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elementary statistics
Just The Essentials Of Elementary Statistics 10th Edition Robert Johnson, Patricia Kuby - Solutions
[EX02-220] The following table shows the age distribution of heads of families:Age of Head Age of Head of Family Number of Family Number 20–25 23 50–55 48 25–30 38 55–60 39 30–35 51 60–65 31 35–40 55 65–70 26 40–45 53 70–75 20 45–50 50 75–80 16a. Find the mean age of the
[EX02-219] USA Today (October 25, 1994)reported in the USA Snapshot “Mystery of the remote”that 44% of the families surveyed never misplaced the family television remote control, 38%misplaced it one to five times weekly, and 17%misplaced it more than five times weekly. One percent of the
[EX02-217] The distribution of credit hours, per student, taken this semester at a certain college was as follows:Credit Hours Frequency Credit Hours Frequency 3 75 15 400 6 150 16 1050 8 30 17 750 9 50 18 515 12 70 19 120 14 300 20 60a. Draw a histogram of the data.b. Find the five measures of
[EX02-216] Outliers! How often do they occur?What do we do with them? Complete part a to see how often outliers can occur. Then complete part b to decide what to do with outliers.a. Use the technology of your choice to take samples of various sizes (10, 30, 100, 300 would be good choices) from a
Repeat Exercise 2.213 using populations with different shaped distributions.a. Use a uniform or rectangular distribution. (Replace the subcommands used in Exercise 2.213;in place of NORMAL use: UNIFORM with a low of 50 and a high of 150, and use class boundaries of 50 to 150 in increments of 10.)b.
Repeat Exercise 2.213 using a different sample size. You might try a few different sample sizes:n 10, n 15, n 20, n 40, n 50, n 75.What effect does increasing the sample size have on the effectiveness of the sample in depicting the population? Explain.
Use a computer to generate a random sample of 500 values of a normally distributed variable x with a mean of 100 and a standard deviation of 20. Construct a histogram of the 500 values.a. Use the computer commands on page 101 to randomly generate a sample of 500 data from a normal distribution with
[EX02-212] When the Internet study “You and the Internet” (Section 2.1, p. 39) was performed, it appeared that the variable x, the number of Internet activities in a week, had an approximately normal distribution. That distribution is approximated by this relative frequency
Construct two different graphs of the points(62, 2), (74, 14), (80, 20), and (94, 34).a. On the first graph, along the horizontal axis, lay off equal intervals and label them 62, 74, 80, and 94; lay off equal intervals along the vertical axis and label them 0, 10, 20, 30, and 40. Plot the points
Make up a set of 18 data (think of them as exam scores) so that the sample meets each of these sets of criteria:a. Mean is 75, and standard deviation is 10.b. Mean is 75, maximum is 98, minimum is 40, and standard deviation is 10.c. Mean is 75, maximum is 98, minimum is 40, and standard deviation
Starting with the data values of 70 and 85, add three data values to your sample so that the sample has the following: (Justify your answer in each case.)a. A standard deviation of 5b. A standard deviation of 10c. A standard deviation of 15d. Compare your three samples and the variety of values
[EX02-207] Each year, stock car drivers compete for NASCAR. Points are earned on the basis of finishes in sanctioned races scheduled on the circuit. At the end of the 2004 season, the standings posted at NASCAR.com; the top 32 drivers are shown in the following table.Driver Points Driver Points
[EX02-206] The manager of Jerry’s Barber Shop recently asked his last 50 customers to punch a time card when they first arrived at the shop and to punch out right after they paid for their haircut.He then used the data on the cards to measure how long it took Jerry and his barbers to cut hair and
[EX02-205] Americans love soups, and soups remain one of the most popular foods for lunch and as an appetizer before dinner. Manufacturers provide the calorie and sodium content on the label. The data for 40 popular multiserving (8 oz.) cans and mixes, most of which were low-fat varieties, appear
[EX02-204] Delco Products, a division of General Motors, produces a bracket that is used as part of a power doorlock assembly. The length of this bracket is constantly being monitored. A sample of 30 power door brackets had the following lengths (in millimeters):a. Without doing any calculations,
[EX02-203] Manufacturing specifications are often based on the results of samples taken from satisfactory pilot runs. The following data resulted from just such a situation, in which eight pilot batches were completed and sampled. The resulting particle sizes are in angstroms (where 1 Å 108
The scores achieved by students in America make the news often, and all kinds of conclusions are drawn based on these scores. The ACT Assessment is designed to assess high school students’general educational development and their ability to complete college-level work. The following table shows
Twins Jean and Joan Wong are in fifth grade(different sections), and the class has been given a series of ability tests. If the scores for these ability tests are approximately normally distributed, which girl has the higher relative score on each of the skills listed? Explain your answers.Skill
Bill and Rob are good friends, although they attend different high schools in their city. The city school system uses a battery of fitness tests to test all high school students. After completing the fitness tests, Bill and Rob are comparing their scores to see who did better in each event. They
For a normal (or bell-shaped) distribution, find the z-score that corresponds to the kth percentile:a. k 20b. k 95c. Sketch the normal curve, showing the relationship between the z-score and the percentiles for parts a and b.
