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statistics for experimentert
Introductory Statistics 10th Global Edition Neil A. Weiss - Solutions
Belief in God. Refer to Exercise 12.110 and find and interpret a 98% confidence interval for the difference between the percentages of teens and adults who believe in God.
Body Mass Index. Refer to Exercise 12.111 and find and interpret a 90% confidence interval for the difference between the percentages of adults in the two degree categories who have an above healthy weight.
Hormone Therapy and Dementia. An issue of Science News (Vol. 163, No. 22, pp. 341–342) reported that the Women’s Health Initiative cast doubts on the benefit of hormone-replacement therapy. Researchers randomly divided 4532 healthy women over the age of 65 years into two groups. One group,
Women in the Labor Force. The Organization for Economic Cooperation and Development (OECD) summarizes data on labor-force participation rates in OECD in Figures. Independent simple random samples were taken of 300 U.S. women and 250 Canadian women. Of the U.S. women, 215 were found to be in the
Is College Worth It? In the New York Times article “College Graduates Fare Well in Jobs Market, Even through Recession,”C. Rampell noted that college graduates have suffered through the recession and lackluster recovery with remarkable resilience. Of a random sample of 1020 college graduates,
Confidence in Banks. Since 1973, Gallup has asked Americans how much confidence they have in a variety of U.S. institutions.One question asked of those polled is whether they have a great deal of confidence in banks. In 2007, of a random sample of 1008 adult Americans, 413 said yes; and, in 2013,
Unemployment Rates. The Organization for Economic Cooperation and Development (OECD) conducts studies on unemployment rates by country and publishes its findings in the document Main Economic Indicators. Independent random samples of 100 and 75 people in the civilian labor forces of Finland and
Federal Gas Tax. The Quinnipiac University Poll conducts nationwide surveys as a public service and for research. In one poll, participants were asked whether they thought eliminating the federal gas tax for the summer months is a good idea. The following problems are based on the results of that
Blockers and Cancer. A Wall Street Journal article, titled“Hypertension Drug Linked to Cancer,” reported on a study of several types of high-blood-pressure drugs and links to cancer. For one type, called calcium-channel blockers, 27 of 202 elderly patients taking the drug developed cancer. For
examine the margin of error and sample size for estimating the difference between two population proportions. 12.132 Obtain a formula for the margin of error, E, in estimating the difference between two population proportions by referring to Step 2 of Procedure 12.4 on page 588.
Use your result from Exercise 12.132 to show that a (1 − α)-level confidence interval for the difference between two population proportions that has a margin of error of at most E can be obtained by choosing n1 = n2 = 0.5 zα/2 E2 rounded up to the nearest whole number.
Suppose that you can make reasonably good educated guesses, pˆ1g and pˆ2g, for the observed values of pˆ1 and pˆ2.a. Use your result from Exercise 12.132 to show that a (1 − α)-level confidence interval for the difference between two population proportions that has an approximate margin of
Eating Out Vegetarian. Refer to the study on ordering vegetarian considered in Examples 12.8–12.10.a. Obtain the margin of error for the estimate of the difference between the proportions of men and women who sometimes order veg by taking half the length of the confidence interval found in
Eating Out Vegetarian. Refer to the study on ordering vegetarian considered in Examples 12.8–12.10.a. Without making a guess for the observed values of the sample proportions, find the common sample size that will ensure a margin of error of at most 0.01 for a 90% confidence interval. Hint:Use
Eating Out Vegetarian. Repeat Exercise 12.136 by applying the formula in Exercise 12.134(a) if you can reasonably presume that at most 41% of the men sampled and at most 49% of the women sampled will be people who sometimes order veg. Compare the results obtained in Exercise 12.136 to those
use and understand the formulas in this chapter.
determine a large-sample confidence interval for a population proportion.
compute the margin of error for the estimate of a population proportion.
understand the relationship between the sample size, confidence level, and margin of error for a confidence interval for a population proportion.
determine the sample size required for a specified confidence level and margin of error for the estimate of a population proportion.
perform a large-sample hypothesis test for a population proportion.
perform large-sample inferences (hypothesis tests and confidence intervals) to compare two population proportions.
understand the relationship between the sample sizes, confidence level, and margin of error for a confidence interval for the difference between two population proportions.
determine the sample sizes required for a specified confidence level and margin of error for the estimate of the difference between two population proportions.
