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Understandable Statistics Concepts And Methods 13th Edition Charles Henry Brase, Corrinne Pellillo Brase - Solutions
Critical Thinking All other conditions being equal, does a larger sample size increase or decrease the corresponding magnitude of the z or t value of the sample test statistic?AppendixLO1
Statistical Literacy What do we mean when we say a test is significant? Does this necessarily mean the results are important?AppendixLO1
Statistical Literacy When testing m or the difference of means m1 2m2 from independent populations, how do we decide whether to use the standard normal distribution or a Student’s t distribution?AppendixLO1
Critical Region Method: Testing p12 p2 Redo Problem 31 using the critical region method and compare your results to those obtained using the P-value method.AppendixLO1
Critical Region Method: Testing m1 2m2; s1, s 2 Unknown Redo Problem 21 using the critical region method and compare your results to those obtained using the P-value method.AppendixLO1
Critical Region Method: Testing m1 2m2; s1, s 2 Known Redo Problem 17 using the critical region method and compare your results to those obtained using the P-value method.AppendixLO1
Sociology: Trusting People Generally speaking, would you say that most people can be trusted? A random sample of n1 5 250 people in Chicago ages 18–25 showed that r1 5 45 said yes. Another random sample of n2 5 280 people in Chicago ages 35–45 showed that r2 5 71 said yes (based on information
Art: Politics Do you prefer paintings in which the people are fully clothed? This question was asked by a professional survey group on behalf of the National Arts Society (see reference in Problem 32). A random sample of n1 5 59 people who are conservative voters showed that r1 5 45 said yes.
Extraterrestrials: Believe It? Based on information from Harper’s Index, r1 5 37 people out of a random sample of n1 5100 adult Americans who did not attend college believe in extraterrestrials. However, out of a random sample of n2 5100 adult Americans who did attend college, r2 5 47 claim that
Political Science: Voters A random sample of n1 5 288 voters registered in the state of California showed that 141 voted in the last general election. A random sample of n2 5 216 registered voters in the state of Colorado showed that 125 voted in the most recent general election. Do these data
Employment: Working Remotely A study was conducted to determine whether there was a difference in the number of employees who worked from home between 2019 and 2020. In 2019, a random sample of n1 5153 employees showed that 49 of them worked from home. In 2020, a random sample of n2 5148 employees
Art Funding: Politics Would you favor spending more federal tax money on the arts? This question was asked by a research group on behalf of The National Institute(Reference: Painting by Numbers, J. Wypijewski, University of California Press). Of a random sample of n1 5 93 politically conservative
Federal Tax Money: Art Funding Would you favor spending more federal tax money on the arts? This question was asked by a research group on behalf of The National Institute (Reference: Painting by Numbers, J. Wypijewski, University of California Press). Of a random sample of n1 5 220 women, r1 5 59
Expand Your Knowledge: Pooled Two-Sample Procedure Consider independent random samples from two populations that are normal or approximately normal, or the case in which both sample sizes are at least AppendixLO1
Management: Intimidators and Stressors This problem is based on information regarding productivity in leading Silicon Valley companies (see reference in Problem 27). In large corporations, an “intimidator”is an employee who tries to stop communication, sometimes sabotages others, and, above
Management: Lost Time In her book Red Ink Behaviors, Jean Hollands reports on the assessment of leading Silicon Valley companies regarding a manager’s lost time due to inappropriate behavior of employees. Consider the following independent random variables. The first variable x1 measures a
Agriculture: Bell Peppers The pathogen Phytophthora capsici causes bell peppers to wilt and die. Because bell peppers are an important commercial crop, this disease has undergone a great deal of agricultural research. It is thought that too much water aids the spread of the pathogen. Two fields are
Wildlife: Fox Rabies A study of fox rabies in southern Germany gave the following information about different regions and the occurrence of rabies in each region (Reference: B. Sayers et al., “A Pattern Analysis Study of a Wildlife Rabies Epizootic,”Medical Informatics, Vol. 2, pp. 11–34).
Education: Remote Learning Does online learning affect student achievement? In an experiment, a group of college students were randomly divided into two groups: the experimental group received instruction through remote learning, and the control group received regular instruction in the classroom.
