Let 0 <α< 1. For a normally distributed variable, show that 100(1 − α)% of all possible observations lie within zα/2 standard deviations to either side of the mean, that is, between μ − zα/2 · σ and μ + zα/2 · σ.
> What are the parameters for a normal curve?
> True or false: The mean of a normal distribution has no effect on its spread. Explain your answer.
> Supermarkets are interested in strategies to increase temporarily the unit sales of a product. In one study, researchers compared the effect of display type and price on unit sales for a particular product. The following display types and pricing schemes
> As you learned on page 450, recent research by R. Brame et al. indicates that almost a third of Americans have been arrested by age 23, and this figure excludes arrests for minor traffic violations. Now that you have studied inferences for proportions, w
> Consider two normal distributions, one with mean −4 and standard deviation 3, and the other with mean −4 and standard deviation 6. Answer true or false to each statement and explain your answers. a. The two normal distributions have the same spread. b. T
> State the two basic properties of every density curve.
> Consider two normal distributions, one with mean −4 and standard deviation 3, and the other with mean 6 and standard deviation 3. Answer true or false to each statement and explain your answers. a. The two normal distributions have the same spread. b. Th
> Which normal distribution has a wider spread: the one with mean 1 and standard deviation 2 or the one with mean 2 and standard deviation 1? Explain your answer.
> Identify two methods for obtaining a simple random sample.
> Two normally distributed variables have the same means and the same standard deviations. What can you say about their distributions? Explain your answer.
> Precisely what is meant by the statement that a population is normally distributed?
> A variable is approximately normally distributed. If you draw a histogram of the distribution of the variable, roughly what shape will it have?
> Desert Samaritan Hospital in Mesa, Arizona, keeps records of emergency room traffic. Those records reveal that the times between arriving patients have a special type of reverse-J-shaped distribution called an exponential distribution. The records also s
> Explain in your own words why a density curve has the two properties listed.
> For humans, gestation periods are normally distributed with a mean of 266 days and a standard deviation of 16 days. a. Use the technology of your choice to simulate four random samples of 50 human gestation periods each. b. Obtain a normal probability pl
> In the journal article “Cardiac Resynchronization Therapy with or without an Implantable Defibrillator in Advanced Chronic Heart Failure” (New England Journal of Medicine, Vol. 350, pp. 2140–2150), M. Bristow et al. reported the results of a study of met
> In 1902, W. R. Macdonell published the article “On Criminal Anthropometry and the Identification of Criminals” (Biometrika,Vol. 1, pp. 177–227). Among other things, the author presented data on the left middle finger length, in centimeters. The following
> Students in an introductory statistics course at the U.S. Air Force Academy participated in Nabisco’s “Chips Ahoy! 1,000 Chips Challenge” by confirming that there were at least 1000 chips in every 18-ounce bag of cookies that they examined. As part of th
> Philosophical and health issues are prompting an increasing number of Taiwanese to switch to a vegetarian lifestyle. In the paper “LDL of Taiwanese Vegetarians Are Less Oxidizable than Those of Omnivores” (Journal of Nutrition, Vol. 130, pp. 1591–1596),
> What does Chebyshev’s rule say about the percentage of observations that lie within one standard deviation to either side of the mean? Discuss your answer.
> According to R. L. Polk & Co., the average age of passenger cars in the United States was 9.1 years in 2000. A sample of 37 passenger cars taken this year provided the ages, in years, displayed in the following table. Construct a dotplot for the ages.
> A study by researchers at the University of Maryland addressed the question of whether the mean body temperature of humans is 98.6◦F. The results of the study by P. Mackowiak et al. appeared in the article “A Critical Appraisal of 98.6◦F, the Upper Limit
> In the article “Material Culture as Memory: Combs and Cremations in Early Medieval Britain” (Early Medieval Europe, Vol. 12, Issue 2, pp. 89–128), H. Williams discussed the frequency of cremation burials found in 17 archaeological sites in eastern Englan
> In the article “Distribution of Oxygen in Surface Sediments from Central Sagami Bay, Japan: In Situ Measurements by Microelectrodes and Planar Optodes” (Deep Sea Research Part I: Oceanographic Research Papers, Vol. 52, Issue 10, pp. 1974–1987), R. Glud e
> The following table provides the daily charges, in dollars, for a sample of 15 hotels and motels operating in South Carolina. The data were found in the report South Carolina Statistical Abstract, sponsored by the South Carolina Budget and Control Board.