Medical Marijuana? An international poll of physicians was conducted on the New England Journal of Medicine website asking“Do you believe that the overall medicinal benefits of marijuana outweigh the risks and potential harms?” Identify thea. specified attribute.b. population.c. population
Holiday Blues. A poll was conducted by Opinion Research Corporation to estimate the proportions of men and women who get the“holiday blues.” Identify thea. specified attribute.b. two populations.c. two population proportions.d. two sample proportions.e. According to the poll, 34% of men and 44%
Suppose that you are using independent samples to compare two population proportions. Fill in the blanks.a. The mean of all possible differences between the two sample proportions equals the .b. For large samples, the possible differences between the two sample proportions have approximately a
Smallpox Vaccine. ABCNEWS.com published the results of a poll that asked U.S. adults whether they would get a smallpox shot if it were available. Sampling, data collection, and tabulation were done by TNS Intersearch of Horsham, Pennsylvania. When the risk of the vaccine was described in detail, 4
Part-Time Job. The New York University’s Wasserman Center for Career Development publishes a report called “Life Beyond the Square” based on the survey conducted on baccalaureate graduates. Part of the survey gauges graduating students for having a part time job. According to the class of
Part-Time Job. Refer to Problem 9.a. Determine a sample size that will ensure a margin of error of at most 0.02 for a 95% confidence interval without making a guess for the observed value of pˆ.b. Find a 95% confidence interval for p if, for a sample of the size determined in part (a), 80% of
Justice in the Courts? In an issue of Parade Magazine, the editors reported on a national survey on law and order. One question asked of the 2512 U.S. adults who took part was whether they believed that juries “almost always” convict the guilty and free the innocent. Only 578 said that they
Height and Breast Cancer. In the article “Height and Weight at Various Ages and Risk of Breast Cancer” (Annals of Epidemiology, Vol. 2, pp. 597–609), L. Brinton and C. Swanson discussed the relationship between height and breast cancer. The study, sponsored by the National Cancer Institute,
Smartphones. A survey of smartphones owned by millennials was conducted by an organization. One aspect of this study involved the gender of smartphone owners. Of 3000 sampled men of 13+ years, 2109 owned a smartphone; and of 2000 sampled women of 13+ years, 1448 owned a smartphone. At the 1%
Smartphones. Refer to Problem 13.a. Find a 99% confidence interval for the difference, p1 − p2, between the proportions of men and women smartphone owners.b. Interpret your answer in part (a) in terms of the difference in percentages of men and women smartphone owners.
Bulletproof Vests. In the New York Times article “A Common Police Vest Fails the Bulletproof Test,” E. Lichtblau reported on a U.S. Department of Justice study of 103 bulletproof vests containing a fiber known as Zylon. In ballistics tests, only 4 of these vests produced acceptable safety
A variable of two populations has a mean of 28 and a standard deviation of 7 for one of the populations and a mean of 28 and a standard deviation of 4 for the other population.a. For independent samples of sizes 15 and 10, respectively, find the mean and standard deviation of x¯1 − x¯2.b. Must
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 populations.a. For independent samples of sizes 3
Faculty Salaries. Suppose, in Example 10.2 on page 463, 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.
Faculty Salaries. Suppose, in Example 10.2 on page 463, 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.In Exercises 10.25–10.30,
Children of Diabetic Mothers. Samples of offspring between the age bracket of6-8yearsof mothers with type 1 diabetes(ODM) and non-diabetic mothers were evaluated for potential differences in vital measurements, including parameters of fasting glucose regulation and lipid metabolism. A hypothesis
Teaching Duties. 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 regards to teaching, research,
Heights. Data on the average height of males and females in various countries are compiled and published by the Disabled World in “Height chart of Men and Women in different Coun-tries”. A hypothesis test is to be performed to decide whether a difference exists in the height of men and women in
Presidential-Election Commercials. 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 published
Visible Skin Color Distribution. A group of professors obtained data on facial skin color distribution of men and women in a country to mark characteristics such as even-toned and wrinkled skin.They wanted to perform a hypothesis test to decide the differences in the facial characteristics between
Wing Length. 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 Behaviour, Vol. 66, Issue 2, pp.
Simulation. To obtain the sampling distribution of the difference between two sample means for independent samples, as stated in Key Fact 10.1 on page 466, we need to know that, for independent observations, the difference of two normally distributed variables is also a normally distributed
Simulation. 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, Key Fact 10.1 on page 466.a. Simulate 1000 samples of size 12 from a normally distributed variable with a mean of 640
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
Gender and Humor. Sense of humor of 200 male and 200 female students was examined in a paper. The researchers studied measures of abstract reasoning, verbal intelligence, humor production ability, and mating success. The students’ humor ability was tested on the basis of the number of
Fortified Juice and PTH. 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 picograms/milliliter
Driving Distances. 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 southern households provided
Indian Spleen Length. Bhavan Dhingra et al. researchers in India, were interested in ultra-sonographic measurement of liver and spleen size in healthy Indian children. They published their findings in the article ”Normal values of liver and spleen size by Ultrasonography in Indian children”
Recess and Wasted Food. Wendy Bounds et al. conducted a study to determine, among other things, scheduling recess before lunch is one way to increase children’s food and nutrient consumption at lunch and reduce plate waste. Results were published in the online article “Investigation of the
Doing Time. 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.
