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Statistics 13th Global Edition James T. McClave And Terry T Sincich - Solutions
Show that the sample mean is relatively more efficient than the sample median when estimating the population mean. LO-1
Xr10-21 The following data represent a random sample of 9 marks (out of 10) on a statistics quiz. The marks are normally distributed with a standard deviation of 2. Estimate the population mean with 90%confidence.7 9 7 5 4 8 3 10 9
Xr10-22 The following observations are the ages of a random sample of 8 men in a bar. It is known that the ages are normally distributed with a standard deviation of 10. Determine the 95% confidence interval estimate of the population mean. Interpret the interval estimate.52 68 22 35 30 56 39 48
Xr10-23 How many rounds of golf do physicians (who play golf) play per year? A survey of 12 physicians revealed the following numbers:3 41 17 1 33 37 18 15 17 12 29 51 Estimate with 95% confidence the mean number of rounds per year played by physicians, assuming that the number of rounds is
Xr10-27 Suppose that the amount of time teenagers spend weekly working at part-time jobs is normally distributed with a standard deviation of 40 minutes.A random sample of 15 teenagers was drawn, and each reported the amount of time spent at part-time jobs (in minutes). These are listed here.
Xr10-30 A survey of 400 statistics professors was undertaken. Each professor was asked how much time was devoted to teaching graphical techniques.We believe that the times are normally distributed with a standard deviation of 30 minutes. Estimate the population mean with 95% confidence.
Xr10-38 A survey of 80 randomly selected companies asked them to report the annual income of their presidents. Assuming that incomes are normally distributed with a standard deviation of $30,000, determine the 90% confidence interval estimate of the mean annual income of all company
Examined the difference between inferential and descriptive statistics (2.1)
Described the key elements of a statistical problem (2.1)
Learned about the two types of data: quantitative and qualitative (2.1)
Discussed the role of statistical thinking in managerial decision making (2.1)
Describe qualitative data with graphs (2.1)
Describe quantitative data with graphs (2.2)
Describe quantitative data with numerical measures (2.3–2.7)
Describe the relationship between two quantitative variables with a graph (2.8)
Detect descriptive methods that distort the truth (2.9)
What is the advantage of a Pareto diagram over a bar graph?
Complete the following table:Grades in Statistics Frequency Relative Frequency A: 90–100 .2 B: 80–89 75 C: 65–79 120 D: 50–64 F: Below 50 15 .05 Total 1.00
A qualitative variable with three classes (X, Y, and Z) is measured for each of 20 units randomly sampled from a target population. The data (observed class for each unit)are as follows:Y X X Z X Y Y Y X X Z X Y Y X Z Y Y Y Xa. Compute the frequency for each of the three classes.b. Compute the
Study of importance of libraries. In The Canadian Journal of Information and Library Science (Vol. 33, 2009), researchers from the University of Western Ontario reported on mall shoppers’ opinions about libraries and their importance to today’s society. Each in a sample of over 200 mall
Do social robots walk or roll? According to the United Nations, social robots now outnumber industrial robots worldwide. A social (or service) robot is designed to entertain, educate, and care for human users. In a paper published by the International Conference on Social Robotics (Vol. 6414,
Paying for music downloads. If you use the Internet, have you ever paid to access or download music? This was one of the questions of interest in a recent Pew Internet &American Life Project Survey (October 2010). Telephone interviews were conducted on a representative sample of 1,003 adults
Cheek teeth of extinct primates. The characteristics of cheek teeth (e.g., molars) can provide anthropologists with information on the dietary habits of extinct mammals. The cheek teeth of an extinct primate species were the subject of research reported in the American Journal of Physical
Humane education and classroom pets. In grade school, did your teacher have a pet in the classroom? Many teachers do so in order to promote humane education.The Journal of Moral Education (Mar. 2010) published a study designed to examine elementary school teachers’experiences with humane