> In the special report “Mousetrap: The Most-Visited Shoe and Apparel E-tailers” (Footwear News, Vol. 58, No. 3, p. 18), we found the following data on the average time, in minutes, spent per user per month from January to June of one year for a sample of
> The Bureau of Labor Statistics publishes information on average annual expenditures by consumers in the Consumer Expenditure Survey. In 2010, the mean amount spent by consumers on nonalcoholic beverages was $333. A random sample of 12 consumers yielded t
> A curve has area 0.613 to the left of 65 and area 0.287 to the right of 65. Could this curve be a density curve for some variable? Explain your answer.
> Prozac (fluoxetine hydrochloride), a product of Eli Lilly and Company, is used for the treatment of depression, obsessive–compulsive disorder (OCD), and bulimia nervosa. An issue of the magazine Arthritis Today contained an advertisement reporting on the
> The following table displays finishing times, in seconds, for the winners of fourteen 1-mile thoroughbred horse races, as found in Thoroughbred Times. a. use Table III in Appendix A to construct a normal probability plot of the given data. b. use part (a
> CTIA–The Wireless Association collects data on cell phones and publishes the results in Semi-annual Wireless Survey. A sample of 15 monthly cell-phone bills gave the following data (to the nearest dollar). a. use Table III in Appendix A to construct a no
> In 1905, R. Pearl published the article “Biometrical Studies on Man. I. Variation and Correlation in Brain Weight” (Biometrika, Vol. 4, pp. 13–104) in which he studied the brain weights of Swedish males. The brain weights of a random sample of 225 Swedis
> A sample of the final exam scores in a large introductory statistics course is as follows. a. use Table III in Appendix A to construct a normal probability plot of the given data. b. use part (a) to identify any outliers. c. use part (a) to assess the no
> Assess the normality of the variable under consideration.
> Assess the normality of the variable under consideration.
> Assess the normality of the variable under consideration.
> Assess the normality of the variable under consideration.
> Assess the normality of the variable under consideration.
> Assess the normality of the variable under consideration.
> Explain how to obtain normal scores from Table III in Appendix A when a sample contains equal observations
> In a designed experiment, there are two factors. One factor has m levels and the other factor has n levels. Determine the number of treatments.
> A curve has area 0.425 to the left of 4 and area 0.585 to the right of 4. Could this curve be a density curve for some variable? Explain your answer.
> The PGA TOUR provides various statistics on performance of players in the Professional Golfers’ Association of America. For the week ending September 9, 2013, the year-to-date leader for longest average drive was Bubba Watson. For his 773 drives, he aver
> How is a normal probability plot used to detect outliers?
> Explain in detail what a normal probability plot is and how it is used to assess the normality of a variable.
> Explain why assessing the normality of a variable is often important.
> Under what circumstances is using a normal probability plot to assess the normality of a variable usually better than using a histogram, stem-and-leaf diagram, or dotplot?
> Express the kth percentile, Pk, of a normally distributed variable in terms of its mean, μ, and standard deviation, σ.
> Express the quartiles, Q1, Q2, and Q3, of a normally distributed variable in terms of its mean, μ, and standard deviation, σ.