For a normal (or bell-shaped) distribution, find the percentile rank that corresponds to:a. z 2b. z1c. Sketch the normal curve, showing the relationship between the z-score and the percentiles for parts a and b.
[EX02-197] Who ate the M&M’s? The following table gives the color counts and net weight(in grams) for a sample of 30 bags of M&M’s. The advertised net weight is 47.9 grams per bag.Case Red Gr. Blue Or. Yel. Br. Weight 1 15 9 3 3 9 19 49.79 2 9 17 19 3 3 8 48.98••• Remainder of data on
[EX02-196] The dollar amounts listed here are the average hourly earnings of production or nonsupervisory workers on private nonfarm payrolls by major industry. Both five years of information and eleven years of information are listed on the CD located on the inside the back cover. Investigate this
[EX02-195] Following are the percentage of high school graduates per state from the class of 2003 who took the ACT exam.0.73 0.07 0.16 0.10 0.52 0.62 0.69 0.70 0.12 0.76 0.32 0.05 0.60 0.69 0.73 0.15 0.12 0.74 0.16 0.73 0.27 0.30 1.00 0.67 0.34 0.15 0.08 0.33 0.63 0.80 0.73 0.41 0.21 0.88 0.08 0.80
[EX02-194] The volume of Christmas trees sold annually in the United States has declined in recent decades according to a USDA National Agricultural Statistics Service report. All 50 states report contributions to the total U.S. sale of about 25 million Christmas trees annually. Furthermore, each
[EX02-193] The National Environmental Satellite, Data, and Information Service, U.S. Department of Commerce, posted the area (sq. mi.)and the 2000 population for the 48 contiguous U.S. states.State Area (sq. mi.) Population AL 51,610 4,447,100 AZ 113,909 5,130,632••• Remainder of data on
[EX02-192] The national highway system is made up of interstate and noninterstate highways.The Federal Highway Administration reported the number of miles of each type in each state. Listed is a random sample of 20.Miles of Interstate and Noninterstate Highways by State State Interstate
[EX02-191] The lengths (in millimeters) of 100 brown trout in pond 2-B at Happy Acres Fish Hatchery on June 15 of last year were as follows:15.0 15.3 14.4 10.4••• Remainder of data on Student’s Suite CD-ROMa. Find the mean.b. Find the median.c. Find the mode.d. Find the midrange.e. Find the
Ask one of your instructors for a list of exam grades (15 to 25 grades) from a class.a. Find five measures of central tendency.b. Find the three measures of dispersion.c. Construct a stem-and-leaf display. Does this diagram suggest that the grades are normally distributed?d. Find the following
[EX02-189] The top 2004 Nationwide Tour money leaders, together with their total earnings, are listed here:Player Money ($) Player Money ($)Jimmy Walker 371,346 D. A. Points 332,815••• Remainder of data on Student’s Suite CD-ROM Source: PGA Tour, Inc.a. Calculate the mean and standard
[EX02-188] One of the first scientists to study the density of nitrogen was Lord Raleigh. He noticed that the density of nitrogen produced from the air seemed to be greater than the density of nitrogen produced from chemical compounds. Do his conclusions seem to be justified even though he has so