Education: Tutoring Does tutoring help support student achievement? In an experiment, a group of college students were randomly divided into two groups: the experimental group received peer tutoring along with regular instruction, and the control group received regular instruction with no peer
Medical: Hay Fever A random sample of n1 516 communities in western Kansas gave the following information for people under 25 years of age.x1: Rate of hay fever per 1000 population for people under 25 98 90 120 128 92 123 112 93 125 95 125 117 97 122 127 88 A random sample of n2 514 regions in
Crime Rate: FBI A random sample of n1 510 regions in New England gave the following violent crime rates(per million population).x1: New England Crime Rate 3.5 3.7 4.0 3.9 3.3 4.1 1.8 4.8 2.9 3.1 Another random sample of n2 512 regions in the Rocky Mountain states gave the following violent crime
Generation Gap: Education Education influences attitude and lifestyle. Differences in education are a big factor in the “generation gap.” Is the younger generation really better educated? Large surveys of people age 65 and older were taken in n1 5 32 U.S.cities. The sample mean for these cities
Survey: Outdoor Activities A Michigan study concerning preference for outdoor activities used a questionnaire with a 6-point Likert-type response in which 1 designated“not important” and 6 designated “extremely important.”A random sample of n1 5 46 adults were asked about fishing as an
Environment: Pollution Index Based on information from The Denver Post, a random sample of n1 512 winter days in Denver gave a sample mean pollution index of x1 5 43. Previous studies show that s1 5 21.For Englewood (a suburb of Denver), a random sample of n2 514 winter days gave a sample mean
Medical: REM Sleep REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both REM and non-REM sleep. However, it is thought that children have more REM sleep than adults (Reference: Secrets of Sleep by Dr. A. Borbely).Assume that REM sleep time is normally
Basic Computation: Test p1 2 p2 For one binomial experiment, 200 binomial trials produced 60 successes.For a second independent binomial experiment, 400 binomial trials produced 156 successes. At the 5% level of significance, test the claim that the probability of success for the second binomial
Basic Computation: Test p1 2 p2 For one binomial experiment, 75 binomial trials produced 45 successes.For a second independent binomial experiment, 100 binomial trials produced 70 successes. At the 5% level of significance, test the claim that the probabilities of success for the two binomial
Basic Computation: Testing μ12 μ2 Two populations have normal distributions. The first has population standard deviation 2 and the second has population standard deviation 3. A random sample of 16 measurements from the first population had a sample mean of 20. An independent random sample of 9
Basic Computation: Testing μ12 μ2 A random sample of 49 measurements from a population with population standard deviation 3 had a sample mean of 10. An independent random sample of 64 measurements from a second population with population standard deviation 4 had a sample mean of 12. Test the
Basic Computation: Testing μ12 μ2 Two populations have mound-shaped, symmetric distributions. A random sample of 16 measurements from the first population had a sample mean of 20, with sample standard deviation 2. An independent random sample of 9 measurements from the second population had a
Basic Computation: Testing μ12 μ2 A random sample of 49 measurements from one population had a sample mean of 10, with sample standard deviation 3.An independent random sample of 64 measurements from a second population had a sample mean of 12, with sample standard deviation 4. Test the claim
Critical Thinking Trinity wanted to determine whether the number of young adult voters (18–25)had a greater concern about climate change than older voters (65 and older). Trinity decides to take a random sample of 40 young adults and 38 older voters. If Trinity only used information based on the
Critical Thinking Emery wanted to conduct a study to determine whether the average amount of time college students spent online is different than the average amount of time employees working at a company spent online. To do this, Emery surveyed a random sample of 32 college students and 31
Critical Thinking When conducting a test for the difference of means for two independent populations x1 and x2, what alternate hypothesis would indicate that the mean of the x2 population is larger than that of the x1 population? Express the alternate hypothesis in two ways.AppendixLO1
Critical Thinking When conducting a test for the difference of means for two independent populations x1 and x2, what alternate hypothesis would indicate that the mean of the x2 population is smaller than that of the x1 population? Express the alternate hypothesis in two ways.AppendixLO1
Critical Thinking Consider use of a Student’s t distribution to test the difference of means for independent populations using random samples of sizes n1 and n2.(a) Which process gives the larger degrees of freedom, Satterthwaite’s approximation or using the smaller of n1 21 and n2 21? Which
Statistical Literacy Consider a hypothesis test of difference of proportions for two independent populations. Suppose random samples produce r1 successes out of n1 trials for the first population and r2 successes out of n2 trials for the second population.What is the best pooled estimate p for the
