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Elementary Statistics 8th Edition Neil A. Weiss - Solutions

Refer to Procedure 8.1. a. Explain in detail the assumptions required for using the z-interval procedure. b. How important is the normality assumption? Explain your answer.
What is a confidence-interval estimate of a parameter? Why is such an estimate superior to a point estimate?
In each part, assume that the population standard deviation is known. Decide whether use of the z-interval procedure to obtain a confidence interval for the population mean is reasonable. Explain your answers. a. The variable under consideration is very close to being normally distributed, and the
In each part, assume that the population standard deviation is known. Decide whether use of the z-interval procedure to obtain a confidence interval for the population mean is reasonable.Explain your answers.a. The sample data contain no outliers, the variable under consideration is roughly
Suppose that you have obtained data by taking a random sample from a population. Before performing a statistical inference, what should you do?
We provide a sample mean, sample size, population standard deviation, and confidence level. In each case, use the one-mean z-interval procedure to find a confidence interval for the mean of the population from which the sample was drawn.x-bar = 20, n = 36, σ = 3, confidence level = 95%
x-bar = 25, n = 36, σ = 3, confidence level = 95%We provide a sample mean, sample size, population standard deviation, and confidence level. In each case, use the one-mean z-interval procedure to find a confidence interval for the mean of the population from which the sample was drawn.
x-bar = 30, n = 25, σ = 4, confidence level = 90% We provide a sample mean, sample size, population standard deviation, and confidence level. In each case, use the one-mean z-interval procedure to find a confidence interval for the mean of the population from which the sample was drawn.
x-bar = 35, n = 25, σ = 4, confidence level = 90% We provide a sample mean, sample size, population standard deviation, and confidence level. In each case, use the one-mean z-interval procedure to find a confidence interval for the mean of the population from which the sample was drawn.
x-bar = 50, n = 16, σ = 5, confidence level = 99% We provide a sample mean, sample size, population standard deviation, and confidence level. In each case, use the one-mean z-interval procedure to find a confidence interval for the mean of the population from which the sample was drawn.
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 data on wedding costs, in dollars.a. Use the
x-bar = 55, n = 16, σ = 5, confidence level = 99% We provide a sample mean, sample size, population standard deviation, and confidence level. In each case, use the one-mean z-interval procedure to find a confidence interval for the mean of the population from which the sample was drawn.
Data on investments in the high-tech industry by venture capitalists are compiled by Venture One Corporation and published in America's Network Telecom Investor Supplement. A random sample of 18 venture capital investments in the fiber optics business sector yielded the following data, in millions
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 Intakes, developed by the Institute 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. Melgar et al. measured the cadmium levels in a
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. Scientists from the University of Antwerp
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, and Perceived Permanent Change" (Journal of
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 earnings is $2.27 million. Assuming a
Refer to Exercise 8.31. 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 8.31? c. Draw a graph similar to that shown in Fig. 8.5 on page 315 to display both confidence intervals. d. Which confidence interval yields a
Refer to Exercise 8.32. 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 8.32? c. Draw a graph similar to that shown in Fig. 8.5 on page 315 to display both confidence intervals. d. Which confidence interval yields a
The Bureau of Justice Statistics provides information on prison sentences in the document National Corrections Reporting Program. A random sample of 20 maximum sentences for murder yielded the data, in months, presented on the WeissStats CD. Use the technology of your choice to do the following.a.
According to the document All About Diabetes, found on the Web site of the American Diabetes Association, ". . .diabetes is a disease in which the body does not produce or properly use insulin, a hormone that is needed to convert sugar, starches, and other food into energy needed for daily life." A
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 of the Normal Body Temperature, and
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, conducted in Azezo, North West Ethiopia,
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.
The U.S. Census Bureau compiles data on family size and presents its findings in Current Population Reports. Suppose that 500 U.S. families are randomly selected to estimate the mean size, Î¼, of all U.S. families. Further suppose that the results are as shown in the following
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. For each sample in part (a), obtain a 95%
Refer to Exercise 8.32. 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 interval found in Exercise 8.32(a).
Refer to Exercise 8.33. 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 Exercise 8.33.
