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elementary statistics

Questions and Answers of Elementary Statistics

[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
[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
[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
[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
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:
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
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
[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
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
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
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
[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
[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
[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
[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
[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
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
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,
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
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
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
[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.
[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
[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
[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
[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
[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
[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
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
[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•••
[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
[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.
[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
[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
[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
[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
[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
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
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
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
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.
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
[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
[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
[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
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
[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
[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
[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
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
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
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
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
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
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
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
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
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
“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
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
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
[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
[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
[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
[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
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
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
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
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
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
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 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
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
[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
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
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
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
[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
[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
[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
[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).
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

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