> Desert Samaritan Hospital in Mesa, Arizona, keeps records of emergency room traffic. Those records reveal that the times between arriving patients have a mean of 8.7 minutes with a standard deviation of 8.7 minutes. Based solely on the values of these tw
> The rare booted eagle of western Europe was the focus of a study by S. Suarez et al. to identify optimal nesting habitat for this raptor. According to their paper “Nesting Habitat Selection by Booted Eagles (Hieraaetus pennatus) and Implications for Mana
> In a designed experiment, there are two factors, say, Factor A and Factor B. Factor A has four levels, say, a1, a2, a3, and a4; Factor B has two levels, say, b1 and b2. a. Construct a schematic for the treatments. b. Use part (a) to determine the number
> A sample of fifth-grade classes was studied in the journal article “Predicting Feelings of School Safety for Lower, Middle, and Upper School Students” (Applied Psychology in Criminal Justice, Vol. 7, Issue 2, pp. 59–76) by R. Bachman et al. One of the va
> In the article “Are Christian/Religious People Poor Tippers?” (Journal of Applied Social Psychology, Vol. 43, Issue 5, pp. 928–935), M. Lynn and B. Katz report that, for customers who receive bad service, the mean percentage tip is 8.56% of the bill with
> Assume that the variable under consideration has a density curve. Note that the answers required here may be only approximately correct. Given that 28.4% of all possible observations of the variable are less than 11, determine the area under the density
> Researchers S. Lesik and M. Mitchell explore the difficulty of predicting success in college-level mathematics in the article “The Investigation of Multiple Paths to Success in College-Level Mathematics” (Journal of Applied Research in Higher Education,
> Research reveals that foot length of women is normally distributed with mean 9.58 inches and standard deviation 0.51 inch. This distribution is useful to shoe manufacturers, shoe stores, and related merchants because it permits them to make informed deci
> Refer to Example. The heights of the 3264 female students attending midwestern college are approximately normally distributed with mean 64.4 inches and standard deviation 2.4 inches. Thus, we can use the normal distribution with μ = 64.4 and σ = 2.4 to a
> The A. C. Nielsen Company reported in the Nielsen Report on Television that the mean weekly television viewing time for children aged 2–6 years is 24.85 hours. Assume that the weekly television viewing times of such children are normally distributed with
> In 1905, R. Pearl published the article “Bio metrical Studies on Man. I. Variation and Correlation in Brain Weight” (Biometrika, Vol. 4, pp. 13–104). According to the study, brain weights of Swedish men are normally distributed with mean 1.40 kg and stan
> In the article “Assessing Friendship Motivation During Preadolescence and Early Adolescence” (Journal of Early Adolescence, Vol. 25, No. 3, pp. 367–385), J. Richard and B. Schneider described the properties of the Friendship Motivation Scale for Children
> A preliminary behavioral study of the Jingdong black gibbon, a primate endemic to the Wuliang Mountains in China, found that the mean song bout duration in the wet season is 12.59 minutes with a standard deviation of 5.31 minutes. [SOURCE: L. Sheeran et
> G. Wittemeyer et al. studied demographic data on African elephants living in Kenya in the article “Comparative Demography of an At-Risk African Elephant Population” (PLOS ONE, Vol. 8. No. 1). Based on this study, we will assume that the time between preg
> 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. F. Costa and F. Perez–Miles
> In a designed experiment, there are two factors, say, Factor A and Factor B. Factor A has three levels, say, a1, a2, and a3; Factor B has four levels, say, b1, b2, b3, and b4. a. Construct a schematic for the treatments similar to Table 1.8 on page 27. b
> Umbilical cord blood analysis immediately after delivery is one way to measure the health of an infant after birth. Researchers G. Natalucci et al. used it as a predictor of brain maturation of preterm infants in the article “Functional Brain Maturation
> From the paper “Effects of Chronic Nitrate Exposure on Gonad Growth in Green Sea Urchin Strongylocentrotus droebachiensis” (Aquaculture, Vol. 242, No. 1–4, pp. 357– 363) by S. Siikavuopio et al., we found that weights of adult green sea urchins are norma
> Assume that the variable under consideration has a density curve. Note that the answers required here may be only approximately correct. Given that 33.6% of all possible observations of the variable exceed 8, determine the area under the density curve th
> What is a density curve?
> The National Center for Education Statistics publishes information about school enrollment in Digest of Education Statistics. According to that document, 85.3% of students attend public schools, 27.9% of students attend college, and 20.1% of students att
> According to America’s Families and Living Arrangements, published by the U.S. Census Bureau, 51.5% of U.S. adults are female, 10.4% of U.S. adults are divorced, and 6.0% of U.S. adults are divorced females. For a U.S. adult selected at random, let F = e
> In the game of craps, a player rolls two balanced dice. Thirty-six equally likely outcomes are possible. Let A = event the sum of the dice is 7, B = event the sum of the dice is 11, C = event the sum of the dice is 2, D = event the sum of the dice is 3,
> The U.S. Bureau of Citizenship and Immigration Services collects and reports information about naturalized persons in Statistical Yearbook. Following is an age distribution for persons naturalized during one year. Suppose that one of these naturalized pe
> The Association of American Universities published a report titled “Looking More Closely at Student Debt.” This report explores the issue of the cost of a college education and its impact on student loan debt. Using information from a credit reporting co
> We have provided simple data sets for you to practice the basics of finding measures of center. 4, 2, 0, 2, 2 a. mean. b. median. c. mode(s).