Refer to Exercise 8.3. Assume that recent wedding costs in the United States are normally distributed with a standard deviation of $8100. a. Determine a 95.44% confidence interval for the mean cost, μ, of all recent U.S. weddings. b. Interpret your result in part (a). c. Does the mean cost of all
In each part, explain the effect on the margin of error and hence the effect on the precision of estimating a population mean by a sample mean. a. Increasing the confidence level while keeping the same sample size. b. Increasing the sample size while keeping the same confidence level.
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 similar to Fig. 8.6 on page 320.
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 similar to Fig. 8.6 on page 320.
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 similar to Fig. 8.6 on page 320.
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 similar to Fig. 8.6 on page 320.
Answer true or false to each statement concerning a confidence interval for a population mean. Give reasons for your answers. a. The length of a confidence interval can be determined if you know only the margin of error. b. The margin of error can be determined if you know only the length of the
Answer true or false to each statement concerning a confidence interval for a population mean. Give reasons for your answers. a. The margin of error can be determined if you know only the confidence level. b. The confidence level can be determined if you know only the margin of error. c. The margin
Formula 8.1 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 you want a whole number? b. Why do you round
Refer to Exercise 8.4. Assume that Ïƒ = 2.4.a. Obtain an approximate 95.44% confidence interval for the mean number of young per litter of all female eastern cottonmouths. b. Interpret your result in part (a). c. Why is the 95.44% confidence interval that you obtained in part (a) not
J. McWhorter et al. of the College of Health Sciences at the University of Nevada, Las Vegas, studied physical therapy students during their graduate-school years. The researchers were interested in the fact that, although graduate physical-therapy students are taught the principles of fitness,
In the paper "Persistent Pulmonary Hypertension of the Neonate and Asymmetric Growth Restriction" (Obstetrics & Gynecology, Vol. 91, No. 3, pp. 336-341), M. Williams et al. reported on a study of characteristics of neonates. Infants treated for pulmonary hypertension, called the PH group, were
In Exercise 8.31, you found a 95% confidence interval for the mean amount of all venture-capital investments in the fiber optics business sector to be from $5.389 million to $7.274 million. Obtain the margin of error by a. Taking half the length of the confidence interval. b. Using the formula in
In Exercise 8.35, you found a 95% confidence interval of 18.8 months to 48.0 months for the mean duration of imprisonment, μ, of all East German political prisoners with chronic PTSD. a. Determine the margin of error, E. b. Explain the meaning of E in this context in terms of the accuracy of the
In Exercise 8.36, you found a 99% confidence interval of $2.03 million to $2.51 million for the mean gross earnings of all Rolling Stones concerts. a. Determine the margin of error, E. b. Explain the meaning of E in this context in terms of the accuracy of the estimate. c. Find the sample size
Consider again the problem of estimating the mean age, μ, of all people in the civilian labor force. In Example 8.7 on page 322, we found that a sample size of 2250 is required to have a margin of error of 0.5 year and a 95% confidence level. Suppose that, due to financial constraints, the largest
Consider again the problem of estimating the mean age, μ, of all people in the civilian labor force. In Example 8.7 on page 322, we found that a sample size of 2250 is required to have a margin of error of 0.5 year and a 95% confidence level. Suppose that, due to financial constraints, the largest
Professor Thomas Stanley of Georgia State University has surveyed millionaires since 1973. Among other information, Professor Stanley obtains estimates for the mean age, μ, of all U.S. millionaires. Suppose that one year's study involved a simple random sample of 36 U.S. millionaires whose mean
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. Find a point estimate for the mean fuel tank
The U.S. Census Bureau estimates the mean value of the land and buildings per corporate farm. Those estimates are published in the Census of Agriculture. Suppose that an estimate, x-bar, is obtained and that the margin of error is $1000. Does this result imply that the true mean, μ, is within
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. Repeat part (a) for a sample size of 16. c. Can
For a fixed confidence level, show that (approximately) quadrupling the sample size is necessary to halve the margin of error. (Hint: Use Formula 8.1 on page 321.)
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-bar. b. Studentized version of x-bar.
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 variable.a.b.
Explain why there is more variation in the possible values of the studentized version of x-bar than in the possible values of the standardized version of x-bar.
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 population mean budget, Î¼, for such home
Two t-curves have degrees of freedom 12 and 20, respectively. Which one more closely resembles the standard normal curve? Explain your answer.
