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statistics for experimentert

Introductory Statistics 10th Global Edition Neil A. Weiss - Solutions

Refer to Exercise 7.10 on page 334.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¯, using only your answer from Exercise
NBA Champs. 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.Player Position Height (in.)Chris Bosh (B) Center 83 Dwyane Wade (W) Guard 76 LeBron James (J) Forward 80 Mario Chalmers (C)
NBA Champs. 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).
NBA Champs. 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).
NBA Champs. 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).
NBA Champs. 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).
Young Adults at Risk. N. Kaseva et al. published a research paperentitled ‘‘Blunted hypothalamic-pituitary-adrenal axis and insulin response to psychosocial stress in young adults born preterm at very low birth weight’’ (Clinical Endocrinology, Vol .80, No. 1, pp. 101−106)].It shows that
Baby Weight. 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 deviation of 581
Menopause in Mexico. 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 phenomenon among
Mobile Homes. 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, find the mean and standard
Undergraduate Binge Drinking. 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 article “Binge
Earthquakes. 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 399 days. Suppose that you
Bachelor’s Completion. 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 following problems.a.
Unbiased and Biased Estimators. 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, whereas a biased
Heights of Starting Players. In Example 7.5, we used the definition of the standard deviation of a variable (Definition 3.12 on page 164) 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 samples of
Finite-Population Correction Factor. Consider simple random samples of size n without replacement from a population of size N.a. Show that if n ≤ 0.05N, then 0.97≤N − n N − 1 ≤ 1.b. Use part (a) to explain why there is little difference in the values provided by Equations (7.1) and (7.2)
Class Project Simulation. 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 each sample.b.
Gestation Periods of Humans. 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 all possible
Catalyst. A catalyst is a substance that starts or accelerates a chemical reaction without undergoing any permanent change itself.A chemist, while adding a particular catalyst to a reaction, observes that the time elapsed for the reaction to complete has a special type of reverse-J-shaped
Unbiased and Biased Estimators. 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, whereas a biased
Heights of Starting Players. In Example 7.5, we used the definition of the standard deviation of a variable (Definition 3.12 on page 164) 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 samples of
Finite-Population Correction Factor. Consider simple random samples of size n without replacement from a population of size N.a. Show that if n ≤ 0.05N, then 0.97≤N − n N − 1 ≤ 1.b. Use part (a) to explain why there is little difference in the values provided by Equations (7.1) and (7.2)
Class Project Simulation. 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 each sample.b.
Gestation Periods of Humans. 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 all possible
Catalyst. A catalyst is a substance that starts or accelerates a chemical reaction without undergoing any permanent change itself.A chemist, while adding a particular catalyst to a reaction, observes that the time elapsed for the reaction to complete has a special type of reverse-J-shaped
Expenditure per Student. According to a report on theestimates of school statisticsin a particular country, the mean expenditure(public) per student is $10.94 thousand annually. Assume a standard deviation of $3.3 thousand. Do the following tasks for the variable“expenditure per student”.a.
Prices of Dwellings. C. P. Barros et al. studied prices of new, resale and unoccupied dwellings in Beijing in the 2011 article “Housing Sale in Urban Beijing” (School of Economics and Management, Technical University of Lisbon). According to the article, the mean price of a newly constructed
Nurses and Hospital Stays. 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. investigated
Ethanol Railroad Tariffs. 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 deviation of such
Taller Young Women. 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 their 20s was 62.6 inches.
Poverty and Dietary Calcium. 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 adequate intake
Early-Onset Dementia. 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 the Experience and
Worker Fatigue. 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 systolic pressure for electric
A variable of a population is normally distributed with mean μand 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. Approximately 95% of all possible samples
Testing for Content Accuracy. 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 normally
Household Size. In Example 7.9 on page 344, 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
Gestation Periods of Humans. 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 2000 samples.c.
Emergency Room Traffic. 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 deviation of such a
use and understand the formulas in this chapter.
define sampling error, and explain the need for sampling distributions.
state and apply the central limit theorem.
determine the sampling distribution of the sample mean when the variable under consideration is normally distributed.
determine the sampling distribution of the sample mean when the sample size is relatively large.
