com, fi nd the link to Maui, and then search for accommodations. The Maui News gave the following costs in dollars per day
Basic Computation: Weighted Average Find the weighted average of a data set where 10 has a weight of 5; 20 has a weight of 3; 30 has a weight of 2
Basic Computation: Weighted Average Find the weighted average of a data set where 10 has a weight of 2; 20 has a weight of 3; 30 has a weight of 5
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, Geometric mean 5 n product of the n data values, assuming all data values are positive To fi nd the
Statistical Literacy Which average—mean, median, or mode—is associated with the standard deviation?
Statistical Literacy What is the relationship between the variance and the standard deviation for a sample data set?
Statistical Literacy When computing the standard deviation, does it matter whether the data are sample data or data comprising the entire population?Explain.
Critical Thinking For a given data set in which not all data values are equal, which value is smaller, s or s? Explain.
Critical Thinking Consider two data sets with equal sample standard deviations.The fi rst data set has 20 data values that are not all equal, and the second has 50 data values that are not all equal. For which data set is the difference between s and s greater? Explain. Hint: Consider the
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, 10, 11, 15.(a) Use the defi ning formula, the computation formula, or a calculator to compute s.(b)
Compute s.(c) Compare the results of parts (a) and (b). In general, how does the standard deviation change if each data value is multiplied by a constant c?(d) You recorded the weekly distances you bicycled in miles and computed the standard deviation to be s 5 3.1 miles. Your friend wants to know
Basic Computation: Variance, Standard Deviation Given the sample data x: 23 17 15 30 25(a) Find the range.(b) Verify that x 5 110 and x2 5 2568.(c) Use the results of part (b) and appropriate computation formulas to compute the sample variance s2 and sample standard deviation s.(d) Use the defi
Basic Computation: Coeffi cient of Variation, Chebyshev Interval Consider sample data with x 5 15 and s 5 3.(a) Compute the coeffi cient of variation.(b) Compute a 75% Chebyshev interval around the sample mean.
Basic Computation: Coeffi cient of Variation, Chebyshev Interval Consider population data with m 5 20 and s 5 2.(a) Compute the coeffi cient of variation.(b) Compute an 88.9% Chebyshev interval around the population mean.
Investing: Socially Responsible Mutual Funds Pax World Balanced is a highly respected, socially responsible mutual fund of stocks and bonds (see Viewpoint). Vanguard Balanced Index is another highly regarded fund that represents the entire U.S. stock and bond market (an index fund). The mean and
Medical: Physician Visits In some reports, the mean and coeffi cient of variation are given. For instance, in Statistical Abstract of the United States, 116th Edition, one report gives the average number of physician visits by males per year. The average reported is 2.2, and the reported coeffi
Grouped Data: Anthropology What was the age distribution of prehistoric Native Americans? Extensive anthropologic studies in the southwestern United States gave the following information about a prehistoric extended family group of 80 members on what is now the Navajo Reservation in northwestern
Grouped Data: Shoplifting What is the age distribution of adult shoplifters(21 years of age or older) in supermarkets? The following is based on information taken from the National Retail Federation. A random sample of 895 incidents of shoplifting gave the following age distribution: Age range
Grouped Data: Hours of Sleep per Day Alexander Borbely is a professor at the University of Zurich Medical School, where he is director of the sleep laboratory. The histogram in Figure 3-2 is based on information from his book Secrets of Sleep. The histogram displays hours of sleep per day for a
Grouped Data: Business Administration What are the big corporations doing with their wealth? One way to answer this question is to examine profi ts as percentage of assets. A random sample of 50 Fortune 500 companies gave the following information (Source: Based on information from Fortune 500,
Expand Your Knowledge: Moving Averages You do not need a lot of money to invest in a mutual fund. However, if you decide to put some money into an investment, you are usually advised to leave it in for (at least) several years.Why? Because good years tend to cancel out bad years, giving you a
Brain Teaser: Sum of Squares If you like mathematical puzzles or love algebra, try this! Otherwise, just trust that the computational formula for the sum of squares is correct. We have a sample of x values. The sample size is n. Fill in the details for the following steps. ( - )2 = - 27. x + 1 = x
Expand Your Knowledge: Stratifi ed Sampling and Students in Sixth Grade This is a technique to break down the variation of a random variable into useful components (called stratum) in order to decrease experimental variation and increase accuracy of results. It has been found that a more accurate
Expand Your Knowledge: Stratifi ed Sampling and Politics Three local districts are “swing” districts for an upcoming election on a contentious political issue. A survey will be conducted in which voters will be asked to rate their opinion regarding this issue on a scale of 0 (strongly oppose)to
Hint: see problem 28.(b) Suppose you took the appropriate random samples from each district and you got the following average political support measures (scale 0 to 10):x1 5 6.2, x2 5 3.1 x3 5 8.5. Compute your best estimate for the population mean m (scale 0 to 10) of voter support for the issue
Expand Your Knowledge: Stratifi ed Sampling, No Preliminary Study, Police Identifi cation Police are tested for their ability to correctly recognize and identify a suspect based on a witness or victim’s verbal description of the suspect. Scores on the identifi cation test range from 0 to 100
Critical Thinking The town of Butler, Nebraska, decided to give a teachercompetency exam and defi ned the passing scores to be those in the 70th percentile or higher. The raw test scores ranged from 0 to
Was a raw score of 82 necessarily a passing score? Explain.
