State the empirical rule as specialized to variables.
> 1, 2, 3, 4 a. obtain the quartiles. b. determine the interquartile range. c. find the five-number summary.
> Fill in the blank: Roughly, when arranged in increasing order, the uppermost 25% of a data set are greater than or equal.
> Fill in the blanks: Roughly, when arranged in increasing order, the middle 50% of a data set are found between ___ and ___.
> Which measure of variation is preferred when a. the mean is used as a measure of center? b. the median is used as a measure of center?
> When are the adjacent values just the minimum and maximum observations?
> Identify a use of the lower and upper limits.
> In the article “Grandchildren Raised by Grandparents, a Troubling Trend” (California Agriculture, Vol. 55, No. 2, pp. 10–17), M. Blackburn considered the rates of children (under 18 years of age) living in California with grandparents as their primary ca
> Wayne Gretzky, a retired professional hockey player, played 20 seasons in the National Hockey League (NHL), from 1980 through 1999. S. Berry explored some of Gretzky’s accomplishments in “A Statistician Reads the Sports Pages” (Chance, Vol. 16, No. 1, pp
> 1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7 a. obtain the quartiles. b. determine the interquartile range. c. find the five-number summary.
> 1, 2, 3, 4, 5, 6, 7 a. obtain the quartiles. b. determine the interquartile range. c. find the five-number summary.
> 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6 a. obtain the quartiles. b. determine the interquartile range. c. find the five-number summary.
> 1, 2, 3, 4, 5, 6 a. obtain the quartiles. b. determine the interquartile range. c. find the five-number summary.
> The members of a population are numbered 1−5. a. List the 10 possible samples (without replacement) of size 3 from this population. b. If an SRS of size 3 is taken from the population, what are the chances of selecting 1, 3, and 5? Explain your answer. c
> 1, 2, 3, 4, 5, 1, 2, 3, 4, 5 a. obtain the quartiles. b. determine the interquartile range. c. find the five-number summary.
> 1, 2, 3, 4, 5 a. obtain the quartiles. b. determine the interquartile range. c. find the five-number summary.
> 1, 2, 3, 4, 1, 2, 3, 4 a. obtain the quartiles. b. determine the interquartile range. c. find the five-number summary.
> Repeat parts (b)–(e) of Exercise 7.17 for samples of size 5. (There are six possible samples.) Data from Exercise 7.17: Each year, Forbes magazine publishes a list of the richest people in the United States. As of September 16, 2013, the six richest Ame
> Repeat parts (b)–(e) of Exercise 7.17 for samples of size 5. (There are six possible samples.) Data from Exercise 7.17: Each year, Forbes magazine publishes a list of the richest people in the United States. As of September 16, 2013, the six richest Ame
> Repeat parts (b)–(e) of Exercise 7.17 for samples of size 4. (There are 15 possible samples.) Data from Exercise 7.17: Each year, Forbes magazine publishes a list of the richest people in the United States. As of September 16, 2013, the six richest Amer
> Why should you generally expect some error when estimating a parameter (e.g., a population mean) by a statistic (e.g., a sample mean)? What is this kind of error called?
> Repeat parts (b)–(e) of Exercise 7.17 for samples of size 3. (There are 20 possible samples.) Data from Exercise 7.17: Each year, Forbes magazine publishes a list of the richest people in the United States. As of September 16, 2013, the six richest Amer
> Repeat parts (b)–(e) of Exercise 7.17 for samples of size 1. Data from Exercise 7.17: Each year, Forbes magazine publishes a list of the richest people in the United States. As of September 16, 2013, the six richest Americans and their wealth (to the ne
> What is the acronym used for simple random sampling without replacement?