Gender and Humor. Refer to Exercise 10.46 and obtain a 98% confidence interval for the difference between the mean number of captions for males and females.
Fortified Juice and PTH. 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.
Driving Distances. 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.
Indian Spleen Length. Refer to Exercise 10.49 and determine a 99% confidence interval for the difference between mean spleen lengths of Indian male and female children.
Recess and Wasted Food. Refer to Exercise 10.50 and find a 98% confidence interval for the difference between the mean score for food wasted for lunches before recess and that for lunches after recess.Working with Large Data Sets
Vegetarians and Omnivores. 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), S. Lu et al.
Children of Diabetic Mothers. The paper “Correlations Between the Intrauterine Metabolic Environment and Blood Pressure in Adolescent Offspring of Diabetic Mothers” (Journal of Pediatrics, Vol. 136, Issue 5, pp. 587–592) by N. Cho et al. presented findings of research on children of diabetic
A Better Golf Tee? 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 was used for the test, and
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 z = (x¯1 − x¯2) − (μ1 − μ2)σ√(1/n1) + (1/n2)cannot be used as a basis for the required test statistic because σ is
The formula for the pooled variance, s2 p, is given on page 469.Show that, if the sample sizes, n1 and n2, are equal, then s2 p is the mean of s2 1 and s2 2 .
Two-Tailed Hypothesis Tests and CIs. As we mentioned on page 475, 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
Left-Tailed Hypothesis Tests and CIs. 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(x¯1 − x¯2) + tα · sp(1/n1) + (1/n2).For a left-tailed hypothesis test at
Right-Tailed Hypothesis Tests and CIs. 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(x¯1 − x¯2) − tα · sp(1/n1) + (1/n2).For a right-tailed hypothesis test
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
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 populations.In each case, decide whether the pooled
Political Prisoners. According to the American Psychiatric Association, posttraumatic stress disorder (PTSD) is a common psychological consequence of traumatic events that involve a threat to life or physical integrity. During the Cold War, some 200,000 people in East Germany were imprisoned for
Pancreatic Carcinoma. Pancreatic ductal adenocrarcinoma is the 4th leading cause of cancer death in the U.S. Researchers D. Delbeke et al. published the article “Optimal Interpretation of FDGPET in the diagnosis staging and management of Pancreatic Carcinoma” (The journal of Nuclear Medicine,
Acute Postoperative Days. Referto Example 10.6 (page 482).The researchers also obtained the following data on the number of acute postoperative days in the hospital using the dynamic and static systems.Dynamic Static 7 588677 6 18 9 9 10 7 7 7 7 8 7 14 9 At the 5% significance level, do the data
Stressed-Out Bus Drivers. An intervention program designed by the Stockholm Transit District was implemented to improve the work conditions of the city’s bus drivers. Improvements were evaluated by G. Evans et al., who collected physiological and psychological data for bus drivers who drove on
Schizophrenia and Dopamine. Previous research has suggested that changes in the activity of dopamine, a neurotransmitter in the brain, may be a causative factor for schizophrenia. In the paper “Schizophrenia: Dopamine β-Hydroxylase Activity and Treatment Response” (Science, Vol. 216, pp.
Wing Length. D. Cristol et al. published results of their studies of two subspecies of dark-eyed juncos in the article “Migratory Dark-Eyed Juncos, Junco Hyemalis, Have Better Spatial Memory and Denser Hippocampal Neurons than Nonmigratory Conspecifics” (Animal Behaviour, Vol. 66, pp.
Political Prisoners. Refer to Exercise 10.79 and obtain a 90% confidence interval for the difference, μ1 − μ2, between the mean ages at arrest of East German prisoners with chronic PTSD and remitted PTSD.
Pancreatic Carcinoma. Refer to Exercise 10.80 and determine a 98% confidence interval for the difference, μ1 − μ2, between the mean SUV levels in malignant and benign Pancreatic Carcinoma.
Acute Postoperative Days. Refer to Exercise 10.81 and find a 90% confidence interval for the difference between the mean numbers of acute postoperative days in the hospital with the dynamic and static systems.
