[SOLVED] Regarding the four conditions required for using

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

> Discuss the relative advantages and disadvantages of using pooled and non-pooled t-procedures.

> Each pair of graphs in Fig. 10.8 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 populatio

> suppose that you know that a variable is normally distributed on each of two populations. Further suppose that you want to perform a hypothesis test based on independent random samples to compare the two population means. Decide whether you would use the

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

> A study published by E. Anionwu et al. in the British Medical Journal (Vol. 282, pp. 283–286) measured the steady-state hemoglobin levels of patients with three different types of sickle cell disease. Following is a stem-and-leaf diagram of the data.

> suppose that you know that a variable is normally distributed on each of two populations. Further suppose that you want to perform a hypothesis test based on independent random samples to compare the two population means. Decide whether you would use the

> Suppose that you want to perform a hypothesis test to compare the means of two populations, using independent simple random samples. Assume that the two distributions of the variable under consideration have the same shape, but are not normal, and both s

> Suppose that you want to perform a hypothesis test to compare the means of two populations, using independent simple random samples. Assume that the two distributions (one for each population) of the variable under consideration are normally distributed

> If the assumptions for a 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 hypothe

> If the assumptions for a 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 hypothes

> As we mentioned, 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 hypothesis Ha:

> In this exercise, you are to perform a computer simulation to illustrate the distribution of the pooled t-statistic, given in Key Fact. a. Simulate 1000 random samples of size 4 from a normally distributed variable with a mean of 100 and a standard devia

> The formula for the pooled variance, s2p. Show that, if the sample sizes, n1 and n2, are equal, then s2p is the mean of s21 and s22.

> In this section, we introduced the pooled t-test, which provides a method for comparing two population means. In deriving the pooled t-test, we stated that the variable cannot be used as a basis for the required test statistic because σ is unknown. Why c

> The primary concern is deciding whether the mean of Population 2 is less than 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.

> According to the National Health and Nutrition Examination Survey, published by the Centers for Disease Control and Prevention, the average cholesterol level for children between 4 and 19 years of age is 165 mg/dL. A pediatrician who tested the cholester

> An independent golf equipment testing facility compared the difference in the performance of golf balls hit off a regular 2-3/4’’ wooden tee to those hit off a 3’’ Stinger Competition golf tee. A Callaway Great Big Bertha driver with 10 degrees of loft w

> 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

> Philosophical and health issues are prompting an increasing number of Taiwanese to switch to a vegetarian lifestyle. In the paper “LDL of Taiwanese Vegetarians Are Less Oxidizable than Those of Omnivores” (Journal of Nutrition, Vol. 130, pp. 1591–1596),

> Refer to Exercise 10.50 and find a 98% confidence interval for the difference between the mean amount of food wasted for lunches before recess and that for lunches after recess. Data from Exercise 10.50: E. Bergman et al. conducted a study to determine,

> Refer to Exercise 10.49 and determine a 99% confidence interval for the difference between mean spleen lengths of Nigerian males and females. Data from Exercise 10.49: O. Ehimwenma and M. Tagbo, researchers in Nigeria, were interested in how characteris

> Refer to Exercise 10.48 and determine a 95% confidence interval for the difference between last year’s mean VMTs by midwestern and southern households. Data from Exercise 10.48: Data on household vehicle miles of travel (VMT) are compiled annually by th

> Refer to Exercise 10.47 and find a 90% confidence interval for the difference between the mean reductions in PTH levels for fortified and unfortified orange juice. Data from Exercise 10.47: V. Tangpricha et al. did a study to determine whether fortifyin

> Refer to Exercise 10.46 and obtain a 98% confidence interval for the difference between the mean absolute pointing errors for males and females. Data from Exercise 10.46: In the paper “The Relation of Sex and Sense of Direction to Spatial Orientation in

> Refer to Exercise 10.45 and obtain a 90% confidence interval for the difference between the mean times served by prisoners in the fraud and firearms offense categories. Data from Exercise 10.45: The Federal Bureau of Prisons publishes data in Prison Sta

> E. Bergman et al. conducted a study to determine, among other things, the impact that scheduling recess before or after the lunch period has on wasted food for students in grades three through five. Results were published in the online article “The Relat

> The Internal Revenue Service (IRS) publishes data on adjusted gross incomes in the document Statistics of Income, Individual Income Tax Returns. The following relative-frequency histogram shows one year’s individual income tax returns for adjusted gross

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

> O. Ehimwenma and M. Tagbo, researchers in Nigeria, were interested in how characteristics of the spleen of residents in their tropical environment compare to those found elsewhere in the world. They published their findings in the article “Determination

> 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. Independent random samples of 15 midwestern households and 14 sou

> V. Tangpricha et al. did a study to determine whether fortifying orange juice with Vitamin D would result in changes in the blood levels of five biochemical variables. One of those variables was the concentration of parathyroid hormone (PTH), measured in

> 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

> 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 yielde

> 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

> Polychlorinated biphenyls (PCBs), industrial pollutants, are known to be carcinogens and a great danger to natural ecosystems. As a result of several studies, PCB production was banned in the United States in 1979 and by the Stockholm Convention on Persi

> 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

> Discuss the basic strategy for performing a hypothesis test to compare the means of two populations, based on independent samples.

> 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.

> 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

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

> 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

Question: Regarding the four conditions required for using