[EX02-187] The Office of Aviation Enforcement& Proceedings, U.S. Department of Transportation, reported the number of mishandled baggage reports filed per 1000 airline passengers during October 2004. The industry average was 4.02.Airline Reports Passengers Reports/1000 AirTran 2084 1,148,779 1.81
[EX02-186] Forbes.com posted the 2004 EPS (earnings per share) in dollars for 17 banking industry companies.Name EPS ($) Name EPS ($)Astoria Financial 2.92 Popular 1.71 Banknorth Group 2.20 State Street 3.13 Bank of America 3.67 Synovus Finl 1.36 BB & T 2.61 UnionBanCal 4.70 Compass Bancshares 2.86
[EX02-185] The stopping distance on a wet surface was determined for 25 cars, each traveling at 30 miles per hour. The data (in feet) are shown on the following stem-and-leaf display:6 3 7 6 3 9 7 4 2 0 1 1 2 0 5 8 5 4 5 5 6 9 4 1 0 0 5 10 5 4 Find the mean and the standard deviation of these
[EX02-184] A survey of 32 workers at building 815 of Eastman Kodak Company was taken last May. Each worker was asked: “How many hours of television did you watch yesterday?”The results were as follows:0 0 1⁄2 1 2 0 3 21⁄2 0 0 1 11⁄2 5 21⁄2 0 2 21⁄2 1 0 2 0 21⁄2 4 06 21⁄2 0 1⁄2 1
[EX02-183] These data are the ages of 118 known offenders who committed an auto theft last year in Garden City, Michigan:11 14 15 15 16 16 17 18 19 21 25 36 12 14 15 15 16 16 17 18 19 21 25 39 13 14 15 15 16 17 17 18 20 22 26 43 13 14 15 15 16 17 17 18 20 22 26 46 13 14 15 16 16 17 17 18 20 22 27
[EX02-182] Gasoline pumped from a supplier’s pipeline is supposed to have an octane rating of 87.5. On 13 consecutive days, a sample of octane ratings was taken and analyzed, with the following results:88.6 86.4 87.2 88.4 87.2 87.6 86.8 86.1 87.4 87.3 86.4 86.6 87.1a. Find the sample mean.b. Find
The addition of a new accelerator is claimed to decrease the drying time of latex paint by more than 4%. Several test samples were conducted with the following percentage decreases in drying time:5.2 6.4 3.8 6.3 4.1 2.8 3.2 4.7a. Find the sample mean.b. Find the sample standard deviation.c. Do you
Consider samples C and D. Notice that the two samples are the same except for two values.C: 20 60 60 70 90 D: 20 30 70 90 90 What effect does changing the two 60s to 30 and 90 have on each of the following statistics?a. Meanb. Medianc. Moded. Midrangee. Rangef. Variance g. Std. dev.
Consider samples A and B. Notice that the two samples are the same except that the 8 in A has been replaced by a 9 in B.A: 2 4 5 5 7 8 B: 2 4 5 5 7 9 What effect does changing the 8 to a 9 have on each of the following statistics?a. Meanb. Medianc. Moded. Midrangee. Vangef. Variance g. Std. dev.
Identify each of the following as examples of (1) attribute (qualitative) or (2) numerical(quantitative) variables.a. The amount of weight lost in the past month by a person following a strict dietb. Batting averages of major league baseball playersc. Decisions by the jury in felony trialsd.