Statistical Literacy Consider a hypothesis test of difference of proportions for two independent populations. Suppose random samples produce r1 successes out of n1 trials for the first population and r2 successes out of n2 trials for the second population.(a) What does the null hypothesis claim
Statistical Literacy Consider a hypothesis test of difference of means for two independent populations x1 and x2. What are two ways of expressing the null hypothesis?AppendixLO1
Statistical Literacy Consider a hypothesis test of difference of means for two independent populations x1 and x2. Suppose that both sample sizes are greater than 30 and that you know s1 but not s2. Is it standard practice to use the normal distribution or a Student’s t distribution?AppendixLO1
Statistical Literacy Consider a hypothesis test of difference of means for two independent populations x1 and x2.(a) What does the null hypothesis say about the relationship between the two population means?(b) If the sample test statistic has a z distribution, give the formula for z.(c) If the
Conclude a statistical test for p1 2 p2.AppendixLO1
Compute the sample test statistics and P-value for tests of p1 2 p2.AppendixLO1
Conclude a statistical test for m1 2m2.AppendixLO1
Compute the sample test statistic and P-value for tests of m1 2m2.AppendixLO1
Explain what is meant by an independent sample.AppendixLO1
Critical Region Method: Student’s t Solve Problem 15 using the critical region method of testing.Compare your conclusions with the conclusion obtained by using the P-value method. Are they the same?AppendixLO1
Critical Region Method: Student’s t Solve Problem 12 using the critical region method of testing.Compare your conclusions with the conclusion obtained by using the P-value method. Are they the same?AppendixLO1
Psychology: Training Rats The same experimental design discussed in Problem 24 was used to test rats trained to climb a sequence of short ladders. Times in seconds for eight rats to perform this task are shown in the following table .Rat A B C D E F G H Time 1 pellets 12.5 13.7 11.4 12.1 11.0 10.4
Psychology: Training Rats The following data are based on information from the Regis University Psychology Department. In an effort to determine if rats perform certain tasks more quickly if offered larger rewards, the following experiment was performed. On day 1, a group of three rats was given a
Golf: Tournaments Do professional golfers play better in their first round? Let row B represent the score in the fourth (and final) round, and let row A represent the score in the first round of a professional golf tournament. A random sample of finalists in the British Open gave the following data
Economics: Cost of Living Index In the following data pairs, A represents the cost of living index for utilities and B represents the cost of living index for transportation. The data are paired by metropolitan areas in the United States. A random sample of 46 metropolitan areas gave the following
Economics: Cost of Living Index In the following data pairs, A represents the cost of living index for housing and B represents the cost of living index for groceries. The data are paired by metropolitan areas in the United States. A random sample of 36 metropolitan areas gave the following
Archaeology: Stone Tools The following is based on information taken from Bandelier Archaeological Excavation Project: Summer 1990 Excavations at Burnt Mesa Pueblo and Casa del Rito, edited by T. A. Kohler (Washington State University, Department of Anthropology). The artifact frequency for an
Weight Loss: Diet Programs A study was conducted to test the effects of a new diet program to determine if weight loss would occur. The following table is a random sample of 10 volunteers whose weight was measured prior to starting the diet and then 60 days after.B: Before 190 165 186 145 140 135
Demographics: Birthrate and Death Rate In the following data pairs, A represents birthrate and B represents death rate per 1000 resident population. The data are paired by counties in the Midwest. A random sample of 16 counties gave the following information(Reference: County and City Data Book,
Wildlife: Wolves In environmental studies, sex ratios are of great importance. Wolf society, packs, and ecology have been studied extensively at different locations in the United States and foreign countries.Sex ratios for eight study sites in northern Europe are shown in the following table (based
Wildlife: Highways The western United States has a number of four-lane interstate highways that cut through long tracts of wilderness. To prevent car accidents with wild animals, the highways are bordered on both sides with 12-foot-high woven wire fences.Although the fences prevent accidents, they
Ecology: Rocky Mountain National Park The following is based on information taken from Winter Wind Studies in Rocky Mountain National Park by D. E. Glidden (Rocky Mountain Nature Association).At five weather stations on Trail Ridge Road in Rocky Mountain National Park, the peak wind gusts (in miles
Academics: Tutoring A study was conducted to determine whether the effect of college tutoring has the ability of raising students’ grades. A random sample of 10 students was asked to participate in a tutoring program at their college where they were given an exam before entering the program.
