The cheetah (Acinonyx jubatus) is the fastest land mammal and is highly specialized to run down prey. The cheetah often exceeds speeds of 60 mph and, according to the online document “Cheetah Conservation in Southern Africa” (Trade & Environment Database (TED) Case Studies, Vol. 8, No. 2) by J. Urbaniak, the cheetah is capable of speeds up to 72 mph. The WeissStats site contains the top speeds, in miles per hour, for a sample of 35 cheetahs. Use the technology of your choice to do the following tasks. a. Find a 95% confidence interval for the mean top speed, μ, of all cheetahs. Assume that the population standard deviation of top speeds is 3.2 mph. b. Obtain a normal probability plot, boxplot, histogram, and stem and-leaf diagram of the data. c. Remove the outliers (if any) from the data, and then repeat part (a). d. Comment on the advisability of using the z-interval procedure on these data.
> Numerous studies have shown that high blood cholesterol leads to artery clogging and subsequent heart disease. One such study by D. Scott et al. was published in the paper “Plasma Lipids as Collateral Risk Factors in Coronary Artery Disease: A Study of 3
> In 1903, K. Pearson and A. Lee published the paper “On the Laws of Inheritance in Man. I. Inheritance of Physical Characters” (Biometrika, Vol. 2, pp. 357–462). The article examined and presented data on forearm length, in inches, for a sample of 140 men
> x¯ = 35, n = 25, σ = 4 a. Find a 95% confidence interval for the population mean. b. Identify and interpret the margin of error. c. Express the endpoints of the confidence interval in terms of the point estimate and the margin of error.
> The subterranean coruro (Spalacopus cyanus) is a social rodent that lives in large colonies in underground burrows that can reach lengths of up to 600 meters. Zoologists S. Begall and M. Gallardo studied the characteristics of the burrow systems of the s
> 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
> In the article “The $350,000 Club” (The Business Journal, Vol. 24, Issue 14, pp. 80–82), J. Trunelle et al. examined Arizona public-company executives with salaries and bonuses totaling over $350,000. The following data provide the salaries, to the neare
> R. Nielsen et al. compared 13,731 annotated genes from humans with their chimpanzee orthologs to identify genes that show evidence of positive selection. The researchers published their findings in “A Scan for Positively Selected Genes in the Genomes of
> Refer to the weight data. Note that there are 37 observations, the smallest and largest of which are 129.2 and 278.8, respectively. Apply the preceding procedure to choose classes for cutpoint grouping. Use approximately eight classes. Note: If in Step 2
> The annual update of U.S. Overseas Loans and Grants, informally known as the “Greenbook,” contains data on U.S. government monetary economic and military assistance loans. The following table shows military assistance loans, in thousands of dollars, to a
> The webpage “Bottlenose Dolphin” produced by the National Geographic Society provides information about the bottlenose dolphin. A random sample of 50 adult bottlenose dolphins have a mean length of 12.04 ft with a standard deviation of 1.03 ft. Find and
> As reported by B. Warner and J. Rutledge in the paper “Checking the Chips Ahoy! Guarantee” (Chance, Vol. 12, Issue 1, pp. 10–14), a random sample of forty-two 18-ounce bags of Chips Ahoy! cookies yielded a mean of 1261.6 chips per bag with a standard dev
> Taking the family to an amusement park has become increasingly costly according to the industry publication Amusement Business, which provides figures on the cost for a family of four to spend the day at one of America’s amusement parks. A random sample
> In 1908, W. S. Gosset published the article “The Probable Error of a Mean” (Biometrika, Vol. 6, pp. 1–25). In this pioneering paper, written under the pseudonym “Student,” Gosset introduced what later became known as Student’s t-distribution. Gosset used
> According to eMarketer, the average time spent per day with digital media in 2010 was 3 hours and 14 minutes. For last year, a random sample of 20 American adults spent the following number of hours per day with digital media. Find and interpret a 90% co
> x¯ = 30, n = 25, σ = 4 a. Find a 95% confidence interval for the population mean. b. Identify and interpret the margin of error. c. Express the endpoints of the confidence interval in terms of the point estimate and the margin of error.
