Question: Refer to Exercise 7.8 on page

> 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

> Repeat parts (b) and (c) of Exercise 7.41 for samples of size 5. For part (b), use your answer to Exercise 7.15(b). Data from Exercise 7.15: Repeat parts (b)–(e) of Exercise 7.11 for samples of size 5. Data from Exercise 7.11: The winner of the 2012–20

> Repeat parts (b) and (c) of Exercise 7.41 for samples of size 4. For part (b), use your answer to Exercise 7.14(b). Data from Exercise 7.14: Repeat parts (b)–(e) of Exercise 7.11 for samples of size 4. Data from Exercise 7.11: The winner of the 2012–20

> Repeat parts (b) and (c) of Exercise 7.41 for samples of size 3. For part (b), use your answer to Exercise 7.13(b). Data from Exercise 7.13: Repeat parts (b)–(e) of Exercise 7.11 for samples of size 3. Data from Exercise 7.11: The winner of the 2012–20

> Repeat parts (b) and (c) of Exercise 7.41 for samples of size 1. For part (b), use your answer to Exercise 7.12(b). Data from Exercise 7.12: Repeat parts (b)–(e) of Exercise 7.11 for samples of size 1. Data from Exercise 7.11: The winner of the 2012–20

> 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. Determine the population mean height, μ, of the five players. b. Consider samples of size 2 wi

> Refer to Exercise 7.10 on page 295. a. Use your answers from Exercise 7.10(b) to determine the mean, μx¯ , of the variable x¯ for each of the possible sample sizes. b. For each of the possible sample sizes, determine the mean, μx¯ , of the variable x¯,

> The number of hospital beds available in community hospitals is decreasing. Through advancement in care and technology, hospitals are getting more efficient. However, the aging and increasingly obese and diabetic population intensifies the need. The Amer

> 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

> Refer to Exercise 7.9 on page 295. a. Use your answers from Exercise 7.9(b) to determine the mean, μx¯ , of the variable x¯ for each of the possible sample sizes. b. For each of the possible sample sizes, determine the mean, μx¯ , of the variable x¯, usi

> Refer to Exercise 7.7 on page 295. a. Use your answers from Exercise 7.7(b) to determine the mean, μx¯ , of the variable x¯ for each of the possible sample sizes. b. For each of the possible sample sizes, determine the mean, μx¯ , of the variable x¯, usi

> Refer to Exercise 7.6 on page 295. a. Use your answers from Exercise 7.6(b) to determine the mean, μx¯ , of the variable x¯ for each of the possible sample sizes. b. For each of the possible sample sizes, determine the mean, μx¯ , of the variable x¯, usi

> Refer to Exercise 7.5 on page 295. a. Use your answers from Exercise 7.5(b) to determine the mean, μx¯ , of the variable x¯ for each of the possible sample sizes. b. For each of the possible sample sizes, determine the mean, μx¯ , of the variable x¯, usi

> Refer to Exercise 7.4 on page 295. a. Use your answers from Exercise 7.4(b) to determine the mean, μx¯ , of the variable x¯ for each of the possible sample sizes. b. For each of the possible sample sizes, determine the mean, μx¯ , of the variable x¯, usi

> Refer to Exercise 7.3 on page 295. a. Use your answers from Exercise 7.3(b) to determine the mean, μx¯ , of the variable x¯ for each of the possible sample sizes. b. For each of the possible sample sizes, determine the mean, μx¯ , of the variable x¯, usi

> You have seen that the larger the sample size, the smaller the sampling error tends to be in estimating a population mean by a sample mean. This fact is reflected mathematically by the formula for the standard deviation of the sample mean: σx¯ = σ/√n. Fo

> What is another name for the standard deviation of the variable x¯? What is the reason for that name?

> According to the National Health and Nutrition Examination Survey, published by the Centers for Disease Control and Prevention, the average cholesterol level for children between 4 and 19 years of age is 165 mg/dL. A pediatrician who tested the cholester

> Explain why increasing the sample size tends to result in a smaller sampling error when a sample mean is used to estimate a population mean.