Critical Thinking Clayton and Timothy took different sections of Introduction to Economics. Each section had a different fi nal exam. Timothy scored 83 out of 100 and had a percentile rank in his class of
Clayton scored 85 out of 100 but his percentile rank in his class was
Who performed better with respect to the rest of the students in the class, Clayton or Timothy? Explain your answer.
Basic Computation: Five-Number Summary, Interquartile Range Consider the following ordered data:2 5 5 6 7 7 8 9 10(a) Find the low, Q1, median, Q3, high.(b) Find the interquartile range.(c) Make a box-and-whisker plot.
Basic Computation: Five-Number Summary, Interquartile Range Consider the following ordered data:2 5 5 6 7 8 8 9 10 12(a) Find the low, Q1, median, Q3 high.(b) Find the interquartile range.(c) Make a box-and-whisker plot.
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.
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 annual premiums for urban customers (married couple with one 17-year-old son) in three states. The
Statistical Literacy In a statistical study what is the difference between an individual and a variable?
Statistical Literacy Are data at the nominal level of measurement quantitative or qualitative?
Statistical Literacy What is the difference between a parameter and a statistic?
Statistical Literacy For a set population, does a parameter ever change? If there are three different samples of the same size from a set population, is it possible to get three different values for the same statistic?
Critical Thinking Numbers are often assigned to data that are categorical in nature.(a) Consider these number assignments for category items describing electronic ways of expressing personal opinions:1 5 Twitter; 2 5 e-mail; 3 5 text message; 4 5 Facebook; 5 5 blog Are these numerical assignments
Interpretation Lucy conducted a survey asking some of her friends to specify their favorite type of TV entertainment from the following list of choices:sitcom; reality; documentary; drama; cartoon; other Do Lucy’s observations apply to all adults? Explain. From the description of the survey
Marketing: Fast Food A national survey asked 1261 U.S. adult fast-food customers which meal (breakfast, lunch, dinner, snack) they ordered.(a) Identify the variable.(b) Is the variable quantitative or qualitative?(c) What is the implied population?
Advertising: Auto Mileage What is the average miles per gallon (mpg) for all new cars? Using Consumer Reports, a random sample of 35 new cars gave an average of 21.1 mpg.(a) Identify the variable.(b) Is the variable quantitative or qualitative?(c) What is the implied population?
Ecology: Wetlands Government agencies carefully monitor water quality and its effect on wetlands (Reference: Environmental Protection Agency Wetland Report EPA 832-R-93-005). Of particular concern is the concentration of nitrogen in water draining from fertilized lands. Too much nitrogen can kill
Archaeology: Ireland The archaeological site of Tara is more than 4000 years old. Tradition states that Tara was the seat of the high kings of Ireland.Because of its archaeological importance, Tara has received extensive study(Reference: Tara: An Archaeological Survey by Conor Newman, Royal Irish
Student Life: Levels of Measurement Categorize these measurements associated with student life according to level: nominal, ordinal, interval, or ratio.(a) Length of time to complete an exam(b) Time of fi rst class(c) Major fi eld of study(d) Course evaluation scale: poor, acceptable, good(e) Score
Business: Levels of Measurement Categorize these measurements associated with a robotics company according to level: nominal, ordinal, interval, or ratio.(a) Salesperson’s performance: below average, average, above average(b) Price of company’s stock(c) Names of new products(d) Temperature (F)
Fishing: Levels of Measurement Categorize these measurements associated with fi shing according to level: nominal, ordinal, interval, or ratio.(a) Species of fi sh caught: perch, bass, pike, trout(b) Cost of rod and reel(c) Time of return home(d) Guidebook rating of fi shing area: poor, fair,
Education: Teacher Evaluation If you were going to apply statistical methods to analyze teacher evaluations, which question form, A or B, would be better?Form A: In your own words, tell how this teacher compares with other teachers you have had.Form B: Use the following scale to rank your teacher
Critical Thinking You are interested in the weights of backpacks students carry to class and decide to conduct a study using the backpacks carried by 30 students.(a) Give some instructions for weighing the backpacks. Include unit of measure, accuracy of measure, and type of scale.(b) Do you think
Statistical Literacy Explain the difference between a stratifi ed sample and a cluster sample.