> Each year, Forbes magazine publishes a list of the richest people in the United States. As of September 16, 2013, the six richest Americans and their wealth (to the nearest billion dollars) are as shown in the following table. Consider these six people a
> This exercise requires that you have done Exercises 7.11–7.15. a. Draw a graph similar to that shown in Fig. 7.3 on page 294 for sample sizes of 1, 2, 3, 4, and 5. b. What does your graph in part (a) illustrate about the impact of increasing sample size
> Repeat parts (b)–(e) of Exercise 7.11 for samples of size 5. Data from Exercise 7.11: The winner of the 2012–2013 National Basketball Association (NBA) championship was the Miami Heat. One possible starting lineup for that team is as follows. a. Find th
> Repeat parts (b)–(e) of Exercise 7.11 for samples of size 4. Data from Exercise 7.11: The winner of the 2012–2013 National Basketball Association (NBA) championship was the Miami Heat. One possible starting lineup for that team is as follows. a. Find th
> Repeat parts (b)–(e) of Exercise 7.11 for samples of size 3. Data from Exercise 7.11: The winner of the 2012–2013 National Basketball Association (NBA) championship was the Miami Heat. One possible starting lineup for that team is as follows. a. Find th
> In sampling from a population, state which type of sampling design corresponds to each of the following experimental designs: a. Completely randomized design b. Randomized block design
> Repeat parts (b)–(e) of Exercise 7.11 for samples of size 1. Data from Exercise 7.11: The winner of the 2012–2013 National Basketball Association (NBA) championship was the Miami Heat. One possible starting lineup for that team is as follows. a. Find th
> The winner of the 2012–2013 National Basketball Association (NBA) championship was the Miami Heat. One possible starting lineup for that team is as follows. a. Find the population mean height of the five players. b. For samples of size 2, construct a tab
> We have given population data for a variable. For each exercise, do the following tasks. a. Find the mean, μ, of the variable. b. For each of the possible sample sizes, construct a table and draw a dotplot for the sampling distribution of the sample mean
> Why is sampling often preferable to conducting a census for the purpose of obtaining information about a population?
> Regarding the interquartile range, a. what type of descriptive measure is it? b. what does it measure?
> As reported in Runner’s World magazine, the times of the finishers in the New York City 10-km run are normally distributed with mean 61 minutes and standard deviation 9 minutes. a. Determine the percentage of finishers who have times between 50 and 70 mi
> According to the National Health and Nutrition Examination Survey, published by the National Center for Health Statistics, the serum (noncellular portion of blood) total cholesterol level of U.S. females 20 years old or older is normally distributed with
> One of the larger species of tarantulas is the Grammostola mollicoma, whose common name is the Brazilian giant tawny red. A tarantula has two body parts. The anterior part of the body is covered above by a shell, or carapace. From a recent article by F.
> A variable is normally distributed with mean 0 and standard deviation 4. a. Determine and interpret the quartiles of the variable. b. Obtain and interpret the second decile. c. Find the value that 15% of all possible values of the variable exceed. d. Fin
> A variable is normally distributed with mean 10 and standard deviation 3. a. Determine and interpret the quartiles of the variable. b. Obtain and interpret the seventh decile. c. Find the value that 35% of all possible values of the variable exceed. d. F
> A variable is normally distributed with mean 68 and standard deviation 10. a. Determine and interpret the quartiles of the variable. b. Obtain and interpret the 99th percentile. c. Find the value that 85% of all possible values of the variable exceed. d.
> We discussed the Salk vaccine experiment. The experiment utilized a technique called double blinding because neither the children nor the doctors involved knew which children had been given the vaccine and which had been given placebo. Explain the advant
> A variable is normally distributed with mean 6 and standard deviation 2. a. Determine and interpret the quartiles of the variable. b. Obtain and interpret the 85th percentile. c. Find the value that 65% of all possible values of the variable exceed. d. F
> A variable is normally distributed with mean 0 and standard deviation 4. Find the percentage of all possible values of the variable that a. lie between −8 and 8. b. exceed −1.5. c. are less than 2.75.