Fishing: Shore or Boat? Is fishing better from a boat or from the shore? Pyramid Lake is located on the Paiute Indian Reservation in Nevada. Presidents, movie stars, and people who just want to catch fish go to Pyramid Lake for really large cutthroat trout. Let row B represent hours per fish caught
Business: CEO Raises Are America’s top chief executive officers (CEOs) really worth all that money?One way to answer this question is to look at row B, the annual company percentage increase in revenue, versus row A, the CEO’s annual percentage salary increase in that same company (Source:
Basic Computation: Paired Differences Test For a random sample of 20 data pairs, the sample mean of the differences was 2. The sample standard deviation of the differences was 5. Assume that the distribution of the differences is mound-shaped and symmetric.At the 1% level of significance, test the
Basic Computation: Paired Differences Test For a random sample of 36 data pairs, the sample mean of the differences was 0.8. The sample standard deviation of the differences was 2. At the 5% level of significance, test the claim that the population mean of the differences is different from 0.(a)
Critical Thinking Alisha is conducting a paired differences test for a “before (B score) and after(A score)” situation. She is interested in testing whether the average of the “before” scores is higher than that of the “after” scores.(a) To use a right-tailed test, how should Alisha
Critical Thinking Ellis wanted to determine whether there is significant evidence a new drug being advertised is helping people sleep longer. If Ellis wanted to conduct a paired difference test using the data, explain how the data needs to be collected.AppendixLO1
Critical Thinking Rowan wanted to conduct a test to determine whether there is a difference in the mean hours spent studying between engineering and liberal arts majors. To do this, Rowan surveyed a random sample of 32 engineering majors and 34 liberal arts majors. Explain why Rowan is unable to
Statistical Literacy List the advantages of using paired data to conduct a statistical test.AppendixLO1
Statistical Literacy When using a Student’s t distribution for a paired differences test with n data pairs, what value do you use for the degrees of freedom?AppendixLO1
Statistical Literacy When conducting a paired differences test, what is the value of n?AppendixLO1
Statistical Literacy When testing the difference of means for paired data, what is the null hypothesis?AppendixLO1
Statistical Literacy Consider a set of data pairs. What is the first step in processing the data for a paired differences test? What is the formula for the sample test statistic t? Describe each symbol used in the formula.AppendixLO1
Statistical Literacy Are data that can be paired independent or dependent?AppendixLO1
Conclude a statistical test using paired data.AppendixLO1
Estimate the P-value for a statistical test using paired data.AppendixLO1
Compute differences and the sample test statistic for paired data.AppendixLO1
Explain the advantages of paired data tests.AppendixLO1
Explain what is meant by paired data and dependent samples.AppendixLO1
Critical Region Method: Testing Proportions Solve Problem 21 using the critical region method of testing.Hint: See Problem 26. Compare your conclusions with the conclusions obtained by using the P-value method.Are they the same?AppendixLO1
Critical Region Method: Testing Proportions Solve Problem 17 using the critical region method of testing.Hint: See Problem 26. Compare your conclusions with the conclusions obtained by using the P-value method.Are they the same?AppendixLO1
Critical Region Method: Testing Proportions Solve Problem 14 using the critical region method of testing. Since the sampling distribution of ˆp is the normal distribution, you can use critical values from the standard normal distribution as shown in Figure 8-8 or part (c) of Table 5, Appendix II.