Identify each of the following as examples of (1) attribute (qualitative) or (2) numerical(quantitative) variables.a. Scores registered by people taking their written state automobile driver’s license examinationb. Whether or not a motorcycle operator possesses a valid motorcycle operator’s
[EX02-176] The U.S. Census Bureau posted the following 2003 age distribution for the people of New York State. The 2003 American Community Survey is limited to the household population and excludes the population living in institutions, college dormitories, and other group quarters.Sex and Age
[EX02-175] The 10 leading causes of death in the United States during 2002 were listed by the National Center for Statistics and Analysis in a January 2005 report. There were a total of 2,443,387 deaths recorded.Number Cause of Death (10,000s)Alzheimer’s disease 5.9 Chronic respiratory disease
[EX02-169] A random sample of 250 people living in the state of New York resulted in the following distribution of ages.Age Group Frequency Age Group Frequency Younger than 5 years 18 45–54 years 48 5–14 years 35 55–64 years 21 15–24 years 20 65–74 years 17 25–34 years 35 75–84 years
The number of sports reports a sports fan watches on television in a typical week was described in a USA Snapshot titled “Fans find sports in print and TV” (December 21, 2004).Reports 0 1–2 3–4 5–6 7 8 or more Percent 35.0% 24.8% 15.4% 11.4% 8.6% 4.8%This information is based on an ESPN
[EX02-042] A USA Snapshot titled “Nuns an aging order” reports that the median age of 94,022 Roman Catholic nuns in the United States is 65 years and the percentages of U.S. nuns by age group are as follows:Under 50 51–70 Over 70 Refused to give age 16% 42% 37% 5%This information is based on
[EX02-165] A random sample of people of all ages was taken from the U.S. population, and the resulting 75 ages (in years) are listed in the following table:22 7 72 32 18 4 9 48 49 18 18 58 47 39 48 1 27 61 48 25 34 75 29 53 37 25 42 49 29 31 10 27 8 78 63 50 39 32 5 39 8 15 8 50 39 46 38 4 9 43 3
[EX02-164] The California Department of Education issues a yearly report on Scholastic Aptitude Test (SAT) scores for students in the various school districts. The following frequency table shows verbal test results for 2003–2004 for Merced County school districts.Number Verbal District Tested
Private industry reported that more than 31,000 workers were absent from work in 2005 because of carpal tunnel syndrome (a nerve disorder causing arm, wrist, and hand pain). The length of time (in days) workers are absent as a result of this problem varies greatly.Days of Absence, x 0–10 10–20
It has been found that 35.2 million Americans 16 years and older fish our waters. A sample of freshwater fishermen produced the following age distribution:Age of Fishermen, x 15–25 25–35 35–45 45–55 55–65 65–75# Fishermen, f 13 20 28 20 10 9 Find the mean and the standard deviation for
A quality-control technician selected twenty-five 1-pound boxes from a production process and found the following distribution of weights (in ounces):Weight Frequency Weight Frequency 15.95–15.98 2 16.04–16.07 3 15.98–16.01 4 16.07–16.10 1 16.01–16.04 15 Find the mean and the standard
The following distribution of commuting distances was obtained for a sample of Mutual of Nebraska employees:Distance (miles) Frequency Distance (miles) Frequency 1.0–3.0 2 9.0–11.0 35 3.0–5.0 6 11.0–13.0 15 5.0–7.0 12 13.0–15.0 5 7.0–9.0 50 Find the mean and the standard deviation for
Find the mean, variance, and standard deviation for this grouped frequency distribution:Class Boundaries 3–6 6–9 9–12 12–15 15–18 f 2 10 12 9 7
Find the mean, variance, and standard deviation of the data shown in the following frequency distribution.Class 2–6 6–10 10–14 14–18 18–22 f 2 10 12 9 7
The weight gains (in grams) for chicks fed on a high-protein diet were as follows:Weight Gain 12.5 12.7 13.0 13.1 13.2 13.8 Frequency 2 6 22 29 12 4a. Find the mean.b. Find the variance.c. Find the standard deviation.
A survey asked a group of medical doctors how many children they had fathered. The results are summarized by this ungrouped frequency distribution:Number of Children 0 1 2 3 4 6 Number of Doctors 15 12 26 14 4 2 Calculate the sample mean, variance, and standard deviation for the number of children
2.154a. Find the mean of the data shown in the frequency distribution in Exercise 2.153.b. Find the variance for the data shown in the frequency distribution in Exercise 2.153.c. Find the standard deviation for the data shown in the frequency distribution in Exercise 2.153.
Find an article or an advertisement containing a graph that in some way misrepresents the information of statistics. Describe how this graph misrepresents the facts.