> Use the complementation rule to find the probability that one of these Type 4A development corporations selected at random has receipts a. of at least $25,000. b. less than $500,000.
> In a designed experiment, there is one factor with five levels. How many treatments are there?
> Use the complementation rule to find the probability that a randomly selected U.S. senator is a. 50 years old or older. b. under 70 years old.
> According to the Religious Landscape Survey, sponsored by the Pew Forum on Religion and Public Life, a distribution of religious affiliation among U.S. adults is as shown in the following table. Find the probability that the religious affiliation of a ra
> From the document “Computer and Internet Use in the United States: Population Characteristics” (Current Population Survey) by T. File, we obtained the following percentage distribution of household income for U.S. households with Internet access. Suppose
> The U.S. Coast Guard maintains a database of the number, source, and location of oil spills in U.S. navigable and territorial waters. The following is a probability distribution for location of oil spill events. Apply the special addition rule to find th
> Interpret each of the following probability statements, using the frequentist interpretation of probability. a. The probability of being dealt a pocket pair in Texas hold’em is 0.059. b. If a balanced dime is tossed three times, the probability that it w
> The National Institute on Drug Abuse issued the report Monitoring the Future, which addressed the issue of drinking, cigarette, and smokeless tobacco use for eighth, tenth, and twelfth graders. During one year, 12,900 twelfth graders were asked the quest
> The State of Texas maintains records pertaining to the economic development of corporations in the state. From the Economic Development Corporation Report, published by the Texas Comptroller of Public Accounts, we obtained the following frequency distrib
> According to the Congressional Directory, the official directory of the U.S. Congress, prepared by the Joint Committee on Printing, the age distribution for senators in the U.S. Congress as of Fall 2013, is as shown in the following table. Suppose that a
> R. Reifen et al. studied various nutritional measures of Ethiopian school children and published their findings in the paper “Ethiopian-Born and Native Israeli School Children Have Different Growth Patterns” (Nutrition, Vol. 19, pp. 427– 431). The study,
> Suppose that A and B are events such that P(A) = 1/4, P(B) = 1/3, and P(A or B) = 1/2. a. Are events A and B mutually exclusive? Explain your answer. b. Find P(A & B).
> Suppose that A and B are events such that P(A) = 1/3, P(A or B) = 1/2, and P(A & B) = 1/10. a. Are events A and B mutually exclusive? Explain your answer. b. Find P(B).
> In a designed experiment, there is one factor with four levels. How many treatments are there?
> Suppose that A and B are events such that P(A) = 0.84, P(B) = 0.46, and P(A & B) = 0.38. Determine P(A or B).
> Suppose that C and D are events such that P(C) = 0.35, P(D) = 0.40, and P(C & D) = 0.30. Determine P(C or D).
> Let F be an event with probability 0.72. Find the probability of (not F).
> Let E be an event with probability 0.35. Find the probability of (not E).
> Suppose that C and D are mutually exclusive events such that P(C) = 0.14 and P(D) = 0.32. Determine P(C or D).
> Interpret each of the following probability statements, using the frequentist interpretation of probability. a. The probability is 0.487 that a newborn baby will be a girl. b. The probability of a single ticket winning a prize in the Powerball lottery is
> Suppose that A and B are mutually exclusive events such that P(A) = 0.25 and P(B) = 0.40. Determine P(A or B).
> The cheetah (Acinonyx jubatus) is the fastest land mammal and is highly specialized to run down prey. The cheetah often exceeds speeds of 60 miles per hour (mph) and, according to the online document “Cheetah Conservation in Southern Africa” (Trade & Env
> A bowl contains 12 poker chips—3 red, 4 white, and 5 blue. One of these poker chips is selected at random from the bowl. Let B denote the event that the chip selected is blue. Find the probability that a blue chip is selected, and express your answer in
> An ordinary deck of playing cards has 52 cards. There are four suits—spades, hearts, diamonds, and clubs— with 13 cards in each suit. Spades and clubs are black; hearts and diamonds are red. One of these cards is selected at random. Let R denote the even
> Let A, B, and C be events of a sample space. Complete the following table.