> According to Scarborough Research, more than 85% of working adults commute by car. Of all U.S. cities, Washington, D.C., and New York City have the longest commute times. A sample of 30 commuters in the Washington, D.C., area yielded the following commut
> x¯ = 55, n = 16, s = 5, confidence level = 99% a. use the one-mean t-interval procedure to find a confidence interval for the mean of the population from which the sample was drawn. b. obtain the margin of error by taking half the length of the confidenc
> x¯ = 50, n = 16, s = 5, confidence level = 99% a. use the one-mean t-interval procedure to find a confidence interval for the mean of the population from which the sample was drawn. b. obtain the margin of error by taking half the length of the confidenc
> Refer to the days-to-maturity data. Note that there are 40 observations, the smallest and largest of which are 36 and 99, respectively. Apply the preceding procedure to choose classes for limit grouping. Use approximately seven classes. Note: If in Step
> As you learned at the beginning of this chapter, Z. Veselska et al. explored connections between aspects of self-perception and physical activity among adolescents. The study involved a sample of adolescents from the Slovak and Czech Republics with ages
> x¯ = 35, n = 25, s = 4, confidence level = 90% a. use the one-mean t-interval procedure to find a confidence interval for the mean of the population from which the sample was drawn. b. obtain the margin of error by taking half the length of the confidenc
> x¯ = 30, n = 25, s = 4, confidence level = 90% a. use the one-mean t-interval procedure to find a confidence interval for the mean of the population from which the sample was drawn. b. obtain the margin of error by taking half the length of the confidenc
> x¯ = 25, n = 36, s = 3, confidence level = 95% a. use the one-mean t-interval procedure to find a confidence interval for the mean of the population from which the sample was drawn. b. obtain the margin of error by taking half the length of the confidenc
> x¯ = 20, n = 36, s = 3, confidence level = 95% a. use the one-mean t-interval procedure to find a confidence interval for the mean of the population from which the sample was drawn. b. obtain the margin of error by taking half the length of the confidenc
> For the one-mean t-interval procedure, express the formula for the endpoints of a confidence interval in the form point estimate ± margin of error.
> Identify the formula for the margin of error for the estimate of a population mean when the population standard deviation is unknown.
> A simple random sample of size 17 is taken from a population with unknown standard deviation. A normal probability plot of the data reveals an outlier but is otherwise roughly linear. Can you reasonably apply the t-interval procedure? Explain your answer
> x¯ = 25, n = 36, σ = 3 a. Find a 95% confidence interval for the population mean. b. Identify and interpret the margin of error. c. Express the endpoints of the confidence interval in terms of the point estimate and the margin of error.
> A simple random sample of size 100 is taken from a population with unknown standard deviation. A normal probability plot of the data displays significant curvature but no outliers. Can you reasonably apply the t-interval procedure? Explain your answer.
> For a t-curve with df = 8, find each t-value, and illustrate your results graphically. a. The t-value having area 0.05 to its right b. t0.10 c. The t-value having area 0.01 to its left d. The two t-values that divide the area under the curve into a middl
> The exam scores for the students in an introductory statistics class are as follows. a. Group these exam scores, using the classes 30–39, 40–49, 50–59, 60–69, 70–79, 80–89, and 90–100. b. What are the widths of the classes? c. If you wanted all the class
> For a t-curve with df = 21, find each t-value, and illustrate your results graphically. a. The t-value having area 0.10 to its right b. t0.01 c. The t-value having area 0.025 to its left d. The two t-values that divide the area under the curve into a mid
> For a t-curve with df = 17, use Table IV to find each t-value. a. t0.05 b. t0.025 c. t0.005
> For a t-curve with df = 6, use Table IV to find each t-value. a. t0.10 b. t0.025 c. t0.01
> Two t-curves have degrees of freedom 12 and 20, respectively. Which one more closely resembles the standard normal curve? Explain your answer.