The best value for price was most often reported by consumers as one of the draws when deciding where to do their holiday shopping. When asked, “What draws holiday shoppers to stores?” at Christmas time in 2004, they responded as follows.What Percent Value 76 Convenient location 68 Quality 62
a. Find and describe at least four incorrect impressions created by truncating the horizontal axis on the Applied Example 2.17’s “Service contractor complaints”graphic on page 116.b. Redraw the bar graph starting the horizontal scale at “zero.”c. Comment on the effect that your graph has
“What’s wrong with this picture?” That’s the question one should be asking when viewing the graphs in Applied Example 2.16 on page 115.a. Find and describe at least four features about the Ithaca Times front-page graph that are incorrectly used.b. Find and describe at least two features
Is it possible for eight employees to earn between$300 and $350, a ninth to earn $1250 per week, and the mean to be $430? Verify your answer.
Chebyshev’s theorem states that “at least 1 k 12”of the data of a distribution will lie within kstandard deviations of the mean.a. Use the computer commands on page 101 to randomly generate a sample of 100 data from a uniform (nonnormal) distribution that has a low value of 1 and a high
The empirical rule states that the 1, 2, and 3 standard deviation intervals about the mean will contain 68%, 95%, and 99.7%, respectively.a. Use the computer or calculator commands on page 101 to randomly generate a sample of 100 data from a normal distribution with mean 50 and standard deviation
[EX02-144] Each year, NCAA college football fans like to learn about the size of the players in the current year’s recruit class. Following are the weights (in pounds) of the nation’s top 100 high school football players for 2005, as rated by recruiting analyst Tom Lemming of ESPN.com.Just
[EX02-143] Each year, NCAA college football fans like to learn about the up-and-coming freshman class of players. Following are the heights (in inches) of the nation’s top 100 high school football players for 2005, as rated by recruiting analyst Tom Lemming of ESPN.com:75 70 71 75 76 76 70 72 70
[EX02-142] One of the many things the U.S. Census Bureau reports to the public is the increase in population for various geographic areas within the country. The percent of increase in population for the 100 fastest-growing counties in the United States from April 1, 2000, to July 1, 2003, are
[EX02-141] On the first day of class last semester, 50 students were asked for the one-way distance from home to college (to the nearest mile). The resulting data follow:6 5 3 24 15 15 6 2 1 3 5 10 9 21 8 10 9 14 16 16 10 21 20 15 9 4 12 27 10 10 3 9 17 6 11 10 12 5 7 11 5 8 22 20 13 1 8 13 4 18a.
The scores achieved by students in America make the news often, and all kinds of conclusions are drawn based on these scores. The ACT Assessment is designed to assess high school students’general educational development and their ability to complete college-level work. One of the categories
Chebyshev’s theorem can be stated in an equivalent form to that given on page 109. For example, to say “at least 75% of the data fall within 2 standard deviations of the mean” is equivalent to stating “at most, 25% will be more than 2 standard deviations away from the mean.”a. At most,
According to Chebyshev’s theorem, what proportion of a distribution will be within k 4 standard deviations of the mean?
Chebyshev’s theorem guarantees that what proportion of a distribution will be included between the following:a. ¯ x 2s and ¯ x 2sb. ¯ x 3s and ¯ x 3s
According to the empirical rule, almost all the data should lie between (¯ x 3s) and (¯ x 3s).The range accounts for all the data.a. What relationship should hold (approximately)between the standard deviation and the range?b. How can you use the results of part a to estimate the standard
Using the empirical rule, determine the approximate percentage of a normal distribution that is expected to fall within the interval described.a. Less than the meanb. Greater than 1 standard deviation above the meanc. Less than 1 standard deviation above the meand. Between 1 standard deviation
a. What proportion of a normal distribution is greater than the mean?b. What proportion is within 1 standard deviation of the mean?c. What proportion is greater than a value that is 1 standard deviation below the mean?
The average clean-up time for a crew of a medium-size firm is 84.0 hours and the standard deviation is 6.8 hours. Assume the empirical rule is appropriate.a. What proportion of the time will it take the clean-up crew 97.6 hours or more to clean the plant?b. Within what interval will the total
The mean lifetime of a certain tire is 30,000 miles and the standard deviation is 2500 miles.a. If we assume the mileages are normally distributed, approximately what percentage of all such tires will last between 22,500 and 37,500 miles?b. If we assume nothing about the shape of the distribution,
Why is it that the z-score for a value that belongs to a normal distribution usually lies between3 and 3?
