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statistics for experimentert
Introductory Statistics 10th Global Edition Neil A. Weiss - Solutions
Math and Physics. A college physics instructor was concerned about the detrimental effects of poor mathematics background on her students. She randomly selected 18 students and divided them according to math background. Their semester averages were the following.Fewer than 2 years Two or more years
Picoplankton in the Bay. Picoplankton are micron-sized, single-cell algae that are an integral component of aquatic ecosystems, both in estuarine and open ocean waters. In the paper “Spatial and Temporal Variability of Picocyanobacteria Synechococcus sp.in San Francisco Bay” (Limnology and
Weekly Earnings. The Bureau of Labor Statistics publishes data on weekly earnings of full-time wage and salary workers in Employment and Earnings. Independent random samples of male and female workers gave the data on weekly earnings, in dollars, found in the following table.Men Women 924 575 2078
SAT Essay Scores. The SAT is a standardized test required for most college admissions in the United States. It is owned, published, and developed by the College Board and results are reported in College-Bound Seniors Total Group Profile Report. In 2006, an essay section with possible scores ranging
Doing Time. The Federal Bureau of Prisons publishes data in Prison Statistics on the times served by prisoners released from federal institutions for the first time. Independent random samples of released prisoners in the fraud and firearms offense categories yielded the following information on
Mutual Funds. A mutual fund is a professionally managed investment that can be sold to the general public. The following table lists the 3-month rates of return, in percent, for samples of healthcarerelated and technology-related mutual funds, as reported by Morningstar, an independent investment
Weekly Earnings. Refer to Exercise 10.127.a. Use the technology of your choice to obtain normal probability plots and boxplots for the two samples.b. Is it reasonable to use the pooled t-test to perform the hypothesis test required in Exercise 10.127? Explain your answer.c. Is it reasonable to use
Gender and Direction. In the paper “The Relation of Sex and Sense of Direction to Spatial Orientation in an Unfamiliar Environment” (Journal of Environmental Psychology, Vol. 20, pp. 17–28), J. Sholl et al. published the results of examining the sense of direction of 30 male and 30 female
Formaldehyde Exposure. One use of the chemical formaldehyde is to preserve animal specimens. In the article “Exposure to Formaldehyde Among Animal Health Students” (American Industrial Hygiene Association Journal, Vol. 63, pp. 647–650), A. Dufresne et al. examined student exposure to
Teacher Salaries. The National Education Association collects data on teacher salaries and publishes results in Estimates of School Statistics Database. Independent samples of 100 secondary school teachers and 125 elementary school teachers yielded the data, in thousands of dollars, on annual
Large-Sample Mann–Whitney Test. Formulate a hypothesis-testing procedure for a Mann–Whitney test that uses the test statistic z given in the preceding box.
Doing Time. Refer to Exercise 10.129.a. Use your procedure from Exercise 10.135 to perform the hypothesis test.b. Compare your result in part (a) to the one you obtained in Exercise 10.129(a), where you didn’t use the normal approximation.
The Distribution of M. In this exercise, you are to obtain the distribution of the variable M when the sample sizes are both 3. Doing so enables you to see how the Mann–Whitney table is constructed. All possible ranks for the data are displayed in the following table; the letter A stands for a
TV Viewing. The A. C. Nielsen Company collects data on the TV viewing habits of Americans and publishes the information in Nielsen Report on Television. Suppose that you want to use a paired sample to decide whether the mean viewing times of married men and married women differ.