> A variable is normally distributed with mean 10 and standard deviation 3. Find the percentage of all possible values of the variable that a. lie between 6 and 7. b. are at least 10. c. are at most 17.5.
> State pertinent properties of boxplots for symmetric, leftskewed, and right-skewed distributions.
> Frustrated passengers, congested streets, time schedules, and air and noise pollution are just some of the physical and social pressures that lead many urban bus drivers to retire prematurely with disabilities such as coronary heart disease and stomach d
> A variable is normally distributed with mean 68 and standard deviation 10. Find the percentage of all possible values of the variable that a. lie between 73 and 80. b. are at least 75. c. are at most 90.
> Assume that the variable under consideration has a density curve. Note that the answers required here may be only approximately correct. The area under the density curve that lies between 15 and 20 is 0.414. What percentage of all possible observations o
> A variable is normally distributed with mean 6 and standard deviation 2. Find the percentage of all possible values of the variable that a. lie between 1 and 7. b. exceed 5. c. are less than 4.
> Explain why the percentage of all possible observations of a normally distributed variable that lie within two standard deviations to either side of the mean equals the area under the standard normal curve between −2 and 2.
> Briefly, for a normally distributed variable, how do you obtain the percentage of all possible observations that lie within a specified range?
> Let 0
> In an experiment reported by J. Singer and D. Andrade in the article “Regression Models for the Analysis of Pretest/Posttest Data” (Biometrics, Vol. 53, pp. 729–735), the effect of using either a conventional or experimental (hugger) toothbrush was inves
> In this section, we mentioned that the total area under any curve representing the distribution of a variable equals 1. Explain why.
> Complete the following table.
> Is an extreme observation necessarily an outlier? Explain your answer.
> Illustrate your work with graphs. Determine the two z-scores that divide the area under the standard normal curve into a middle 0.99 area and two outside 0.005 areas.
> Illustrate your work with graphs. Determine the two z-scores that divide the area under the standard normal curve into a middle 0.90 area and two outside 0.05 areas.
> Illustrate your work with graphs. Obtain the following z-scores. a. z0.20 b. z0.06
> Assume that the variable under consideration has a density curve. Note that the answers required here may be only approximately correct. The area under the density curve that lies between 30 and 40 is 0.832. What percentage of all possible observations o
> Illustrate your work with graphs. Find the following z-scores. a. z0.03 b. z0.005
> Illustrate your work with graphs. Determine z0.015.
> Illustrate your work with graphs. Determine z0.33.
> Illustrate your work with graphs. Obtain the z-score that has area 0.70 to its right.
> Two different options are under consideration for comparing the lifetimes of four brands of flashlight battery, using 20 flashlights. a. One option is to randomly divide 20 flashlights into four groups of 5 flashlights each and then randomly assign each
> Illustrate your work with graphs. Obtain the z-score that has an area of 0.95 to its right.
> Explain why the minimum and maximum observations are added to the three quartiles to describe better the variation in a data set.
> Illustrate your work with graphs. Obtain the z-score that has area 0.80 to its left under the standard normal curve.
> Illustrate your work with graphs. Find the z-score that has an area of 0.75 to its left under the standard normal curve.
> Illustrate your work with graphs. Determine the z-score for which the area under the standard normal curve to its left is 0.01.
> Illustrate your work with graphs. Obtain the z-score for which the area under the standard normal curve to its left is 0.025.
> The total area under the following standard normal curve is divided into eight regions. a. Determine the area of each region. b. Complete the following table.
> Assume that the variable under consideration has a density curve. Note that the answers required here may be only approximately correct. The area under the density curve that lies to the right of 15 is 0.324. What percentage of all possible observations
> In each part, find the area under the standard normal curve that lies between the specified z-scores, sketch a standard normal curve, and shade the area of interest. a. −1 and 1 b. −2 and 2 c. −3 and 3
> Use Table II to obtain each shaded area under the standard normal curve.
