Assume that the population standard deviation is known and decide whether use of the z-interval procedure to obtain a confidence interval for the population mean is reasonable. Explain your answers. The sample data contain no outliers, the sample size is 250, and the variable under consideration is far from being normally distributed.
> A simple random sample is taken from a population and yields the following data for a variable of the population: Find a point estimate for the population mean (i.e., the mean of the variable).
> Refer to Exercise 8.77. a. Determine the margin of error for the 95% confidence interval. b. Determine the margin of error for the 90% confidence interval. c. Compare the margins of error found in parts (a) and (b). d. What principle is being illustrated
> Multi-sensor data loggers were attached to free-ranging American alligators in a study conducted by Y. Watanabe for the article “Behavior of American Alligators Monitored by Multi-Sensor Data Loggers” (Aquatic Biology, Vol. 18, pp. 1–8). The mean duratio
> An issue with legalization of medical marijuana is “diversion,” the process in which medical marijuana prescribed for one person is given, traded, or sold to someone who is not registered for medical marijuana use. Researchers S. Sautel et al. study the
> Refer to Exercise 8.70. a. Find a 90% confidence interval for μ. b. Why is the confidence interval you found in part (a) shorter than the one in Exercise 8.70? c. Draw a graph similar to that shown in Fig. 8.6 on page 326 to display both confidence inter
> Refer to Exercise 8.69. a. Find a 99% confidence interval for μ. b. Why is the confidence interval you found in part (a) longer than the one in Exercise 8.69? c. Draw a graph like that shown in Fig. 8.6 on page 326 to display both confidence intervals. d
> The Rolling Stones, a rock group formed in the 1960s, have toured extensively in support of new albums. Pollstar has collected data on the earnings from the Stones’s North American tours. For 30 randomly selected Rolling Stones concerts, the mean gross e
> A. Ehlers et al. studied various characteristics of political prisoners from the former East Germany and presented their findings in the paper “Posttraumatic Stress Disorder (PTSD) Following Political Imprisonment: The Role of Mental Defeat, Alienation,
> Snakes deposit chemical trails as they travel through their habitats. These trails are often detected and recognized by lizards, which are potential prey. The ability to recognize their predators via tongue flicks can often mean life or death for lizards
> In the special report “Mouse trap: 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
> Cadmium, a heavy metal, is toxic to animals. Mushrooms, however, are able to absorb and accumulate cadmium at high concentrations. The Czech and Slovak governments have set a safety limit for cadmium in dry vegetables at 0.5 part per million (ppm). M. Me
> Calcium is the most abundant mineral in the human body and has several important functions. Most body calcium is stored in the bones and teeth, where it functions to support their structure. Recommendations for calcium are provided in Dietary Reference I
> A simple random sample is taken from a population and yields the following data for a variable of the population: Find a point estimate for the population mean (i.e., the mean of the variable).
> Data on investments in the high-tech industry by venture capitalists are compiled by VentureOne Corporation and published in America’s Network Telecom Investor Supplement. A random sample of 18 venture-capital investments in the fiber optics business sec
> x¯ = 55, n = 16, σ = 5, confidence level = 99% a. Use the one-mean z-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, σ = 5, confidence level = 99% a. Use the one-mean z-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¯ = 35, n = 25, σ = 4, confidence level = 90% a. Use the one-mean z-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, σ = 4, confidence level = 90% a. Use the one-mean z-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, σ = 3, confidence level = 95% a. Use the one-mean z-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, σ = 3, confidence level = 95% a. Use the one-mean z-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
> The Florida State Center for Health Statistics reported in Women and Cardiovascular Disease Hospitalizations that, for cardiovascular hospitalizations, the mean age of women is 71.9 years. At one hospital, a random sample of 20 female cardiovascular pati
> The margin of error is also called the maximum error of the estimate. Explain why.
> Formula 8.2 provides a method for computing the sample size required to obtain a confidence interval with a specified confidence level and margin of error. The number resulting from the formula should be rounded up to the nearest whole number. a. Why do
> Answer true or false to each statement concerning a confidence interval for a population mean. Give reasons for your answers. The confidence level can be determined if you know only the margin of error, population standard deviation, and sample size.
> Suppose that you take 500 simple random samples from a population and that, for each sample, you obtain a 90% confidence interval for an unknown parameter. Approximately how many of those confidence intervals will not contain the value of the unknown par
> Answer true or false to each statement concerning a confidence interval for a population mean. Give reasons for your answers. The margin of error can be determined if you know only the confidence level, population standard deviation, and sample size.
> Answer true or false to each statement concerning a confidence interval for a population mean. Give reasons for your answers. The confidence level can be determined if you know only the margin of error.
> Answer true or false to each statement concerning a confidence interval for a population mean. Give reasons for your answers. The margin of error can be determined if you know only the confidence level.
> Answer true or false to each statement concerning a confidence interval for a population mean. Give reasons for your answers. The confidence interval can be obtained if you know only the margin of error and the sample mean.
