[SOLVED] we have presented a confidence interval (CI)

> We have provided summary statistics for independent simple random samples from two populations. In each case, use the pooled t -test and the pooled t -interval procedure to conduct the required hypothesis test and obtain the specified confidence interval

> We have provided summary statistics for independent simple random samples from two populations. Preliminary data analyses indicate that the variable under consideration is normally distributed on each population. Decide, in each case, whether use of the

> Explain why sp is called the pooled sample standard deviation.

> Regarding the four conditions required for using the pooled t-procedures: a. what are they? b. how important is each condition?

> In this exercise, you are to perform a computer simulation to illustrate the sampling distribution of the difference between two sample means for independent samples. a. Simulate 1000 samples of size 12 from a normally distributed variable with a mean of

> From Player Roster, the official roster of the 2013 Super Bowl champion Baltimore Ravens, we obtained the heights, in inches, of the players on that team. A dotplot of those heights is as follows.

> To obtain the sampling distribution of the difference between two sample means for independent samples, as stated in Key Fact 10.1 on page 404, we need to know that, for independent observations, the difference of two normally distributed variables is al

> D. Cristol et al. published results of their studies of two subspecies of dark-eyed juncos in the paper “Migratory Dark-Eyed Juncos, Junco hyemalis, Have Better Spatial Memory and Denser Hippocampal Neurons Than Nonmigratory Conspecifics” (Animal Behavio

> Consider the quantities μ1, σ1, x¯1, s1, μ2, σ2, x¯2, and s2. a. Which quantities represent parameters and which represent statistics? b. Which quantities are fixed numbers and which are variables?

> An Arizona State University professor, R. Jacobowitz, Ph.D., in consultation with G. Vishteh, M.D., and other neurosurgeons obtained data on operative times, in minutes, for both a dynamic system (Z-plate) and a static system (ALPS plate). They wanted to

> Television commercials are becoming increasingly important and prevalent in presidential elections. A study by D. Lowry and M. Naser examined whether rhetoric in presidential TV commercials is different between the winners and losers. The researchers pub

> Data on household vehicle miles of travel (VMT) are compiled annually by the Federal Highway Administration and are published in National Household Travel Survey Summary of Travel Trends. A hypothesis test is to be performed to decide whether a differenc

> Contingent faculty members in higher education are non-tenure track faculty, adjuncts, postdocs, lecturers, or instructors. R. Bowden and L. Gonzalez researched whether contingent faculty members are different from tenure-track faculty members with regar

> Samples of adolescent offspring of diabetic mothers (ODM) and nondiabetic mothers (ONM) were taken by N. Cho et al. and evaluated for potential differences in vital measurements, including blood pressure and glucose tolerance. The study was published in

> Suppose you want to decide whether the mean salary of faculty in private institutions is less than the mean salary of faculty in public institutions. State the null and alternative hypotheses for that hypothesis test.

> Suppose you want to decide whether the mean salary of faculty in private institutions is greater than the mean salary of faculty in public institutions. State the null and alternative hypotheses for that hypothesis test.

> 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

> A variable of two populations has a mean of 7.9 and a standard deviation of 5.4 for one of the populations and a mean of 7.1 and a standard deviation of 4.6 for the other population. Moreover, the variable is normally distributed on each of the two popul

> A variable of two populations has a mean of 40 and a standard deviation of 12 for one of the populations and a mean of 40 and a standard deviation of 6 for the other population. Moreover, the variable is normally distributed on each of the two population

> A variable of two populations has a mean of 7.9 and a standard deviation of 5.4 for one of the populations and a mean of 7.1 and a standard deviation of 4.6 for the other population. a. For independent samples of sizes 3 and 6, respectively, find the mea

> Define the phrase independent samples.

> A variable of two populations has a mean of 40 and a standard deviation of 12 for one of the populations and a mean of 40 and a standard deviation of 6 for the other population. a. For independent samples of sizes 9 and 4, respectively, find the mean and

> we have presented a confidence interval (CI) for the difference, μ1 − μ2, between two population means. Interpret each confidence interval. 99% CI is from −10 to 5.

> we have presented a confidence interval (CI) for the difference, μ1 − μ2, between two population means. Interpret each confidence interval. 99% CI is from −20 to 15.

> we have presented a confidence interval (CI) for the difference, μ1 − μ2, between two population means. Interpret each confidence interval. 90% CI is from 5 to 10.

> we have presented a confidence interval (CI) for the difference, μ1 − μ2, between two population means. Interpret each confidence interval. 90% CI is from −10 to −5.