Estimating the rhino population. The International Rhino Foundation estimates that there are 28,933 rhinoceroses living in the wild in Africa and Asia. A breakdown of the number of rhinos of each species is reported in the accompanying table:Rhino Species Population Estimate African Black 5,055
STEM experiences for girls. The National Science Foundation (NSF) sponsored a study on girls’ participation in informal science, technology, engineering, and mathematics(STEM) programs (see Exercise 1.13). The results of the study were published in Cascading Influences: Long-Term Impacts of
STEM experiences for girls. The National Science Foundation (NSF) sponsored a study on girls’ participation in informal science, technology, engineering, and mathematics(STEM) programs (see Exercise 1.13). The results of the study were published in Cascading Influences: Long-Term Impacts of
Genealogy research. The Journal of Family History (Jan.2010) investigated the genealogy of a certain Korean clan.Of interest was whether or not a family name continued into the next generation in the clan genealogy (called acontinued line) or dropped out (called a dropout line). Sideby-side pie
Characteristics of ice melt ponds. The National Snow and Ice Data Center (NSIDC) collects data on the albedo, depth, and physical characteristics of ice melt ponds in the Canadian Arctic. Environmental engineers at the University of Colorado are using these data to study how climate affects the sea
Railway track allocation. One of the problems faced by transportation engineers is the assignment of tracks to trains at a busy railroad station. Overused and/or underused tracks cause increases in maintenance costs and inefficient allocation of resources. The Journal of Transportation
Curbing street gang gun violence. Operation Ceasefire is a program implemented to reduce street gang gun violence in the city of Boston. The effectiveness of the program was examined in the Journal of Quantitative Criminology(Mar. 2014). Over a 5-year period (2006–2010), there were 80 shootings
Interactions in a children’s museum. The nature of child-led and adult-led interactions in a children’s museum was investigated in Early Childhood Education Journal (Mar. 2014).Interactions by visitors to the museum were classified as(1) show-and-tell, (2) learning, (3) teaching, (4)
Motivation and right-oriented bias. Evolutionary theory suggests that motivated decision makers tend to exhibit a right-oriented bias. (For example, if presented with two equally valued brands of detergent on a supermarket shelf, consumers are more likely to choose the brand on the right.) In
Do you believe in the Bible? Each year the National Opinion Research Center conducts the General Social Survey(GSS), eliciting opinions of Americans on a wide variety of social topics. One question in the survey asked about a person’s belief in the Bible. A sample of 4,826 respondents selected
Museum management. What criteria do museums use to evaluate their performance? In a worldwide survey reported in Museum Management and Curatorship(June 2010), managers of 30 leading museums of contemporary art were asked to provide the performance measure used most often. The data are provided in
Groundwater contamination in wells. In New Hampshire, about half the counties mandate the use of reformulated gasoline. This has led to an increase in the contamination of groundwater with methyl tert-butyl ether (MTBE).Environmental Science & Technology (Jan. 2005) reported on the factors related
Extinct New Zealand birds. Refer to the Evolutionary Ecology Research (July 2003) study of the patterns of extinction in the New Zealand bird population, Exercise 1.20(p. 49). Data on flight capability (volant or flightless), habitat (aquatic, ground terrestrial, or aerial terrestrial), nesting
Between a bar chart and a stem-and-leaf display, which one can you use for interval data?
Explain the difference between a stem-and-leaf display and a histogram for representing numeric data.
How many classes are recommended in a histogram of a data set with less than 25 observations?
Refer to Exercise 2.32. Calculate the number of the 500 measurements falling into each of the measurement classes. Then graph a frequency histogram of these data.