The empirical rule indicates that we can expect to find what proportion of the sample included between the following:a. x s and x sb. x 2s and x 2sc. x 3s and x 3s
Instructions for an essay assignment include the statement “The length is to be within 25 words of 200.” What values of x, number of words, satisfy these instructions?
Which x value has the lower position relative to the set of data from which it comes?A: x 28.1, where ¯ x 25.7 and s 1.8 B: x 39.2, where ¯ x 34.1 and s 4.3
Which x value has the higher position relative to the set of data from which it comes?A: x 85, where mean 72 and standard deviation 8 B: x 93, where mean 87 and standard deviation 5
The ACT Assessment is designed to assess high school students’ general educational development and their ability to complete college-level work. The following table lists the mean and standard deviation of scores attained by the 1,171,460 high school students of the 2004 graduating class who took
[EX02-098] Consider the percentage of interstate and state-owned bridges that were structurally deficient or functionally obsolete (SD/FO)listed in Exercise 2.98 on page 92.a. Omit the names of the states and rank the SD/FO values in ascending order, reading horizontally in each row.b. Construct a
a. What does it mean to say that x 152 has a standard score of 1.5?b. What does it mean to say that a particular value of x has a z-score of 2.1?c. In general, the standard score is a measure of what?
A sample has a mean of 120 and a standard deviation of 20.0. Find the value of x that corresponds to each of these standard scores:a. z 0.0b. z 1.2c. z1.4d. z 2.05
A nationally administered test has a mean of 500 and a standard deviation of 100. If your standard score on this test was 1.8, what was your test score?
An exam produced grades with a mean score of 74.2 and a standard deviation of 11.5. Find the z-score for each test score x:a. x 54b. x 68c. x 79d. x 93
A sample has a mean of 50 and a standard deviation of 4.0. Find the z-score for each value of x:a. x 54b. x 50c. x 59d. x 45
Find the z-score for test scores of 92 and 63 on a test that has a mean of 72 and a standard deviation of 12.
[EX02-118] Henry Cavendish, an English chemist and physicist (1731–1810), approached many of his experiments using quantitative measurements.He was the first to accurately measure the density of the Earth. Following are 29 measurements(ranked for your convenience) of the density of the Earth done
What property does the distribution need for the median, the midrange, and the midquartile to all be the same value?
[EX02-116] Major league baseball stadiums vary in age, style, number of seats, and many other ways, but to the baseball players, the size of the field is of the utmost importance. Suppose we agree to measure the size of the field by using the distance from home plate to the centerfield
[EX02-115] Are airline flight arrivals ever on time? The general public thinks they are always late—but are they? The U.S. Bureau of Transportation Statistics keeps records and periodically reports the findings. Listed here are the percentages of on-time arrivals at the 31 major U.S. airports for
[EX02-114] The fatality rate on the nation’s highways in 2003 was the lowest since record keeping began 29 years ago, but these numbers are still mind-boggling. The number of persons killed in motor vehicle traffic crashes, by state, including the District of Columbia, in 2003 is listed here:1001
[EX02-113] The NCAA men’s basketball“Big Dance” kicks into full gear every March. If you look at the graduation rate of these athletes, however, you will find that many teams do not make the grade, according to a study released in March 2005. Following are the graduation rates for 64 of the
[EX02-112] The U.S. Geological Survey collected atmospheric deposition data in the Rocky Mountains. Part of the sampling process was to determine the concentration of ammonium ions (in percentages). Here are the results from the 52 samples:2.9 4.1 2.7 3.5 1.4 5.6 13.3 3.9 4.0 2.9 7.0 4.2 4.9 4.6
Draw a box-and-whiskers display for the set of data with the 5-number summary 42–62–72–82–97.
[EX02-110] A research study of manual dexterity involved determining the time required to complete a task. The time required for each of 40 individuals with disabilities is shown here (data are ranked):7.1 7.2 7.2 7.6 7.6 7.9 8.1 8.1 8.1 8.3 8.3 8.4 8.4 8.9 9.0 9.0 9.1 9.1 9.1 9.1 9.4 9.6 9.9 10.1
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