> Answer true or false to each statement concerning a confidence interval for a population mean. Give reasons for your answers. The confidence interval can be obtained if you know only the margin of error.
> Answer true or false to each statement concerning a confidence interval for a population mean. Give reasons for your answers. The margin of error can be determined if you know only the length of the confidence interval.
> Refer to the speed data given in Exercise 2.89. a. Construct a table for the data, based on the classes specified in Exercise 2.89. Interpret your results. b. Construct an ogive for the data. In constructing a stem-and leaf diagram, rounding or truncatin
> Answer true or false to each statement concerning a confidence interval for a population mean. Give reasons for your answers. The length of the confidence interval can be determined if you know only the margin of error.
> A confidence interval for a population mean has a length of 162.6. a. Determine the margin of error. b. If the sample mean is 643.1, determine the confidence interval. c. Construct a graph that illustrates your results.
> A confidence interval for a population mean has length 20. a. Determine the margin of error. b. If the sample mean is 60, obtain the confidence interval. c. Construct a graph that illustrates your results
> A confidence interval for a population mean has a margin of error of 0.047. a. Determine the length of the confidence interval. b. If the sample mean is 0.205, obtain the confidence interval. c. Construct a graph that illustrates your results.
> Suppose that you take 1000 simple random samples from a population and that, for each sample, you obtain a 95% confidence interval for an unknown parameter. Approximately how many of those confidence intervals will contain the value of the unknown parame
> A confidence interval for a population mean has a margin of error of 3.4. a. Determine the length of the confidence interval. b. If the sample mean is 52.8, obtain the confidence interval. c. Construct a graph that illustrates your results.
> Explain the effect on the margin of error and hence the effect on the accuracy of estimating a population mean by a sample mean. Decreasing the sample size while keeping the same confidence Level.
> Explain the effect on the margin of error and hence the effect on the accuracy of estimating a population mean by a sample mean. Increasing the confidence level while keeping the same sample Size.
> Explain the effect on the margin of error and hence the effect on the accuracy of estimating a population mean by a sample mean. Decreasing the confidence level while keeping the same sample size.
> Explain the effect on the margin of error and hence the effect on the accuracy of estimating a population mean by a sample mean. Increasing the sample size while keeping the same confidence level.
> Refer to the energy consumption data given in Exercise 2.84. a. Construct a table similar to Table 2.14 for the data, based on the classes specified in Exercise 2.84. Interpret your results. b. Construct an ogive for the data. Data from Problem 2.84: Us
> Explain why the margin of error determines the accuracy with which a sample mean estimates a population mean.
> Discuss the relationship between the margin of error and the standard error of the mean.
> Suppose that you will be taking a random sample from a population and that you intend to find a 95% confidence interval for the population mean, μ. Which sample size, 25 or 50, will result in the confidence interval giving a more accurate estimate of μ?
> Suppose that you have obtained data by taking a random sample from a population and that you intend to find a confidence interval for the population mean, μ. Which confidence level, 95% or 99%, will result in the confidence interval giving a more accurat
> Suppose that you have obtained data by taking a random sample from a population. Before performing a statistical inference, what should you do?
> Express the form of most of the confidence intervals that you will encounter in your study of statistics in terms of “point estimate” and “margin of error.”
> Assume that the population standard deviation is known and decide whether use of the z-interval procedure to obtain a confidence interval for the population mean is reasonable. Explain your answers. The distribution of the variable under consideration is
> Assume that the population standard deviation is known and decide whether use of the z-interval procedure to obtain a confidence interval for the population mean is reasonable. Explain your answers. The sample data contain no outliers, the variable under
> Assume that the population standard deviation is known and decide whether use of the z-interval procedure to obtain a confidence interval for the population mean is reasonable. Explain your answers. The sample data contain outliers, and the sample size i
> As mentioned, for relative-frequency polygons, we label the horizontal axis with class marks in limit grouping and class midpoints in cutpoint grouping. How do you think the horizontal axis is labeled in single-value grouping? Cumulative information can
> Assume that the population standard deviation is known and decide whether use of the z-interval procedure to obtain a confidence interval for the population mean is reasonable. Explain your answers. The variable under consideration is very close to being
> Assume that the population standard deviation is known and decide whether use of the z-interval procedure to obtain a confidence interval for the population mean is reasonable. Explain your answers. The variable under consideration is very close to being
> What is meant by saying that a statistical procedure is robust?
> Refer to Procedure. a. Explain in detail the assumptions required for using the z-interval procedure. b. How important is the normality assumption? Explain your answer.
> For what is normal population an abbreviation?
> In developing Procedure 8.1, we assumed that the variable under consideration is normally distributed. a. Explain why we needed that assumption. b. Explain why the procedure yields an approximately correct confidence interval for large samples, regardles
> When estimating an unknown parameter, what does the margin of error indicate?
> What is meant by saying that a 1 − α confidence interval is a. exact? b. approximately correct?
> Find the confidence level and α for a. an 85% confidence interval. b. a 95% confidence interval.