Self-Reported Weight. The article “Accuracy of SelfReported Height and Weight in a Community-Based Sample of Older African Americans and Whites” (Journal of Gerontology Series A: Biological Sciences and Medical Sciences, Vol. 65A, No. 10, pp. 1123–1129) by G. Fillenbaum et al. explores the
Hypnosis and Pain. In the paper “An Analysis of Factors That Contribute to the Efficacy of Hypnotic Analgesia” (Journal of Abnormal Psychology, Vol. 96, No. 1, pp. 46–51), D. Price and J. Barber examined the effects of hypnosis on pain. They measured response to pain using a visual analogue
Sports Stadiums and Home Values. In the paper “Housing Values Near New Sporting Stadiums” (Land Economics, Vol. 81, Issue 3, pp. 379–395), C. Tu examined the effects of construction of new sports stadiums on home values. Suppose that you want to use a paired sample to decide whether
Breastmilk and Antioxidants. There is convincing evidence that breastmilk containing antioxidants is important in the prevention of diseases in infants. Researchers A. Xavier et al. studied the effects of storing breastmilk on antioxidant levels in the article “Total Antioxidant Concentrations of
Fiber Density. In the article “Comparison of Fiber Counting by TV Screen and Eyepieces of Phase Contrast Microscopy” (American Industrial Hygiene Association Journal, Vol. 63, pp. 756–761), I. Moa et al. reported on determining fiber density by two different methods. The fiber density of 10
Behavioral Genetics. In the article “Growth references for height, weight and BMI of Twins aged 0–2.5 years” (ACTA Pediatrica, Vol. 97, pp. 1099–1104), the researchers P. Dommelen et al.determined the size of the growth deficit in Dutch monozygotic and dizygotic twins aged between 0–2.5
Sleep. In 1908, W. S. Gosset published “The Probable Error of a Mean” (Biometrika, Vol. 6, pp. 1–25). In this pioneering paper, published under the pseudonym “Student,” he introduced what later became known as Student’s t-distribution. Gosset used the following data set, which gives the
Anorexia Treatment. Anorexia nervosa is a serious eating disorder, particularly among young women. The following data provide the weights, in pounds, of 17 anorexic young women before and after receiving a family therapy treatment for anorexia nervosa.[SOURCE: D. Hand et al. (ed.) A Handbook of
Measuring Treadwear. R. Stichler et al. compared two methods of measuring treadwear in their paper “Measurement of Treadwear of Commercial Tires” (Rubber Age, Vol. 73:2). Eleven tires were each measured for treadwear by two methods, one based on weight and the other on groove wear. The data, in
Glaucoma and Corneal Thickness. Glaucoma is a leading cause of blindness in the United States. N. Ehlers measured the corneal thickness of eight patients who had glaucoma in one eye but not in the other. The results of the study were published as the paper“On Corneal Thickness and Intraocular
Cooling Down. Cooling down with a cold drink before exercise in the heat is believed to help an athlete perform. Researcher J. Dugas explored the difference between cooling down with an ice slurry (slushy) and with cold water in the article “Ice Slurry Ingestion Increases Running Time in the
Behavioral Genetics. Refer to Exercise 10.155.a. Determine a 95% confidence interval for the difference between the mean heights of the twins.b. Repeat part (a) for a 99% confidence level.
Sleep. Refer to Exercise 10.156.a. Determine a 90% confidence interval for the additional sleep that would be obtained, on average, by using laevohysocyamine hydrobromide.b. Repeat part (a) for a 98% confidence level.
Anorexia Treatment. Refer to Exercise 10.157 and find a 90% confidence interval for the weight gain that would be obtained, on average, by using the family therapy treatment.
Measuring Treadwear. Refer to Exercise 10.158 and find a 95% confidence interval for the mean difference in measurement by the weight and groove methods.
Glaucoma and Corneal Thickness. Refer to Exercise 10.159 and obtain an 80% confidence interval for the difference between the mean corneal thickness of normal eyes and that of eyes with glaucoma.