> Suppose that you want to perform a hypothesis test to compare the means of two populations, using a paired sample. For each part, decide whether you would use the paired t-test, the paired Wilcoxon signed-rank test, or neither of these tests, if prelimin

> 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,

> Refer to the vasectomy / prostate cancer study discussed. a. How could the study be modified to make it a designed experiment? b. Comment on the feasibility of the designed experiment that you described in part (a).

> Suppose that you want to perform a hypothesis test to compare the means of two populations, using a paired sample. For each part, decide whether you would use the paired t-test, the paired Wilcoxon signed-rank test, or neither of these tests, if prelimin

> A hypothesis test is to be performed to compare the means of two populations, using a paired sample. The sample of 15 paired differences contains an outlier but otherwise is roughly bell shaped. Assuming that it is not legitimate to remove the outlier, w

> 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

> Explain exactly how a paired t-test can be formulated as a one mean t-test.

> 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,

> we have presented a confidence interval (CI) for the difference, μ1 − μ2, between two population means. Interpret each confidence interval. 95% CI is from −20 to −15.

> 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

> 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 409–411, we performed a hypothesis

> 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

> 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 strai

> 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

> 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 fon

> Refer to Exercise 10.128 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. Data from Exerci

> Refer to Exercise 10.127 and obtain an 80% confidence interval for the difference between the mean corneal thickness of normal eyes and that of eyes with glaucoma. Data from Exercise 10.127: Glaucoma is a leading cause of blindness in the United States.

> Refer to Exercise 10.126 and find a 95% confidence interval for the mean difference in measurement by the weight and groove methods. Data from Exercise 10.126: R. Stichler et al. compared two methods of measuring treadwear in their paper “Measurement of

> Refer to Exercise 10.125 and find a 90% confidence interval for the weight gain that would be obtained, on average, by using the family therapy treatment. Data from Exercise 10.125: Anorexia nervosa is a serious eating disorder, particularly among young

> Refer to Exercise 10.124. 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. Data from Exercise 10.124: In 1908, W. S

> Refer to Exercise 10.123. a. Determine a 95% confidence interval for the difference between the mean heights of cross-fertilized and self-fertilized Zea mays. b. Repeat part (a) for a 99% confidence level. Data from Exercise 10.123: Charles Darwin, auth

> 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 Incre

> 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 Int

> The Information Please Almanac provides the number of children of each of the U.S. presidents. A frequency histogram for number of children by president, through President Barack H. Obama, is as follows. Is distribution (roughly) symmetric, right skewed,

> 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 groov

> 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. Does family therapy a

> 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

> Charles Darwin, author of Origin of Species, investigated the effect of cross-fertilization on the heights of plants. In one study he planted 15 pairs of Zea mays plants. Each pair consisted of one cross-fertilized plant and one self-fertilized plant gro

> The null hypothesis is H0: μ1 = μ2 and the alternative hypothesis is as specified. We have provided data from a simple random paired sample from the two populations under consideration. In each case, use the paired t-test to perform the required hypothes

> The null hypothesis is H0:μ1 = μ2 and the alternative hypothesis is as specified. We have provided data from a simple random paired sample from the two populations under consideration. In each case, use the paired t-test to perform the required hypothesi

> Identify the assumption for using the two-means z-test and the two-means z-interval procedure that renders those procedures generally impractical.

> The null hypothesis is H0:μ1 = μ2 and the alternative hypothesis is as specified. We have provided data from a simple random paired sample from the two populations under consideration. In each case, use the paired t-test to perform the required hypothesi

> We have drawn a smooth curve that represents a distribution. In each case, do the following: a. Identify the shape of the distribution with regard to modality. b. Identify the shape of the distribution with regard to symmetry (or non-symmetry). c. If the

> The null hypothesis is H0:μ1 = μ2 and the alternative hypothesis is as specified. We have provided data from a simple random paired sample from the two populations under consideration. In each case, use the paired t-test to perform the required hypothesi

> 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. T

> 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 Con

> 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 con

> 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

> The article “Accuracy of Self-Reported 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 a

> 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

> Provide an example (different from the ones considered in this section) of a procedure based on a paired sample being more appropriate than one based on independent samples.

> Why do you need to know the sampling distribution of the difference between two sample means in order to perform a hypothesis test to compare two population means?

> State the two conditions required for performing a paired t-procedure. How important are those conditions?

> We have drawn a smooth curve that represents a distribution. In each case, do the following: a. Identify the shape of the distribution with regard to modality. b. Identify the shape of the distribution with regard to symmetry (or non-symmetry). c. If the

> What constitutes each pair in a paired sample?