Stressed-Out Bus Drivers. Refer to Exercise 10.82 and find a 90% confidence interval for the difference between the mean heart rates of urban bus drivers in Stockholm in the two environments.
Schizophrenia and Dopamine. Refer to Exercise 10.83 and determine a 98% confidence interval for the difference between the mean dopamine activities of psychotic and nonpsychotic patients.
Wing Length. Refer to Exercise 10.84 and find a 99% confidence interval for the difference between the mean wing lengths of the two subspecies.
Sleep Apnea. In the article “Sleep Apnea in Adults With Traumatic Brain Injury: A Preliminary Investigation” (Archives of Physical Medicine and Rehabilitation, Vol. 82, Issue 3, pp. 316–321), J. Webster et al. investigated sleep-related breathing disorders in adults with traumatic brain
Mandate Perceptions. L. Grossback et al. examined mandate perceptions and their causes in the paper “Comparing Competing Theories on the Causes of Mandate Perceptions” (American Journal of Political Science, Vol. 49, Issue 2, pp. 406–419). Following are data on the percentage of members in
Mutual Funds. A mutual fund is a professionally managed investment that can be sold to the general public. Mutual funds can be specialized into different categories such as healthcare-related or technology-related mutual funds. The following table lists the 3-month rates of return, in percent, for
Acute Postoperative Days. In Exercise 10.81, you conducted a nonpooled t-test to decide whether the mean number of acute postoperative days spent in the hospital is smaller with the dynamic system than with the static system. Use the technology of your choice to perform the following tasks.a. Using
Neurosurgery Operative Times. In Example 10.6 on pages 482–484, we conducted a nonpooled t-test, at the 5% significance level, to decide whether the mean operative time is less with the dynamic system than with the static system. Use the technology of your choice to perform the following tasks.a.
Treating Psychotic Illness. L. Petersen et al. evaluated the effects of integrated treatment for patients with a first episode of psychotic illness in the paper “A Randomised Multicentre Trial of Integrated Versus Standard Treatment for Patients With a First Episode of Psychotic Illness”
A Better Golf Tee? 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 was used for the test and a
The Etruscans. 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 their civilization suggest,
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 nonpooled t-statistics will be identical. (Hint: Refer to Exercise 10.61 on page 479.)b. Explain why part (a) does not imply that the two t-tests
Two-Tailed Hypothesis Tests and CIs. As we mentioned on page 475, 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
Left-Tailed Hypothesis Tests and CIs. If the assumptions for a nonpooled t-interval are satisfied, the formula for a (1 − α)-level upper confidence bound for the difference, μ1 − μ2, between two population means is(x¯1 − x¯2) + tα ·(s2 1 /n1) + (s2 2 /n2).For a left-tailed hypothesis
Right-Tailed Hypothesis Tests and CIs. If the assumptions for a nonpooled t-interval are satisfied, the formula for a (1 − α)-level lower confidence bound for the difference, μ1 − μ2, between two population means is(x¯1 − x¯2) − tα ·(s2 1 /n1) + (s2 2 /n2).For a right-tailed
Suppose that, for two populations, the distributions of the variable under consideration have the same shape. Further suppose that you want to perform a hypothesis test based on independent random samples to compare the two population means. If the distributions of the variable are normal, would
Suppose that, for two populations, the distributions of the variable under consideration have the same shape. Further suppose that you want to perform a hypothesis test based on independent random samples to compare the two population means. If the distributions of the variable are not normal,
Suppose that you want to perform a hypothesis test based on independent random samples to compare the means of two populations. For each part, decide whether you would use the pooled t-test, the nonpooled t-test, the Mann–Whitney test, or none of these tests if preliminary data analyses of the
Suppose that you want to perform a hypothesis test based on independent random samples to compare the means of two populations. For each part, decide whether you would use the pooled t-test, the nonpooled t-test, the Mann–Whitney test, or none of these tests if preliminary data analyses of the
Suppose that you want to perform a hypothesis test based on independent random samples to compare the means of two populations. You know that the two distributions of the variable under consideration have the same shape and may be normal. You take the two samples and find that the data for one of
Wing Stroke Frequency. T. Casey et al. investigated wing stroke frequencies among two species of Euglossine bees, Friese and Cockerell, in the paper “Flight Energetics of Euglossine Bees in Relation to Morphology and Wing Stroke Frequency” (Journal of Experimental Biology, Vol. 116, Issue 1,
Mandate Perceptions. L. Grossback et al. examined mandate perceptions and their causes in the paper “Comparing Competing Theories on the Causes of Mandate Perceptions” (American Journal of Political Science, Vol. 49, Issue 2, pp. 406–419). Following are data on the percentage of members in
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