Statistical Literacy Explain the difference between a simple random sample and a systematic sample.
Statistical Literacy Marcie conducted a study of the cost of breakfast cereal.She recorded the costs of several boxes of cereal. However, she neglected to take into account the number of servings in each box. Someone told her not to worry because she just had some sampling error. Comment on that
Statistical Literacy A random sample of students who use the college recreation center were asked if they approved increasing student fees for all students in order to add a climbing wall to the recreation center. Describe the sample frame. Does the sample frame include all students enrolled in the
Interpretation In a random sample of 50 students from a large university, all the students were between 18 and 20 years old. Can we conclude that the entire population of students at the university is between 18 and 20 years old?Explain.
Interpretation A campus performance series features plays, music groups, dance troops, and stand-up comedy. The committee responsible for selecting the performance groups include three students chosen at random from a pool of volunteers. This year the 30 volunteers came from a variety of
Critical Thinking Consider the students in your statistics class as the population and suppose they are seated in four rows of 10 students each. To select a sample, you toss a coin. If it comes up heads, you use the 20 students sitting in the fi rst two rows as your sample. If it comes up tails,
Critical Thinking Suppose you are assigned the number 1, and the other students in your statistics class call out consecutive numbers until each person in the class has his or her own number. Explain how you could get a random sample of four students from your statistics class.(a) Explain why the
Critical Thinking In each of the following situations, the sampling frame does not match the population, resulting in undercoverage. Give examples of population members that might have been omitted.(a) The population consists of all 250 students in your large statistics class.You plan to obtain a
Sampling: Random Use a random-number table to generate a list of 10 random numbers between 1 and 99.Explain your work.
Sampling: Random Use a random-number table to generate a list of eight random numbers from 1 to 976.Explain your work.
Sampling: Random Use a random-number table to generate a list of six random numbers from 1 to 8615. Explain your work.
Simulation: Coin Toss Use a random-number table to simulate the outcomes of tossing a quarter 25 times. Assume that the quarter is balanced (i.e., fair).
Computer Simulation: Roll of a Die A die is a cube with dots on each face.The faces have 1, 2, 3, 4, 5, or 6 dots. The table below is a computer simulation(from the software package Minitab) of the results of rolling a fair die 20 times.DATA DISPLAY ROW C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 1 5 2 2 2 5 3
Simulation: Birthday Problem Suppose there are 30 people at a party. Do you think any two share the same birthday? Let’s use the random-number table to simulate the birthdays of the 30 people at the party. Ignoring leap year, let’s assume that the year has 365 days. Number the days, with 1
Education: Test Construction Professor Gill is designing a multiple-choice test. There are to be 10 questions. Each question is to have fi ve choices for answers. The choices are to be designated by the lettersa, b,c, d, and e.Professor Gill wishes to use a random-number table to determine which
Education: Test Construction Professor Gill uses true–false questions. She wishes to place 20 such questions on the next test. To decide whether to place a true statement or a false statement in each of the 20 questions, she uses a random-number table. She selects 20 digits from the table. An
Sampling Methods: Benefi ts Package An important part of employee compensation is a benefi ts package, which might include health insurance, life insurance, child care, vacation days, retirement plan, parental leave, bonuses, etc. Suppose you want to conduct a survey of benefi ts packages available
Statistical Literacy A study involves three variables: income level, hours spent watching TV per week, and hours spent at home on the Internet per week. List some ways the variables might be confounded.