> State one possible advantage of using paired samples instead of independent samples.

> If the assumptions for a non-pooled t-interval are satisfied, the formula for a (1 − α)- level lower confidence bound for the difference, μ1 − μ2, between two population means is For a right-tailed hypothesis test at the significance level α, the null hy

> If the assumptions for a non-pooled t-interval are satisfied, the formula for a (1 − α)- level upper confidence bound for the difference, μ1 − μ2, between two population means is For a left-tailed hypothesis test at the significance level α, the null hyp

> As we mentioned on page 413, the following relationship holds between hypothesis tests and confidence intervals: For a two-tailed hypothesis test at the significance level α, the null hypothesis H0: μ1 = μ2 will be rejected in favor of the alternative hy

> We examine an alternative method, conceived by the late Professor John Tukey, for performing a two-tailed hypothesis test for two population means based on independent random samples. To apply this procedure, one of the samples must contain the largest o

> Suppose that the sample sizes, n1 and n2, are equal for independent simple random samples from two populations. a. Show that the values of the pooled and non-pooled t-statistics will be identical. b. Explain why part (a) does not imply that the two t-tes

> Refer to where each pair of graphs shows the distributions of a variable on two populations. Suppose that, in each case, you want to perform a small-sample hypothesis test based on independent simple random samples to compare the means of the two populat

> Anthropologists are still trying to unravel the mystery of the origins of the Etruscan empire, a highly advanced Italic civilization formed around the eighth century B.C. in central Italy. Were they native to the Italian peninsula or, as many aspects of

> The primary concern is deciding whether the mean of Population 2 differs from the mean of Population 1. a. Determine the null and alternative hypotheses. b. Classify the hypothesis test as two tailed, left tailed, or right tailed.

> We have drawn a smooth curve that represents a distribution. In each case, do the following: a. Identify the shape of the distribution with regard to modality. b. Identify the shape of the distribution with regard to symmetry (or non-symmetry). c. If the

> Suppose that you want to perform a hypothesis test for a population mean based on a small sample but that preliminary data analyses indicate either the presence of outliers or that the variable under consideration is far from normally distributed. a. Is

> What is the difference in assumptions between the one-mean t-test and the one-mean z-test?

> We introduced one-sided one-mean z-intervals. The following relationship holds between hypothesis tests and confidence intervals for one-mean z-procedures: For a right-tailed hypothesis test at the significance level α, the null hypothesis H0: μ = μ0 wil

> We introduced one-sided one-mean z-intervals. The following relationship holds between hypothesis tests and confidence intervals for one-mean z-procedures: For a left-tailed hypothesis test at the significance level α, the null hypothesis H0: μ = μ0 will

> As we mentioned on page 378, the following relationship holds between hypothesis tests and confidence intervals for one-mean z-procedures: For a two-tailed hypothesis test at the significance level α, the null hypothesis H0: μ = μ0 will be rejected in fa

> This exercise can be done individually or, better yet, as a class project. For the pretzel-packaging hypothesis test in Example 9.1 on page 352, the null and alternative hypotheses are, respectively, H0: μ = 454 g (machine is working properly) Ha: μ ≠ 45

> The number of cell phone users has increased dramatically since 1987. According to the Semiannual Wireless Survey, published by the Cellular Telecommunications & Internet Association, the mean local monthly bill for cell phone users in the United States

> Data on salaries in the public school system are published annually in Ranking of the States and Estimates of School Statistics by the National Education Association. The mean annual salary of (public) classroom teachers is $55.4 thousand. A random sampl

> 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

> The daily charges, in dollars, for a sample of 15 hotels and motels operating in South Carolina are provided on the WeissStats site. The data were found in the report South Carolina Statistical Abstract, sponsored by the South Carolina Budget and Control

> We have drawn a smooth curve that represents a distribution. In each case, do the following: a. Identify the shape of the distribution with regard to modality. b. Identify the shape of the distribution with regard to symmetry (or non-symmetry). c. If the

> Answer true or false and explain your answer: If it is important not to reject a true null hypothesis, the hypothesis test should be performed at a small significance level.

> In the article “Business Employment Dynamics: New Data on Gross Job Gains and Losses” (Monthly Labor Review, Vol. 127, Issue 4, pp. 29–42), J. Spletzer et al. examined gross job gains and losses as a percentage of the average of previous and current empl

> 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 steelplant workers due to heat stress. A random sample of 29 casting workers

Question: we have presented a confidence interval (CI)