Irrelevant speech effects. In a psychological study of shortterm memory, irrelevant speech effects refer to the degree to which the memorization process is impaired by irrelevant background speech (for example, trying to memorize a list of numbers while listening to a speech in an unfamiliar
Corporate sustainability of CPA firms. Refer to the Business and Society (Mar. 2011) study on the sustainability behaviors of CPA corporations, Exercise 1.26(p. 50). Recall that corporate sustainability refers to business practices designed around social and environmental considerations. Data on
Shaft graves in ancient Greece. Archeologists have discovered a rise in shaft graves during the Middle Helladic period in ancient Greece (i.e., around 2000 BC). Shaft graves are named for the beautifully decorated sword shafts that are buried along with the bodies. An analysis of shaft graves was
Cheek teeth of extinct primates. Refer to the American Journal of Physical Anthropology (Vol. 142, 2010) study of the characteristics of cheek teeth (e.g., molars) in an extinct primate species, Exercise 2.9 (p. 66). In addition to degree of wear, the researchers recorded the dentary depth of
Music performance anxiety. The nature of performance anxiety by music students was investigated in the British Journal of Music Education (Mar. 2014). Symptoms of music performance anxiety include increased heart rate, shallow breathing, anxious thoughts, and the avoidance of practice.A Performance
Is honey a cough remedy? Does a teaspoon of honey before bed really calm a child’s cough? To test the folk remedy, pediatric researchers at Pennsylvania State University carried out a designed study involving a sample of 105 children who were ill with an upper respiratory tract infection
Sanitation inspection of cruise ships. To minimize the potential for gastrointestinal disease outbreaks, all passenger cruise ships arriving at U.S. ports are subject to unannounced sanitation inspections. Ships are rated on a 100-point scale by the Centers for Disease Control and Prevention. A
Crab spiders hiding on flowers. Crab spiders use camouflage to hide on flowers while lying in wait to prey on other insects. Ecologists theorize that this natural camouflage also enables the spiders to hide from their own predators, such as birds and lizards. Researchers at the French Museum of
Sound waves from a basketball. An experiment was conducted to characterize sound waves in a spherical cavity(American Journal of Physics, June 2010). A fully inflated basketball, hanging from rubber bands, was struck with a metal rod, producing a series of metallic-sounding pings. Of particular
Research on eating disorders. Data from a psychology experiment were reported and analyzed in The American Statistician (May 2001). Two samples of female students participated in the experiment. One sample consisted of 11 students known to suffer from the eating disorder bulimia;the other sample
Research on brain specimens. The postmortem interval(PMI) is defined as the time elapsed (in days) between death and an autopsy. Knowledge of the PMI is considered essential to conducting medical research on human cadavers. The data in the accompanying table are the PMIs of 22 human brain specimens
State SAT scores. Educators are constantly evaluating the efficacy of public schools in the education and training of U.S. students. One quantitative assessment of change over time is the difference in scores on the SAT, which has been used for decades by colleges and universities as one criterion
Phishing attacks to e-mail accounts. Phishing is the term used to describe an attempt to extract personal/financial information (e.g., PIN numbers, credit card information, bank account numbers) from unsuspecting people through fraudulent e-mail. An article in Chance (Summer 2007)demonstrates how
Mineral flotation in water study. A high concentration of calcium and gypsum in water can affect the water quality and limit mineral flotation. In Minerals Engineering(Vol. 46–47, 2013), chemical and materials engineers published a study of the impact of calcium and gypsum on the flotation
Give three different measures of central tendency.
Explain the difference between the mean and the median as measures of central tendency.
Which of the three measures of central tendency may not be unique for a given data set?
What are the typical relative positions of the mean and the median for a skewed distribution?
Between the mean and the median, which one is affected by the minimum and maximum values of the observed data?