Cooling Down. Refer to Exercise 10.160 and find a 98% confidence interval for the difference between the mean times to fatigue on a treadmill in a hot and humid environment after cooling down with cold water and after cooling down with an ice slurry
Font Readability. In the online paper “A Comparison of Two Computer Fonts: Serif versus Ornate Sans Serif” (Usability News, Issue 5.3), researchers S. Morrison and J. Noyes studied whether the type of font used in a document affects reading speed or comprehension. The fonts used for the
Tobacco Mosaic Virus. To assess the effects of two different strains of the tobacco mosaic virus, W. Youden and H. Beale randomly selected eight tobacco leaves. Half of each leaf was subjected to one of the strains of tobacco mosaic virus and the other half to the other strain. The researchers then
Antiviral Therapy. In the article “Improved Outcome for Children With Disseminated Adenoviral Infection Following Allogeneic Stem Cell Transplantation” (British Journal of Haematology, Vol. 130, Issue 4, p. 595), B. Kampmann et al. examined children who received stem cell transplants and
Faculty Salaries. The American Association of University Professors (AAUP) conducts salary studies of college professors and publishes its findings in AAUP Annual Report on the Economic Status of the Profession. In Example 10.3 on pages 471–473, we performed a hypothesis test based on independent
Marriage Ages. In the Statistics Norway on-line article“The Times They Are a Changing,” J. Kristiansen discussed the changes in age at the time of marriage in Norway. The ages, in years, at the time of marriage for 75 Norwegian couples are presented on the WeissStats site. Use the technology of
Storm Hydrology and Clear Cutting. In the document“Peak Discharge from Unlogged and Logged Watersheds,” J. Jones and G. Grant compiled (paired) data on peak discharge from storms in two watersheds, one unlogged and one logged (100% clear-cut). If there is an effect due to clear-cutting, one
Explain exactly how a paired t-test can be formulated as a onemean t-test. (Hint: Work solely with the paired-difference variable.)
Gasoline Additive. This exercise shows what can happen when a hypothesis-testing procedure designed for use with independent samples is applied to perform a hypothesis test on a paired sample. The gas mileages, in miles per gallon (mpg), of 10 randomly selected cars, both with and without a new
Permutation Tests. With the advent of high-speed computing, new procedures have been developed that permit statistical inferences to be performed under less restrictive conditions than those of classical procedures. Permutation tests constitute one such collection of new procedures. To perform a
Suppose that you want to perform a hypothesis test based on a simple random paired sample to compare the means of two populations. For each part, decide whether you would use the paired t-test, the paired Wilcoxon signed-rank test, or neither of these tests. Preliminary data analyses of the sample
Suppose that you want to perform a hypothesis test based on a simple random paired sample to compare the means of two populations. For each part, decide whether you would use the paired t-test, the paired Wilcoxon signed-rank test, or neither of these tests. Preliminary data analyses of the sample
Behavioral Genetics. In the article “Growth references for height, weight and BMI of Twins aged 0–2.5 years” (ACTA Pediatrica, Vol. 97, pp. 1099–1104), the researchers, P. Dommelen et al.determines the size of the growth deficit in Dutch monozygotic and dizygotic twins aged between 0–2.5
Sleep. In 1908, W. S. Gosset published “The Probable Error of a Mean” (Biometrika, Vol. 6, pp. 1–25). In this pioneering paper, published under the pseudonym “Student,” he introduced what later became known as Student’s t-distribution. Gosset used the following data set, which gives the
Anorexia Treatment. Anorexia nervosa is a serious eating disorder, particularly among young women. The following data provide the weights, in pounds, of 17 anorexic young women before and after receiving a family therapy treatment for anorexia nervosa.[SOURCE: D. Hand et al., ed., A Handbook of
Measuring Treadwear. R. Stichler et al. compared two methods of measuring treadwear in their paper “Measurement of Treadwear of Commercial Tires” (Rubber Age, 73:2). Eleven tires were each measured for treadwear by two methods, one based on weight and the other on groove wear. The following are
Glaucoma and Corneal Thickness. Glaucoma is a leading cause of blindness in the United States. N. Ehlers measured the corneal thickness of eight patients who had glaucoma in one eye but not in the other. The results of the study were published in the paper “On Corneal Thickness and Intraocular
Cooling Down. Cooling down with a cold drink before exercise in the heat is believed to help an athlete perform. Researcher J. Dugas explored the difference between cooling down with an ice slurry (slushy) and with cold water in the article “Ice Slurry Ingestion Increases Running Time in the
Font Readability. In the online paper “A Comparison of Two Computer Fonts: Serif versus Ornate Sans Serif” (Usability News, Issue 5.3), researchers S. Morrison and J. Noyes studied whether the type of font used in a document affects reading speed or comprehension. The fonts used for the
Tobacco Mosaic Virus. To assess the effects of two different strains of the tobacco mosaic virus, W. Youden and H. Beale randomly selected eight tobacco leaves. Half of each leaf was subjected to one of the strains of tobacco mosaic virus and the other half to the other strain. The researchers then
Consonantal Inventory Size. In the article “Intervocalic Consonants in the Speech of Typically Developing Children: Emergence and Early Use” (Clinical Linguistics and Phonetics, Vol. 16, Issue 3, pp. 155–168), C. Stoel-Gammon examined the development of intervocalic consonants (consonants
Faculty Salaries. The American Association of University Professors (AAUP) conducts salary studies of college professors and publishes its findings in AAUP Annual Report on the Economic Status of the Profession. Pairs were formed by matching faculty in private and public institutions by rank and
on page 519, where the paired t-test was used.c. Which test do you think is preferable: the paired t-test or the paired Wilcoxon signed-rank test? Explain your answer.