For a t-curve with df = 6, use Table IV to find each t-value. a. t0.10 b. t0.025 c. t0.01
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 = 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 (A t-curve is symmetric about 0.) d. The two t-values that divide the area under the curve into a middle 0.90
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 (A t-curve is symmetric about 0.) d. The two t-values that divide the area under the curve into a middle 0.95 area
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.
x-bar = 20, n = 36, s = 3, confidence level = 95% We have provided a sample mean, sample size, sample standard deviation, and confidence level. In each case, use the one-mean t-interval procedure to find a confidence interval for the mean of the population from which the sample was drawn.
x-bar = 25, n = 36, s = 3, confidence level = 95% We have provided a sample mean, sample size, sample standard deviation, and confidence level. In each case, use the one-mean t-interval procedure to find a confidence interval for the mean of the population from which the sample was drawn.
x-bar = 30, n = 25, s = 4, confidence level = 90% We have provided a sample mean, sample size, sample standard deviation, and confidence level. In each case, use the one-mean t-interval procedure to find a confidence interval for the mean of the population from which the sample was drawn.
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 discussed a large species of tarantula whose
x-bar = 35, n = 25, s = 4, confidence level = 90% We have provided a sample mean, sample size, sample standard deviation, and confidence level. In each case, use the one-mean t-interval procedure to find a confidence interval for the mean of the population from which the sample was drawn.
x-bar = 50, n = 16, s = 5, confidence level = 99% We have provided a sample mean, sample size, sample standard deviation, and confidence level. In each case, use the one-mean t-interval procedure to find a confidence interval for the mean of the population from which the sample was drawn.
x-bar = 55, n = 16, s = 5, confidence level = 99% We have provided a sample mean, sample size, sample standard deviation, and confidence level. In each case, use the one-mean t-interval procedure to find a confidence interval for the mean of the population from which the sample was drawn.
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 commute times, in minutes.a. Find a 90% confidence
According to Communications Industry Forecast, published by Veronis Suhler Stevenson of New York, NY, the average person watched 4.55 hours of television per day in 2005. A random sample of 20 people gave the following number of hours of television watched per day for last year.a. Find a 90%
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 the following data set, which gives the
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 of 25 families of four that attended
In the paper "A Randomized Trial of Intensive Lipid-Lowering Therapy in Calcific Aortic Stenosis" (New England Journal of Medicine, Vol. 352, No. 23, pp. 2389-2397), S. Cowell et al. reported the results of a doubleblind, placebo controlled trial designed to determine whether intensive
Adrenomedullin, a hormone found in the adrenal gland, participates in bloodpressure and heart-rate control. The level of adrenomedullin is raised in a variety of diseases, and medical complications, including recurrent pregnancy loss, can result. In an article by M. Nakatsuka et al. titled
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 et al. explored the distributions of oxygen in
Explain the difference between a point estimate of a parameter and a confidence-interval estimate of a parameter.
In each part of this problem, we have provided a scenario for a confidence interval. Decide whether the appropriate method for obtaining the confidence interval is the z-interval procedure, the t-interval procedure, or neither. a. A random sample of size 17 is taken from a population. A normal
Dr. Thomas Stanley of Georgia State University has surveyed millionaires since 1973. Among other information, Stanley obtains estimates for the mean age, Î¼, of all U.S. millionaires. Suppose that 36 randomly selected U.S. millionaires are the following ages, in years.Determine a 95%
From Problem 13, we know that "a 95% confidence interval for the mean age of all U.S. millionaires is from 54.3 years to 62.8 years." Decide which of the following sentences provide a correct interpretation of the statement in quotes. Justify your answers. a. Ninety-five percent of all U.S.
In a 1903 paper, Abigail Camp Dimon discussed the effect of environment on the shape and form of two sea snail species, Nassa obsoleta and Nassa trivittata. One of the variables that Dimon considered was length of shell. She found the mean shell length of 461 randomly selected specimens of N.