Describe how the mean compares with the median for a distribution as follows:a. Skewed to the leftb. Skewed to the rightc. Symmetric
Calculate the mean and median of the following grade point averages:3.2 2.5 2.1 3.7 2.8 2.0
Calculate the mean for samples for whicha. n = 10, ax = 85b. n = 16, ax = 400c. n = 45, ax = 35d. n = 18, ax = 242
Shaft graves in ancient Greece. Refer to the American Journal of Archaeology (Jan. 2014) study of sword shaft graves in ancient Greece, Exercise 2.37 (p. 78). The number of sword shafts buried at each of 13 recently discovered grave sites is reproduced in the following table.1 2 3 1 5 6 2 4 1 2 4 2
Characteristics of a rock fall. In Environmental Geology(Vol. 58, 2009) computer simulation was employed to estimate how far a block from a collapsing rock wall will bounce—called rebound length—down a soil slope.Based on the depth, location, and angle of block-soil impact marks left on the
Music performance anxiety. Refer to the British Journal of Music Education (Mar. 2014) study of music performance anxiety, Exercise 2.39 (p. 78). Scores on the Performance Anxiety Inventory (PAI) scale for participants in eight different studies are reproduced in the table.54 42 51 39 41 43 55 40
Corporate sustainability of CPA firms. Refer to the Business and Society (Mar. 2011) study on the sustainability behaviors of CPA corporations, Exercise 2.36(p. 78). Recall that the level of support for corporate sustainability (measured on a quantitative scale rangingfrom 0 to 160 points) was
Is honey a cough remedy? Refer to the Archives of Pediatrics and Adolescent Medicine (Dec. 2007) study of honey as a remedy for coughing, Exercise 2.40 (p. 79).Recall that the 105 ill children in the sample were randomly divided into three groups: those who received a dosage of an over-the-counter
Cheek teeth of extinct primates. Refer to the American Journal of Physical Anthropology (Vol. 142, 2010) study of the characteristics of cheek teeth (e.g., molars) in an extinct primate species, Exercise 2.38 (p. 78). The data on dentary depth of molars (in millimeters) for 18 cheek teeth extracted
Ranking driving performance of professional golfers.A group of Northeastern University researchers developed a new method for ranking the total driving performance of golfers on the Professional Golf Association (PGA) tour(The Sport Journal, Winter 2007). The method requires knowing a golfer’s
Symmetric or skewed? Would you expect the data sets that follow to possess relative frequency distributions that are symmetric, skewed to the right, or skewed to the left? Explain.a. The salaries of all persons employed by a large universityb. The grades on an easy testc. The grades on a difficult
Mongolian desert ants. The Journal of Biogeography (Dec.2003) published an article on the first comprehensive study of ants in Mongolia (Central Asia). Botanists placed seed baits at 11 study sites and observed the ant species attracted to each site. Some of the data recorded at each study site are
Permeability of sandstone during weathering. Natural stone, such as sandstone, is a popular building construction material. An experiment was carried out in order to better understand the decay properties of sandstone when exposed to the weather (Geographical Analysis, Vol. 42, 2010). Blocks of
Mineral flotation in water study. Refer to the Minerals Engineering (Vol. 46–47, 2013) study of the impact of calcium and gypsum on the flotation properties of silica in water, Exercise 2.48 (p. 81). The zeta potential (mV) was determined for each of 50 liquid solutions prepared without
Contact lenses for myopia. Myopia (i.e., nearsightedness)is a visual condition that affects over 100 million Americans. Two treatments that may slow myopia progression are the use of (1) corneal reshaping contact lenses and (2) bifocal soft contact lenses. In Optometry and Vision Science (Jan.,
Active nuclear power plants. The U.S. Energy Information Administration monitors all nuclear power plants operating in the United States. The table below lists the number of active nuclear power plants operating in each of a sample of 20 states.a. Find the mean, median, and mode of this data
Can there be two data sets that are different with respect to data variation but both have the same range?
What is advantage of the range as a measure of variability?
Why do we square the deviation from the mean before adding them to compute the variance?
If data set A has more variance than data set B, which one would have the lower standard deviation?
Calculate the variance and standard deviation for samples for whicha. n = 10, ax2= 84, ax = 20b. n = 40, ax2= 380, ax = 100c. n = 20, ax2= 18, ax = 17
Using only integers between −10 and 10, construct two data sets each with 10 observations such that the two sets have the same mean, but different variances. The two data sets should not have any common units.
Using only integers between −10 and 10, construct two data sets each with 10 observations such that the two sets have the same range, but different means.Moreover, the two data sets should not have any common units.