> 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

> Does the sample size have an effect on the standard deviation of all possible sample means? Explain your answer.

> Does the sample size have an effect on the mean of all possible sample means? Explain your answer.

> Why is obtaining the mean and standard deviation of x¯ a first step in approximating the sampling distribution of the sample mean by a normal distribution?

> Although, in general, you cannot know the sampling distribution of the sample mean exactly, by what distribution can you often approximate it?

> Suppose that a random sample of size 1 is to be taken from a finite population of size N. a. How many possible samples are there? b. Identify the relationship between the possible sample means and the possible observations of the variable under considera

> Suppose that a sample is to be taken without replacement from a finite population of size N. If the sample size is the same as the population size, a. how many possible samples are there? b. what are the possible sample means? c. what is the relationship

> Explain what the dotplots in part (c) of Exercises 7.17–7.22 illustrate about the impact of increasing sample size on sampling error. Data from Exercise 7.17: Each year, Forbes magazine publishes a list of the richest people in the United States. As of

> Repeat parts (b)–(e) of Exercise 7.17 for samples of size 6. What is the relationship between the only possible sample here and the population? Data from Exercise 7.17: Each year, Forbes magazine publishes a list of the richest people in the United Stat

> The Internal Revenue Service (IRS) publishes data on adjusted gross incomes in Statistics of Income, Individual Income Tax Returns. The following relative frequency histogram shows one year’s individual income tax returns for adjusted gross incomes of le

> At the beginning of this chapter, we presented a cross classification of data on eye color and hair color collected as part of a class project by students in an elementary statistics course at the University of Delaware. a. Explain what it would mean for

> We presented some information on the 12 studio albums by The Beatles, specifically, names, release dates, and number of songs per album. The following table gives the lengths, in seconds, of the songs, by album: Please Please Me (PPM), With The Beatles (

> n = 10, p = 0.2

> n = 9, p = 0.75

> n = 8, p = 0.5

> n = 6, p = 0.3

> n = 11, p = 0.75, x ≥ 8

> n = 12, p = 0.35, x ≤ 4

> n = 20, p = 0.7, x ≥ 12

> n = 7, p = 0.5, x > 3

> n = 10, p = 0.65, x < 5

> n = 9, p = 0.2, x ≤ 3

> What does it mean when sampling is done without replacement?

> n = 20, p = 0.6, x = 17

> n = 8, p = 0.35, x = 3

> n = 50, p = 0.02, x = 3

> n = 40, p = 0.99, x = 38

> n = 15, p = 0.85, x = 12

> n = 10, p = 0.4, x = 3

> In a town with 400 citizens, 100 randomly selected citizens are asked to identify their religion. The number who identify with a Christian religion is recorded.

> One hundred randomly selected U.S. parents with at least one child under the age of 18 are surveyed and asked if they have ever spanked their child. The number of parents who have spanked their child is recorded.

> A baseball player who reaches base safely 30% of the time is allowed to bat until he reaches base safely for the third time. The number of at-bats required is recorded.

> A basketball player who makes 80% of her free throws is asked to shoot free throws until she misses. The number of free- throw attempts is recorded.

> Define simple random sampling.

> Three cards are selected from a standard 52-card deck with replacement. The number of kings selected is recorded.

> Three cards are selected from a standard 52-card deck without replacement. The number of aces selected is recorded.

> A poll of 1200 registered voters is conducted in which the respondents are asked whether they believe Congress should reform Social Security.

> An experimental drug is administered to 100 randomly selected individuals, with the number of individuals responding favorably recorded.

> A random sample of 30 cars in a used car lot is obtained, and their mileages recorded.

> A random sample of 15 college seniors is obtained, and the individuals selected are asked to state their ages.

> As a rule of thumb, if______ , the probability distribution of a binomial random variable X is approximately bell shaped.

> The expected number of successes in a binomial experiment with n trials and probability of success p is______ .