> Explain why there is more variation in the possible values of the studentized version of x¯ than in the possible values of the standardized version of x¯.
> An issue of Scientific American revealed that batting averages, x, of major-league baseball players are normally distributed and have a mean of 0.270 and a standard deviation of 0.031. For samples of 20 batting averages, identify the distribution of each
> 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., the weights, x, of adult green sea urchins are normally dis
> A variable of a population has a normal distribution. Suppose that you want to find a confidence interval for the population mean. a. If you know the population standard deviation, which procedure would you use? b. If you do not know the population stan
> x¯ = 20, n = 36, σ = 3 a. Find a 95% confidence interval for the population mean. b. Identify and interpret the margin of error. c. Express the endpoints of the confidence interval in terms of the point estimate and the margin of error.
> A variable has a mean of 100 and a standard deviation of 16. Four observations of this variable have a mean of 108 and a sample standard deviation of 12. Determine the observed value of the a. standardized version of x¯. b. studentized version of x¯.
> 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
> Why do you need to consider the studentized version of x¯ to develop a confidence-interval procedure for a population mean when the population standard deviation is unknown?
> Refer to Exercise 8.71. a. Determine and interpret a 99% lower confidence bound for the mean cadmium level of all Boletus pinicola mushrooms. b. Compare your one-sided confidence interval in part (a) to the (two sided) confidence interval found in Exerci
> Refer to Exercise 8.70. a. Determine and interpret a 95% upper confidence bound for the mean calcium intake of all people with incomes below the poverty level. b. Compare your one-sided confidence interval in part (a) to the (two-sided) confidence interv
> Presuming that the assumptions for a one-mean z-interval are satisfied, we have the following formulas for (1 − α) level confidence bounds for a population mean μ: - Lower confidence bound x¯ − zα · σ/√n - Upper confidence bound x¯ + zα · σ/√n Interpret
> For a fixed confidence level, show that (approximately) quadrupling the sample size is necessary to halve the margin of error.
> Suppose that a simple random sample is taken from a normal population having a standard deviation of 10 for the purpose of obtaining a 95% confidence interval for the mean of the population. a. If the sample size is 4, obtain the margin of error. b. Repe
> This exercise can be done individually or, better yet, as a class project. Gestation periods of humans are normally distributed with a mean of 266 days and a standard deviation of 16 days. a. Simulate 100 samples of nine human gestation periods each. b.
> 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,
> Refer to Exercise 8.8 and find a point estimate for the population standard deviation (i.e., the standard deviation of the variable). Data from Exercise 8.8: A simple random sample is taken from a population and yields the following data for a variable
> As reported by the U.S. Census Bureau in Educational Attainment in the United States, the percentage of adults in each state and the District of Columbia who have completed a bachelor’s degree is provided on the WeissStats site. Apply the technology of y
> The value of a statistic used to estimate a parameter is called a ____ of the parameter.