Officer Salaries. The following table gives the monthly salaries(in $1000s) of the six officers of a company.Officer AB C D E F Salary 8 12 16 20 24 28a. Calculate the population mean monthly salary, μ.There are 15 possible samples of size 4 from the population of six officers. They are listed in
Officer Salaries. Refer to Problem 5.a. Use the answer you obtained in Problem 5(b) and Definition 3.11 on page 162 to find the mean of the variable x¯. Interpret your answer.b. Can you obtain the mean of the variable x¯ without doing the calculation in part (a)? Explain your answer.
The following graph shows the curve for a normally distributed variable. Superimposed are the curves for the sampling distributions of the sample mean for two different sample sizes.A BNormal curve for variablea. Explain why all three curves are centered at the same place.b. Which curve corresponds
Income Tax and the IRS. In 2010, the Internal Revenue Service (IRS) sampled 308,946 tax returns to obtain estimates of various parameters. Data were published in Statistics of Income, Individual Income Tax Returns. According to that document, the mean income tax per return for the returns sampled
New Car Passion. Edmunds.com publishes information on new car prices in Car Shopping Trends Report. During a recent year, Americans spent an average of $30,803 for a new car. Assume a standard deviation of $10,200.a. Identify the population and variable under consideration.b. For samples of 50 new
Hours Actually Worked. In the article “How Hours of Work Affect Occupational Earnings” (Monthly Labor Review, Vol. 121), D. Hecker discussed the number of hours actually worked as opposed to the number of hours paid for. The study examines both men and women in 87 different full-time
Hours Actually Worked. Repeat Problem 10, assuming that the number of hours per week worked by men in firefighting is normally distributed.
Western Pygmy-Possum. The foraging behavior of the western pygmy-possum was investigated in the article “Strategies of a Small Nectarivorous Marsupial, the Western Pygmy-Possum, in Response to Seasonal Variation in Food Availability” (Journal of Mammalogy, Vol. 96, No. 6, pp. 1525–1535) by D.
Western Pygmy-Possum. Refer to Problem 12.a. Find the percentage of all samples of four pygmy-possums that have mean weights within 0.225 g of the population mean weight of 8.5 g.b. Obtain the probability that the mean weight of four randomly selected pygmy-possums will be within 0.225 g of the
Blood Glucose Level. In the article “Drinking Glucose Improves Listening Span in Students Who Miss Breakfast” (Educational Research, Vol. 43, No. 2, pp. 201–207), authors N. Morris and P. Sarll explored the relationship between students who skip breakfast and their performance on a number of
Life Insurance in Force. The American Council of Life Insurers provides information about life insurance in force per covered family in the Life Insurers Fact Book. Assume that the standard deviation of life insurance in force is $50,900.a. Determine the probability that the sampling error made in
Paint Durability. A paint manufacturer in Pittsburgh claims that his paint will last an average of 5 years. Assuming that paint life is normally distributed and has a standard deviation of 0.5 year, answer the following questions:a. Suppose that you paint one house with the paint and that the paint
Cloudiness in Breslau. In the paper “Cloudiness: Note on a Novel Case of Frequency” (Proceedings of the Royal Society of London, Vol. 62, pp. 287–290), K. Pearson examined data on daily degree of cloudiness, on a scale of 0 to 10, at Breslau (Wroclaw), Poland, during the decade 1876–1885. A
Psychological Skills of Dancers. The Athletic Coping Skills Inventory (ACSI) is a test to measure psychological skills believed to influence athletic performance. Researcher Ellinor Klockare studied and evaluated the effects of a psychological skills training program on dancers and its usefulness
Random Numbers. A variable is said to be uniformly distributed or to have a uniform distribution with parameters a and b if its distribution has the shape of the horizontal line segment with equation y = 1/(b − a), for a < x
A simple random sample is taken from a population and yields the following data for a variable of the population:40 25 32 9 28 16 21 13 10 37 24 39 Find a point estimate for the population mean (i.e., the mean of the variable).