Refer to Problem 15. a. Find the margin of error, E. b. Explain the meaning of E as far as the accuracy of the estimate is concerned. c. Determine the sample size required to have a margin of error of 0.1 mm and a 90% confidence level. d. Find a 90% confidence interval for μ if a sample of the
For a t-curve with df = 18, obtain the t-value and illustrate your results graphically. a. The t-value having area 0.025 to its right b. t0.05 c. The t-value having area 0.10 to its left d. The two t-values that divide the area under the curve into a middle 0.99 area and two outside 0.005 areas
The paper "Correlations between the Intrauterine Metabolic Environment and Blood Pressure in Adolescent Offspring of Diabetic Mothers" (Journal of Pediatrics, Vol. 136, Issue 5, pp. 587-592) by N. Cho et al. presented findings of research on children of diabetic mothers. Past studies showed that
In a Singapore edition of Business Times, diamond pricing was explored. The price of a diamond is based on the diamond's weight, color, and clarity. A simple random sample of 18 one-half-carat diamonds had the following prices, in dollars.a. Apply the t-interval procedure to these data to find a
Answer true or false to the following statement, and give a reason for your answer: If a 95% confidence interval for a population mean, μ, is from 33.8 to 39.0, the mean of the population must lie somewhere between 33.8 and 39.0.
The convict surgeonfish is a common tropical reef fish that has been found to delay metamorphosis into adult by extending its larval phase. This delay often leads to enhanced survivorship in the species by increasing the chances of finding suitable habitat. In the paper "Delayed Metamorphosis of a
The U.S. Department of Energy collects fuel-economy information on new motor vehicles and publishes its findings in Fuel Economy Guide. The data included are the result of vehicle testing done at the Environmental Protection Agency's National Vehicle and Fuel Emissions Laboratory in Ann Arbor,
In the online article "Old Faithful at Yellowstone, a Bimodal Distribution," D. Howell examined various aspects of the Old Faithful Geyser at Yellowstone National Park. Despite its name, there is considerable variation in both the length of the eruptions and in the time interval between eruptions.
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 Management" (Journal of Applied Ecology, Vol. 37,
a. Open the Focus sample (FocusSample) in the statistical software package of your choice and then obtain and interpret a 95% confidence interval for the mean high school percentile of all UWEC undergraduate students. Interpret your result.b. In practice, the (population) mean of the variable under
a. Obtain and interpret a point estimate for the mean number of chocolate chips per bag for all bags of Chips Ahoy! cookies. (Note: The sum of the data is 52,986.) b. Construct and interpret a normal probability plot, boxplot, and histogram of the data. c. Use the graphs in part (b) to identify
Must the variable under consideration be normally distributed for you to use the z-interval procedure or t-interval procedure? Explain your answer.
Suppose that you intend to find a 95% confidence interval for a population mean by applying the one-mean z-interval procedure to a sample of size 100. a. What would happen to the precision of the estimate if you used a sample of size 50 instead but kept the same confidence level of 0.95? b. What
A confidence interval for a population mean has a margin of error of 10.7. a. Obtain the length of the confidence interval. b. If the mean of the sample is 75.2, determine the confidence interval.
A variable of a population has a mean of 266 and a standard deviation of 16. Ten observations of this variable have a mean of 262.1 and a sample standard deviation of 20.4. Obtain the observed value of the a. Standardized version of x-bar. b. Studentized version of x-bar.
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. Among other things, the researchers monitored the heart rates of a random sample
x-bar = 20, s = 4, n = 24, H0: μ = 22, Ha: μ ≠ 22We have provided a sample mean, sample standard deviation, and sample size. In each case, use the one-mean t-test to perform the required hypothesis test at the 5% significance level.
TV Viewing. According to Communications Industry Forecast & Report, published by Veronis Suhler Stevenson, the average person watched 4.55 hours of television per day in 2005. A random sample of 20 people gave the following number of hours of television watched per day for last year.At the 10%
Serious golfers and golf equipment companies sometimes use golf equipment testing labs to obtain precise information about particular club heads, club shafts, and golf balls. One golfer requested information about the Jazz Fat Cat 5 iron from Golf Laboratories, Inc. The company tested the club by
Because many industrial wastes contain nutrients that enhance crop growth, efforts are being made for environmental purposes to use such wastes on agricultural soils. Two researchers, M. Ajmal and A. Khan, reported their findings on experiments with brewery wastes used for agricultural purposes in

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