> Find the confidence level and α for a. a 90% confidence interval. b. a 99% confidence interval.
> Construct a relative-frequency polygon for the speed data given in Exercise 2.89. Use the classes specified in that exercise. Data from Exercise 2.89: Use the specified grouping method to a. determine a frequency distribution. b. obtain a relative-frequ
> Use the data in Table 8.1 on page 315 to obtain a 68% confidence interval for the mean price of all new mobile homes.
> Use the data in Table 8.1 to obtain a 99.7% confidence interval for the mean price of all new mobile homes.
> Information on serum total cholesterol level is published by the Centers for Disease Control and Prevention in National Health and Nutrition Examination Survey. A simple random sample of 12 U.S. females 20 years old or older provided the following data o
> A tarantula has two body parts. The anterior part of the body is covered above by a shell, or carapace. In the paper “Reproductive Biology of Uruguayan Theraphosids” (The Journal of Arachnology, Vol. 30, No. 3, pp. 571–587), F. Costa and F. Perez–Miles d
> The American Express Retail Index provides information on budget amounts for home improvements. The following table displays the budgets, in dollars, of 45 randomly sampled home improvement jobs in the United States. a. Determine a point estimate for the
> Consumer Reports provides information on new automobile models—including price, mileage ratings, engine size, body size, and indicators of features. A simple random sample of 35 new models yielded the following data on fuel tank capacity, in gallons. a.
> Assume that σ = 2.4. a. Obtain a 95% confidence interval for the mean number of young per litter of all female eastern cottonmouths. b. Interpret your result in part (a). c. Does the mean number of young per litter of all female eastern cottonmouths lie
> What is a confidence-interval estimate of a parameter? Why is such an estimate superior to a point estimate?
> Assume that recent wedding costs in the United States are normally distributed with a standard deviation of $8100. a. Determine a 95% confidence interval for the mean cost, μ, of all recent U.S. weddings. b. Interpret your result in part (a). c. Does the
> In the article “The Eastern Cottonmouth (Agkistrodon piscivorus) at the Northern Edge of Its Range” (Journal of Herpetology, Vol. 29, No. 3, pp. 391–398), C. Blem and L. Blem examined the reproductive characteristics of the eastern cottonmouth, a once wi
> Construct a relative frequency polygon for the energy-consumption data given in Exercise 2.84. Use the classes specified in that exercise. Data from Exercise 2.84: Use the specified grouping method to a. determine a frequency distribution. b. obtain a r
> According to Bride’s Magazine, getting married these days can be expensive when the costs of the reception, engagement ring, bridal gown, pictures—just to name a few—are included. A simple random sample of 20 recent U.S. weddings yielded the following da
> x¯ = 55, n = 16, σ = 5 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.
> With the advent of highspeed computing, new procedures have been developed that permit statistical inferences to be performed under less restrictive conditions than those of classical procedures. Bootstrap confidence intervals constitute one such collect
> Examine one-sided confidence intervals. In a national poll of 1039 U.S. adults, conducted November 7–10, 2013, Gallup asked “Roughly how much money do you think you personally will spend on Christmas gifts this year?”. The data provided on the WeissStat
> x¯ = 50, n = 16, σ = 5 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.
> Examine one-sided confidence intervals. In the article “Sweetening Statistics—What M&M’s Can Teach Us” (Minitab Inc., August 2008), M. Paret and E. Martz discussed several statistical analyses that they performed on bags of M&Ms. The authors took a rando
> Examine one-sided confidence intervals. Refer to Exercise 8.130. a. Find and interpret a 90% lower confidence bound for last year’s mean time spent per day with digital media by American adults. b. Compare your one-sided confidence interval in part (a) t
> Examine one-sided confidence intervals. Refer to Exercise 8.129. a. Determine and interpret a 90% upper confidence bound for the mean commute time of all commuters in Washington, DC. b. Compare your one-sided confidence interval in part (a) to the (two s
> Examine one-sided confidence intervals. Presuming that the assumptions for a one-mean t-interval are satisfied, we have the following formulas for (1 − α)-level confidence bounds for a population mean μ: - Lower confidence bound: x¯ − tα · s/ √n - Upper
> An issue of Scientific American revealed that the batting averages of major-league baseball players are normally distributed with mean .270 and standard deviation .031. a. Simulate 2000 samples of five batting averages each. b. Determine the sample mean
> The following bivariate data on age (in years) and gender were obtained from the students in a freshman calculus course. The data show, for example, that the first student on the list is 21 years old and is a male. a. Group these data in the following co
> Let 0
> Appendix A contains degrees of freedom from 1 to 75 consecutively but then contains only selected degrees of freedom. a. Why couldn’t we provide entries for all possible degrees of freedom? b. Why did we construct the table so that consecutive entries ap
> A city planner working on bikeways designs a questionnaire to obtain information about local bicycle commuters. One of the questions asks how long it takes the rider to pedal from home to his or her destination. A sample of local bicycle commuters yields
> 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