Statistical Literacy Consider a completely randomized experiment in which a control group is given a placebo for congestion relief and a treatment group is given a new drug for congestion relief. Describe a double-blind procedure for this experiment and discuss some benefi ts of such a procedure.
Critical Thinking A brief survey regarding opinions about recycling was carefully designed so that the wording of the questions would not infl uence the responses. Jill administered the survey at a farmer’s market. She approached adults and asked if they would fi ll out the survey, explaining
Critical Thinking A randomized block design was used to study the amount of grants awarded to students at a large university. One block consisted of undergraduate students and the other block consisted of graduate students.Samples of size 30 were taken from each block. Could the combined sample of
Interpretation Zane is examining two studies involving how different generations classify specifi ed items as either luxuries or necessities. In the fi rst study, the Echo generation is defi ned to be people ages 18–29. The second study defi ned the Echo generation to be people ages 20–31. Zane
Interpretation Suppose you are looking at the 2006 results of how the Echo generation classifi ed specifi ed items as either luxuries or necessities. Do you expect the results to refl ect how the Echo generation would classify items in 2016? Explain.
Ecology: Gathering Data Which technique for gathering data (observational study or experiment) do you think was used in the following studies?(a) The Colorado Division of Wildlife netted and released 774 fi sh at Quincy Reservoir. There were 219 perch, 315 blue gill, 83 pike, and 157 rainbow
General: Gathering Data Which technique for gathering data (sampling, experiment, simulation, or census) do you think was used in the following studies?(a) An analysis of a sample of 31,000 patients from New York hospitals suggests that the poor and the elderly sue for malpractice at one-fi fth the
General: Completely Randomized Experiment How would you use a completely randomized experiment in each of the following settings? Is a placebo being used or not? Be specifi c and give details.(a) A veterinarian wants to test a strain of antibiotic on calves to determine their resistance to common
Surveys: Manipulation The New York Times did a special report on polling that was carried in papers across the nation. The article pointed out how readily the results of a survey can be manipulated. Some features that can infl uence the results of a poll include the following: the number of
Critical Thinking An agricultural study is comparing the harvest volume of two types of barley. The site for the experiment is bordered by a river. The fi eld is divided into eight plots of approximately the same size. The experiment calls for the plots to be blocked into four plots per block.
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 statistics site at http://www.cengagebrain.com and fi nd a link to the Census Bureau’s site, as well as
Statistical Literacy What is the difference between a class boundary and a class limit?
Statistical Literacy A data set has values ranging from a low of 10 to a high of 52.What’s wrong with using the class limits 10–19, 20–29, 30–39, 40–49 for a frequency table?
Statistical Literacy A data set has values ranging from a low of 10 to a high of 50.What’s wrong with using the class limits 10–20, 20–30, 30–40, 40–50 for a frequency table?
Statistical Literacy A data set has values ranging from a low of 10 to a high of 50.The class width is to be 10.What’s wrong with using the class limits 10–20, 21–31, 32–42, 43–53 for a frequency table with a class width of 10?
Basic Computation: Class Limits A data set with whole numbers has a low value of 20 and a high value of 82.Find the class width and class limits for a frequency table with 7 classes.
Basic Computation: Class Limits A data set with whole numbers has a low value of 10 and a high value of 120.Find the class width and class limits for a frequency table with 5 classes.
Interpretation You are manager of a specialty coffee shop and collect data throughout a full day regarding waiting time for customers from the time they enter the shop until the time they pick up their order.(a) What type of distribution do you think would be most desirable for the waiting times:
Critical Thinking A web site rated 100 colleges and ranked the colleges from 1 to 100, with a rank of 1 being the best. Each college was ranked, and there were no ties. If the ranks were displayed in a histogram, what would be the shape of the histogram: skewed, uniform, mound-shaped?
Critical Thinking Look at the histogram in Figure 2-10(a), which shows mileage, in miles per gallon (mpg), for a random selection of passenger cars(Reference: Consumer Reports).(a) Is the shape of the histogram essentially bimodal?(b) Jose looked at the raw data and discovered that the 54 data
Critical Thinking The following data represent salaries, in thousands of dollars, for employees of a small company. Notice that the data have been sorted in increasing order.54 55 55 57 57 59 60 65 65 65 66 68 68 69 69 70 70 70 75 75 75 75 77 82 82 82 88 89 89 91 91 97 98 98 98 280(a) Make a

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