Shell lengths of sea turtles. Aquatic Biology (Vol. 9, 2010)reported on a study of green sea turtles inhabiting the Grand Cayman South Sound lagoon. The data on curved carapace(shell) length (in centimeters) for 76 captured turtles are saved in the TURTLES file. Descriptive statistics for the data
Shaft graves in ancient Greece. Refer to the American Journal of Archaeology (Jan. 2014) study of sword shaft graves in ancient Greece, Exercise 2.60 (p. 89). The number of sword shafts buried at each of 13 recently discovered grave sites is reproduced in the following table.1 2 3 1 5 6 2 4 1 2 4 2
Music performance anxiety. Refer to the British Journal of Music Education (Mar. 2014) study of music performance anxiety, Exercise 2.62 (p. 89). Scores (measured in points) on the Performance Anxiety Inventory (PAI) scale for participants in eight different studies are reproduced in the table.54
Characteristics of a rockfall. Refer to the Environmental Geology (Vol. 58, 2009) study of how far a block from a collapsing rock wall will bounce, Exercise 2.61 (p. 89).The rebound lengths (meters) for a sample of 13 rock bounces are reproduced in the table below.10.94 13.71 11.38 7.26 17.83 11.92
Is honey a cough remedy? Refer to the Archives of Pediatrics and Adolescent Medicine (Dec. 2007) study of honey as a remedy for coughing, Exercise 2.64(p. 90). The coughing improvement scores for the patients in the over-the-counter cough medicine dosage(DM) group, honey dosage group, and control
Permeability of sandstone during weathering. Refer to the Geographical Analysis (Vol. 42, 2010) study of the decay properties of sandstone when exposed to the weather, Exercise 2.69 (p. 91). Recall that slices of sandstone blocks were tested for permeability under three conditions: no exposure to
Cheek teeth of extinct primates. Refer to the American Journal of Physical Anthropology (Vol. 142, 2010) study of the characteristics of cheek teeth (e.g., molars) in an extinct primate species, Exercise 2.65 (p. 90). The data on dentary depth of molars (in millimeters) for 18 cheek teeth extracted
Active nuclear power plants. Refer to Exercise 2.72 (p. 92)and the U.S. Energy Information Administration’s data on the number of nuclear power plants operating in each of 20 states.a. Find the range, variance, and standard deviation of this data set.b. Eliminate the largest value from the data
What do you mean by a mound-shaped, symmetric distribution?
As per Chebyshev’s rule how many measurements fall within 1m - 2s, m + 2s2?
The output from a statistical computer program indicates that the mean and standard deviation of a data set consisting of 200 measurements are $1,500 and $300, respectively.a. What are the units of measurement of the variable of interest? On the basis of the units, what type of data is this,
For any set of data, what can be said about the percentage of the measurements contained in each of the following intervals?a. x - s to x + sb. x - 2s to x + 2sc. x - 3s to x + 3s The following is a sample of 25 measurements.7 6 6 11 8 9 11 9 10 8 7 7 5 9 10 7 7 7 7 9 12 10 10 8 6For a set of data
The following is a sample of 25 measurements.7 6 6 11 8 9 11 9 10 8 7 7 5 9 10 7 7 7 7 9 12 10 10 8 6a. Compute x, s2, and s for this sample.b. Count the number of measurements in the intervals x { s, x { 2s, and x { 3s. Express each count as a percentage of the total number of measurements.c.
Given a data set with a largest value of 760 and a smallest value of 135, what would you estimate the standard deviation to be? Explain the logic behind the procedure you used to estimate the standard deviation. Suppose the standard deviation is reported to be 25. Is this number reasonable?Explain.
Do social robots walk or roll? Refer to the International Conference on Social Robotics (Vol. 6414, 2010) study on the current trend in the design of social robots, Exercise 2.7(p. 66). Recall that in a random sample of social robots obtained through a Web search, 28 were built with wheels. The
Sanitation inspection of cruise ships. Refer to Exercise 2.41(p. 79) and the Centers for Disease Control and Prevention listing of the sanitation scores for 186 cruise ships. The data are saved in the SANIT file.a. Find the mean and standard deviation of the sanitation scores.b. Calculate the
Motivation of drug dealers. Researchers at Georgia State University investigated the personality characteristics of drug dealers in order to shed light on their motivation for participating in the illegal drug market (Applied Psychology in Criminal Justice, Sept. 2009). The sample consisted of 100
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