Marriage Ages. In the Statistics Norway on-line article“The Times They Are a Changing,” J. Kristiansen discussed the changes in age at the time of marriage in Norway. The ages, in years, at the time of marriage for 75 Norwegian couples is presented on the WeissStats site. Use the technology of
Storm Hydrology and Clear Cutting. In the document“Peak Discharge from Unlogged and Logged Watersheds,” J. Jones and G. Grant compiled (paired) data on peak discharge from storms in two watersheds, one unlogged and one logged (100% clear-cut). If there is an effect due to clear-cutting, one
Explain why the paired Wilcoxon signed-rank test is simply a Wilcoxon signed-rank test on the sample of paired differences with null hypothesis H0: μd = 0.Paired Sign Test. Recall that the paired Wilcoxon signed-rank test, which can be used to perform a hypothesis test to compare two population
use and understand the formulas in this chapter.
perform inferences based on independent simple random samples to compare the means of two populations when the population standard deviations are unknown but are assumed to be equal.
perform inferences based on independent simple random samples to compare the means of two populations when the population standard deviations are unknown but are not assumed to be equal.
perform a hypothesis test based on independent simple random samples to compare the means of two populations when the distributions of the variable under consideration have the same shape.
perform inferences based on a simple random paired sample to compare the means of two populations.
perform a hypothesis test based on a simple random paired sample to compare the means of two populations when the paired-difference variable has a symmetric distribution.
decide which procedure should be used to perform an inference to compare the means of two populations.
Discuss the basic strategy for comparing the means of two populations based on independent simple random samples.
Regarding the pooled and nonpooled t-procedures,a. what is the difference in assumptions between the two procedures?b. how important is the assumption of independent simple random samples for these procedures?c. how important is the normality assumption for these procedures?
Suppose that the variable under consideration is normally distributed on each of the two populations and that you are going to use independent simple random samples to compare the population means. Fill in the blank and explain your answer: Unless you are quite sure that the are equal, the
Suppose that a simple random paired sample is taken from two populations to compare their means. Further suppose that the distribution of the paired-difference variable has a symmetric distribution.Under what conditions would the paired t-test be preferable to the paired Wilcoxon signed-rank test?
Grip and Leg Strength. In the paper, “Sex Differences in Static Strength and Fatigability in Three Different Muscle Groups” (Research Quarterly for Exercise and Sport, Vol. 61(3), pp. 238–242), J. Misner et al. published results of a study on grip and leg strength of males and females. The
Grip and Leg Strength. Refer to Problem 8. Determine a 90% confidence interval for the difference between the mean right-leg strengths of males and females. Interpret your result.
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. The data in the
Cottonmouth Litter Size. Refer to Problem 10. Find a 98% confidence interval for the difference between the mean litter sizes of cottonmouths in Florida and Virginia. Interpret your result.* Home Prices.
The National Association of Realtors publishes information on the cost of existing single-family homes in Median Sales Price of Existing Single-Family Homes for Metropolitan Areas.Independent random samples of 10 homes each in Atlantic City and Las Vegas yielded the following data on home prices in
Ecosystem Response. In the on-line paper “Changes in Lake Ice: Ecosystem Response to Global Change” (Teaching Issues and Experiments in Ecology, tiee.ecoed.net, Vol. 3), R. Bohanan et al.questioned whether there is evidence for global warming in long-term data on changes in dates of ice cover
Ecosystem Response. Refer to Problem 13, and find a 90% confidence interval for the difference in the mean lengths of time that ice stays on the two lakes. Interpret your result.* Antidepressants and Lipid Profile.