> Use Table II to obtain each shaded area under the standard normal curve.
> In the paper “Outcomes at School Age After Postnatal Dexamethasone Therapy for Lung Disease of Prematurity” (New England Journal of Medicine, Vol. 350, No. 13, pp. 1304–1313), T. Yeh et al. studied the outcomes at school age in children who had participa
> Explain what each symbol represents. a. Σ b. n c. x¯
> Sketch a standard normal curve and shade the area of interest. Find the area under the standard normal curve that lies a. either to the left of −1 or to the right of 2. b. either to the left of −2.51 or to the right of −1.
> Sketch a standard normal curve and shade the area of interest. Find the area under the standard normal curve that lies a. either to the left of −2.12 or to the right of 1.67. b. either to the left of 0.63 or to the right of 1.54.
> Sketch a standard normal curve and shade the area of interest. Determine the area under the standard normal curve that lies between a. −0.88 and 2.24. b. −2.5 and −2. c. 1.48 and 2.72. d. −5.1 and 1.
> Sketch a standard normal curve and shade the area of interest. Determine the area under the standard normal curve that lies between a. −2.18 and 1.44. b. −2 and −1.5. c. 0.59 and 1.51. d. 1.1 and 4.2.
> Sketch a standard normal curve and shade the area of interest. Find the area under the standard normal curve that lies to the right of a. 2.02. b. −0.56. c. −4.
> Sketch a standard normal curve and shade the area of interest. Find the area under the standard normal curve that lies to the right of a. −1.07. b. 0.6. c. 0. d. 4.2.
> Sketch a standard normal curve and shade the area of interest. Determine the area under the standard normal curve that lies to the left of a. −0.87. b. 3.56. c. 5.12.
> Assume that the variable under consideration has a density curve. Note that the answers required here may be only approximately correct. The area under the density curve that lies to the left of 10 is 0.654. What percentage of all possible observations o
> Sketch a standard normal curve and shade the area of interest. Determine the area under the standard normal curve that lies to the left of a. 2.24. b. −1.56. c. 0. d. −4.
> The area under the standard normal curve that lies to the left of a z-score is always strictly between ____ and ____.
> Identify an advantage that the median and interquartile range have over the mean and standard deviation, respectively.
> In a study by A. Elliot et al., titled “Women’s Use of Red Clothing as a Sexual Signal in Intersexual Interaction” (Journal of Experimental Social Psychology, Vol. 49, Issue 3, pp. 599–602), women were studied to determine the effect of apparel color cho
> Explain how Table II is used to determine the area under the standard normal curve that lies a. to the left of a specified z-score. b. to the right of a specified z-score. c. between two specified z-scores.
> Why is the standard normal curve sometimes referred to as the z-curve?
> Property 4 of Key Fact 6.5 states that most of the area under the standard normal curve lies between −3 and 3. Use Table II to determine precisely the percentage of the area under the standard normal curve that lies between −3 and 3.
> According to Table II, the area under the standard normal curve that lies to the left of 1.96 is 0.975. Without further consulting Table II, determine the area under the standard normal curve that lies to the left of −1.96. Explain your reasoning.
> According to Table II, the area under the standard normal curve that lies to the left of 0.43 is 0.6664. Without further consulting Table II, determine the area under the standard normal curve that lies to the right of 0.43. Explain your reasoning.
> According to Table II, the area under the standard normal curve that lies to the left of −2.08 is 0.0188. Without further consulting Table II, determine the area under the standard normal curve that lies to the right of 2.08. Explain your reasoning.
> Without consulting Table II, explain why the area under the standard normal curve that lies to the right of 0 is 0.5.
> With which normal distribution is the standard normal curve associated?
> Assume that the variable under consideration has a density curve. Note that the answers required here may be only approximately correct. The percentage of all possible observations of the variable that lie to the right of 4 equals the area under its dens
> Identify by name three important groups of percentiles.