Myers–Briggs: Extroverts Are most student government leaders extroverts? According to Myers–Briggs estimates, about 82% of college student government leaders are extroverts (Source: Myers–Briggs Type Indicator Atlas of Type Tables). Suppose that a Myers–Briggs personality preference test
Medical: Hypertension Diltiazem is a commonly prescribed drug for hypertension (see source in Problem 23). However, diltiazem causes headaches in about 12% of patients using the drug. It is hypothesized that regular exercise might help reduce the headaches.If a random sample of 209 patients using
Medical: Hypertension This problem is based on information taken from The Merck Manual(a reference manual used in most medical and nursing schools). Hypertension is defined as a blood pressure reading over 140 mm Hg systolic and/or over 90 mmHg diastolic. Hypertension, if not corrected, can cause
Supermarket: Prices Harper’s Index reported that 80% of all supermarket prices end in the digit 9 or 5.Suppose you check a random sample of 115 items in a supermarket and find that 88 have prices that end in 9 or 5. Does this indicate that less than 80% of the prices in the store end in the
Consumers: Product Loyalty USA Today reported that about 47% of the general consumer population in the United States is loyal to the automobile manufacturer of their choice. Suppose Chevrolet did a study of a random sample of 1006 Chevrolet owners and found that 490 said they would buy another
Plato’s Dialogues: Prose Rhythm Symposium is part of a larger work referred to as Plato’s Dialogues.Wishart and Leach (see source in Problem 19)found that about 21.4% of five-syllable sequences in Symposium are of the type in which four are short and one is long. Suppose an antiquities store in
Plato’s Republic: Syllable Patterns Prose rhythm is characterized by the occurrence of five-syllable sequences in long passages of text.This characterization may be used to assess the similarity among passages of text and sometimes the identity of authors. The following information is based on an
Fishing: Northern Pike Athabasca Fishing Lodge is located on Lake Athabasca in northern Canada. In one of its recent brochures, the lodge advertises that 75% of its guests catch northern pike over 20 pounds.Suppose that last summer 64 out of a random sample of 83 guests did, in fact, catch northern
Wildlife: Wolves The following is based on information from The Wolf in the Southwest: The Making of an Endangered Species by David E. Brown(University of Arizona Press). Before 1918, the proportion of female wolves in the general population of all southwestern wolves was about 50%. However, after
Preference: Color What is your favorite color? A large survey of countries, including the United States, China, Russia, France, Turkey, Kenya, and others, indicated that most people prefer the color blue. In fact, about 24% of the population claim blue as their favorite color (Reference: Study by
College Athletics: Graduation Rate Female athletes at the University of Colorado, Boulder, have a longterm graduation rate of 67% (Source: Chronicle of Higher Education). Over the past several years, a random sample of 38 female athletes at the school showed that 21 eventually graduated. Does this
Sociology: Crime Rate Is the national crime rate really going down? Some sociologists say yes! They say that the reason for the decline in crime rates in the 1980s and 1990s is demographics. It seems that the population is aging, and older people commit fewer crimes. According to the FBI and the
College: Depression Is depression a common problem among college students? Research has shown many college students suffer some form of depression due to the stress of school work, finances, relationships, etc.This is why all schools offer some form of counseling to help those in need. A study by
Social Media: Facebook Has the proportion of Facebook accounts decreased worldwide? Many young adults believe that is the case because of several other social media platforms now taking center stage. In 2020, a report by eMarketer claimed that 59% of social media users use Facebook. Suppose you
Focus Problem: Benford’s Law Again, suppose you are the auditor for a very large corporation. The revenue file contains millions of numbers in a large computer data bank (see Problem 10). You draw a random sample of n 5 228 numbers from this file and r 5 92 have a first nonzero digit of 1. Let p
Focus Problem: Benford’s Law Please read the Focus Problem at the beginning of this chapter. Recall that Benford’s Law claims that numbers chosen from very large data files tend to have “1” as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly
Basic Computation: Testing p A random sample of 60 binomial trials resulted in 18 successes. Test the claim that the population proportion of successes exceeds 18%. Use a level of significance of 0.01.(a) Check Requirements Can a normal distribution be used for the ˆp distribution? Explain.(b)
Basic Computation: Testing p A random sample of 30 binomial trials resulted in 12 successes. Test the claim that the population proportion of successes does not equal 0.50. Use a level of significance of 0.05.(a) Check Requirements Can a normal distribution be used for the ˆp distribution?
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