A simple random sample is taken from a population and yields the following data for a variable of the population:20 2 6 2 12 6 9 8 16 8 21 Find a point estimate for the population mean (i.e., the mean of the variable).
Refer to Exercise
and find a point estimate for the population standard deviation (i.e., the standard deviation of the variable).
Refer to Exercise 8.8 and find a point estimate for the population standard deviation (i.e., the standard deviation of the variab
Wedding Costs. 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
Cottonmouth Litter Size. 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 widely
Wedding Costs. A random sample of 20 recent weddings in a country yielded a mean wedding cost of $26,324.61. Assume that recent wedding costs in this country are normally distributed with a standard deviation of $8000. Complete parts (a) through (c)below.a. Determine a 95% confidence interval for
Cottonmouth Litter Size. Refer to Exercise 8.18. 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
A simple random sample of 20 new automobile models yielded the data shown to the right on fuel tank capacity, in gallons. 15.1 16.5 22.9 16.7 18.9 21.6 20.7 16.2 18.8 20.2 15.9 21.8 16.6 22.9 22.7 20.8 16.2 21.6 17.6 21.8a. Find a point estimate for the mean fuel tank capacity for all new
Home Improvements. 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.3179 1032 1822 4093 2285 1478 955 2773 514 3915 4800 3843 5265
Giant Tarantulas. 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
Serum Cholesterol Levels. 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 on serum total
New Mobile Homes. A government bureau publishes annual price figures for new mobile homes. A simple random sample of 36 new mobile homes yielded the following prices, in thousands of dollars. Assume that the population standard deviation of all such prices is $10.2 thousand, that is, $10,200. Use
New Mobile Homes. Refer to Examples 8.1 and 8.2. Use the data in Table 8.1 on page 354 to obtain a 68% confidence interval for the mean price of all new mobile homes. (Hint: Proceed as in Example 8.2, but use Property 1 of the empirical rule on page 304 instead of Property 2.)
The variable under consideration is very close to being normally distributed, and the sample size is 10.
The variable under consideration is very close to being normally distributed, and the sample size is 75.
The sample data contain outliers, and the sample size is 20.
The sample data contain no outliers, the variable under consideration is roughly normally distributed, and the sample size is 20.
The distribution of the variable under consideration is highly skewed, and the sample size is 20.
The sample data contain no outliers, the sample size is 250, and the variable under consideration is far from being normally distributed.
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 accurate estimate of μ?
Suppose that you will be taking a random sample from a population and that you intend to find a 99% confidence interval for the population mean, μ. Which sample size, 50 or 100, will result in the confidence interval giving a more accurate estimate of μ?
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.
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.
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 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.In each of Exercises 8.53–8.60, answer true or false to each statement concerning
The length of the confidence interval can be determined if you know only the margin of error.
The margin of error can be determined if you know only the length of the confidence interval.
The confidence interval can be obtained if you know only the margin of error.
The confidence interval can be obtained if you know only the margin of error and the sample mean.
The margin of error can be determined if you know only the confidence level.
The confidence level can be determined if you know only the margin of error.
The margin of error can be determined if you know only the confidence level, population standard deviation, and sample size.
The confidence level can be determined if you know only the margin of error, population standard deviation, and sample size.
Formula 8.2 on page 366 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 we want a whole number?b. Why do
A random sample of 10 venture-capital investments in the fiber optics business sector yielded the following data, in millions of dollars. Determine a 95% confidence interval for the mean amount, μ, of all venture-capital investments in the fiber optics business sector. Assume that the population
Poverty and Dietary Calcium. 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,
Toxic Mushrooms? 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
Smelling Out the Enemy. 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
Political Prisoners. According to a study of political prisoners, the mean duration of imprisonment for 40 prisoners with chronic post-traumatic stress disorder (PTSD) was 33.5 months. Assuming that σ = 35 months, determine a 90% confidence interval for the mean duration of imprisonment, μ, of
Concert Tours. Concert tours by famous pop stars or music groups such as Michael Jackson and Pink Floyd became really popular since the 1980s. Pollster has collected data on the highestgrossing concert tours till 2008. For the top 30 highest-grossing concert tours,mean tickets sold were 579,824

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