> 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
> A variable is said to have an exponential distribution or to be exponentially distributed if its distribution has the shape of an exponential curve, that is, a curve of the form y = e−x/μ/μ for x > 0, where μ is the mean of the variable. The standard dev
> 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 2000 samples of nine human gestation periods each. b. Find the sample mean of each of the
> We conducted a simulation to check the plausibility of the central limit theorem. The variable under consideration there is household size, and the population consists of all U.S. households. A frequency distribution for household size of U.S. households
> A brand of water-softener salt comes in packages marked “net weight 40 lb.” The company that packages the salt claims that the bags contain an average of 40 lb of salt and that the standard deviation of the weights is 1.5 lb. Assume that the weights are
> 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
> A variable of a population has mean μ and standard deviation σ. For a large sample size n, fill in the blanks. Justify your answers. a. Approximately % of all possible samples have means within σ/√n of the population mean, μ. b. Approximately % of all po
> A variable of a population is normally distributed with mean μ and standard deviation σ. For samples of size n, fill in the blanks. Justify your answers. a. Approximately 68% of all possible samples have means that lie within of the population mean, μ. b
> A study by M. Chen et al. titled “Heat Stress Evaluation and Worker Fatigue in a Steel Plant” (American Industrial Hygiene Association, Vol. 64, pp. 352–359) assessed fatigue in steel plant workers due to heat stress. If the mean post-work heart rate for
> As reported by the U.S. Census Bureau in Educational Attainment in the United States, the percentage of adults in each state and the District of Columbia who have completed high school is provided on the WeissStats site. Apply the technology of your choi
> Dementia is the loss of the intellectual and social abilities severe enough to interfere with judgment, behavior, and daily functioning. Alzheimer’s disease is the most common type of dementia. In the article “Living with Early Onset Dementia: Exploring
> Calcium is the most abundant mineral in the human body and has several important functions. Recommendations for calcium are provided in Dietary Reference Intakes, developed by the Institute of Medicine of the National Academy of Sciences. The recommended
> In the document Anthropometric Reference Data for Children and Adults, C. Fryer et al. present data from the National Health and Nutrition Examination Survey on a variety of human body measurements. A half-century ago, the mean height of (U.S.) women in
> An ethanol railroad tariff is a fee charged for shipments of ethanol on public railroads. The Agricultural Marketing Service publishes tariff rates for railroad-car shipments of ethanol in the Biofuel Transportation Database. Assuming that the standard d
> In the article “Job Mobility and Wage Growth” (Monthly Labor Review, Vol. 128, No. 2, pp. 33–39), A. Light examined data on employment and answered questions regarding why workers separate from their employers. According to the article, the standard devi
> In the article “A Multifactorial Intervention Program Reduces the Duration of Delirium, Length of Hospitalization, and Mortality in Delirious Patients” (Journal of the American Geriatrics Society, Vol. 53, No. 4, pp. 622–628), M. Lundstrom et al. investi
> Ciochetti et al. studied mortgage loans in the article “A Proportional Hazards Model of Commercial Mortgage Default with Originator Bias” (Journal of Real Estate and Economics, Vol. 27, No. 1, pp. 5–23). According to the article, the loan amounts of loan
> 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
> Data on salaries in the public school system are published annually in Ranking of the States and Estimates of School Statistics by the National Education Association. The mean annual salary of (public) classroom teachers is $55.4 thousand. Assume a stand
> As reported by Runner’s World magazine, the times of the finishers in the New York City 10-km run are normally distributed with a mean of 61 minutes and a standard deviation of 9 minutes. Do the following for the variable “finishing time” of finishers in
> In the article, “Length of The Beatles’ Songs” (Chance, Vol. 25, No. 1, pp. 30–33), T. Koyama discusses aspects and interpretations of the lengths of songs by The Beatles. Data on the length, in seconds, of 229 Beatles’ songs are presented on the WeissSt
> In 1905, R. Pearl published the article “Biometrical 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 a mean of 1.40 kg and
> According to the central limit theorem, for a relatively large sample size, the variable x¯ is approximately normally distributed. a. What rule of thumb is used for deciding whether the sample size is relatively large? b. Roughly speaking, what property
> Refer to Fig. 7.6 on page 306. a. Why are the four graphs in Fig. 7.6(a) all centered at the same place? b. Why does the spread of the graphs diminish with increasing sample size? How does this result affect the sampling error when you estimate a populat