In the online article “Comparing the Effects of Fluoxetine and Imipramine on Total Cholesterol, Triglyceride, and Weight in Patients with Major Depression” (Journal of Pharmaceutical Sciences, Vol. 21, No. 4), E. Ananloo et al.study the effect of antidepressants on lipid profiles. Nineteen
Drink and Be Merry? In the paper, “Drink and Be Merry?Gender, Life Satisfaction, and Alcohol Consumption Among College Students” (Psychology of Addictive Behaviors, Vol. 19, Issue 2, pp. 184–191), J. Murphy et al. examined the impact of alcohol use and alcohol-related problems on several
Refer to Problem 16. Use the technology of your choice to do the following.a. Obtain histograms of the two samples.b. Based on your histograms in part (a), do you think that conducting a Mann–Whitney test is reasonable here?c. Apply the Mann–Whitney test to decide, at the 5% significance level,
Weekly Earnings. The Bureau of Labor Statistics publishes data on weekly earnings of full-time wage and salary workers in Employment and Earnings. Male and female workers were paired according to occupation and experience. Their weekly earnings, in dollars, are provided on the WeissStats site. Use
Refer to Problem 19. Use the technology of your choice to do the following.a. Apply the paired Wilcoxon signed-rank test to decide, at the 5% significance level, whether the data provide sufficient evidence to conclude that, on average, the weekly earnings of male full-time wage and salary workers
NBA Champs. The winner of the 2012–20 13 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)–(e) of Exercise 7.11 for samples of size 1.
NBA Champs. Repeat parts (b)–(e) of Exercise 7.11 for samples of size 3.
NBA Champs. Repeat parts (b)–(e) of Exercise 7.11 for samples of size 4.
NBA Champs. Repeat parts (b)–(e) of Exercise 7.11 for samples of size 5.
NBA Champs. This exercise requires that you have done Exercises 7.11–7.15.a. Draw a graph similar to that shown in Fig. 7.3 on page 333 for sample sizes of 1, 2, 3, 4, and 5.b. What does your graph in part (a) illustrate about the impact of increasing sample size on sampling error?c. Construct a
Highest Peak. From the Website 8000ers.com, we obtained a table of the highest mountain peaks in the world as of March 2015.The six highest mountains are shown in the following table, with their heights in meters. Consider these six mountains a population of interest.Mountain Height (meters)Mount
Highest Peak. Repeat parts (b)–(e) of Exercise 7.17 for samples of size 1.
Highest Peak. Repeat parts (b)–(e) of Exercise 7.17 for samples of size 3. (There are 20 possible samples.)
Highest Peak. Repeat parts (b)–(e) of Exercise 7.17 for samples of size 4. (There are 15 possible samples.)
Highest Peak. Repeat parts (b)–(e) of Exercise 7.17 for samples of size 5. (There are six possible samples.)
Highest Peak. 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?
Highest Peak. Explain what the dotplots in part (c) of Exercises 7.17–7.22 illustrate about the impact of increasing sample size on sampling error.Extending the Concepts and Skills
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. For a fixed sample size, explain what this
Refer to Exercise 7.3 on page 334.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¯, using only your answer from Exercise 7.3(a).
Refer to Exercise 7.4 on page 334.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¯, using only your answer from Exercise 7.4(a).
Refer to Exercise 7.5 on page 334.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¯, using only your answer from Exercise 7.5(a).
Refer to Exercise 7.6 on page 334.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¯, using only your answer from Exercise 7.6(a).
Refer to Exercise 7.7 on page 334.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¯, using only your answer from Exercise 7.7(a).
Refer to Exercise 7.8 on page 334.a. Use your answers from Exercise 7.8(b) to determine the m ean, 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 7.8(a).
Refer to Exercise 7.9 on page 334.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¯, using only your answer from Exercise 7.9(a).
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