> A variable of a population has mean μ and standard deviation σ. For a large sample size n, answer the following questions. a. Identify the distribution of x¯. b. Does your answer to part (a) depend on n being large? Explain your answer. c. Identify the m
> A variable of a population is normally distributed with mean μ and standard deviation σ. a. Identify the distribution of x¯. b. Does your answer to part (a) depend on the sample size? Explain your answer. c. Identify the mean and the standard deviation o
> A variable of a population has a mean of μ = 35 and a standard deviation of σ = 42. a. If the variable is normally distributed, identify the sampling distribution of the sample mean for samples of size 9. b. Can you answer part (a) if the distribution of
> A variable of a population has a mean of μ = 100 and a standard deviation of σ = 28. a. Identify the sampling distribution of the sample mean for samples of size 49. b. In answering part (a), what assumptions did you make about the distribution of the va
> 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. They also indicate
> 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
> For humans, gestation periods are normally distributed with a mean of 266 days and a standard deviation of 16 days. Suppose that you observe the gestation periods for a sample of nine humans. a. Theoretically, what are the mean and standard deviation of
> In an article titled “Great White, Deep Trouble” (National Geographic, Vol. 197(4), pp. 2–29), Peter Benchley—the author of JAWS—discussed various aspects of the Great White Shark (Carcharodon carcharias). Data on the number of pups borne in a lifetime b
> This exercise can be done individually or, better yet, as a class project. a. Use a random-number table or random-number generator to obtain a sample (with replacement) of four digits between 0 and 9. Do so a total of 50 times and compute the mean of eac
> Consider simple random samples of size n without replacement from a population of size N. a. Show that if n ≤ 0.05N, then b. Use part (a) to explain why there is little difference in the values provided by Equations (7.1) and (7.2) when the sample size i
> In Example 7.5, we used the definition of the standard deviation of a variable (Definition 3.12 on page 142) to obtain the standard deviation of the heights of the five starting players on a men’s basketball team and also the standard deviation of x¯ for
> Suppose that a simple random sample is taken without replacement from a finite population of size N. a. Show mathematically that Equations (7.1) and (7.2) are identical for samples of size 1. b. Explain in words why part (a) is true. c. Without doing any
> A statistic is said to be an unbiased estimator of a parameter if the mean of all its possible values equals the parameter; otherwise, it is said to be a biased estimator. An unbiased estimator yields, on average, the correct value of the parameter, wher
> Each year, thousands of high school students bound for college take the Scholastic Assessment Test (SAT). This test measures the verbal and mathematical abilities of prospective college students. Student scores are reported on a scale that ranges from a
> As reported by the U.S. Census Bureau in Educational Attainment in the United States, the percentage of adults in each state who have completed a bachelor’s degree is provided on the WeissStats site. Use the technology of your choice to solve the followi
> According to The Earth: Structure, Composition and Evolution (The Open University, S237), for earthquakes with a magnitude of 7.5 or greater on the Richter scale, the time between successive earthquakes has a mean of 437 days and a standard deviation of
> Alcohol consumption on college and university campuses has gained attention because undergraduate students drink significantly more than young adults who are not students. Researchers I. Balodis et al. studied binge drinking in undergraduates in the arti
> 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
> Parkinson’s disease affects internally generated movements such as movements recalled from memory. L-Dopa is a drug that is used in clinical treatment of Parkinson’s disease. In the article, “L-Dopa Induces Under-Damped Visually Guided Motor Responses in
> According to the U.S. Census Bureau publication Manufactured Housing Statistics, the mean price of new mobile homes is $65,100. Assume a standard deviation of $7200. Let x¯ denote the mean price of a sample of new mobile homes. a. For samples of size 50,
> In the article ‘‘Age at Menopause in Puebla, Mexico” (Human Biology, Vol. 75, No. 2, pp. 205 206), authors L. Sievert and S. Hautaniemi compared the age of menopause for different populations. Menopause, the last menstrual period, is a universal phenomen
> The paper ‘‘Are Babies Normal?’’ by T. Clemons and M. Pagano (The American Statistician, Vol. 53, No. 4, pp. 298–302) focused on birth weights of babies. According to the article, the mean birth weight is 3369 grams (7 pounds, 6.5 ounces) with a standard
> Research by R. Pyhala et al. shows that young adults who were born prematurely with very low birth weights (below 1500 grams) have higher blood pressure than those born at term. The study can be found in the article, “Blood Pressure Responses to Physiolo
