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Understanding Basic Statistics 7th Edition Charles Henry Brase, Corrinne Pellillo Brase - Solutions

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
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
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
Plato’s Republic: Syllable Patterns Prose rhythm is characterized by the occurrence of fi ve-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
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 15) found that about 21.4% of fi ve-syllable sequences in Symposium are of the type in which four are short and one is long. Suppose an antiquities store
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
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 fi nd 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
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 defi ned as a blood pressure reading over 140 mm Hg systolic and/or over 90 mm Hg diastolic. Hypertension, if not corrected, can
Medical: Hypertension Diltiazem is a commonly prescribed drug for hypertension(see source in Problem 19). 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
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 was
Critical Region Method: Testing Proportions Solve Problem 9 using the critical region method of testing. Since the sampling distribution of pˆ is the normal distribution, you can use critical values from the standard normal distribution as shown in Figure 9-8 or part (c) of Table 3 of the
Critical Region Method: Testing Proportions Solve Problem 11 using the critical region method of testing. Hint: See Problem 22.Compare your conclusions with the conclusions obtained by using the P-value method.Are they the same?
Critical Region Method: Testing Proportions Solve Problem 17 using the critical region method of testing. Hint: See Problem 22.Compare your conclusions with the conclusions obtained by using the P-value method.Are they the same?
Statistical Literacy When testing m how do we decide whether to use the standard normal distribution or a Student’s t distribution?
Critical Thinking All other conditions being equal, does a z or t value with larger magnitude have a larger or smaller corresponding P-value?Before you solve each problem below, fi rst categorize it by answering the following question: Are we testing a single mean or a single proportion? Assume
Matches: Number per Box The Nero Match Company sells matchboxes that are supposed to have an average of 40 matches per box, with s 5
A random sample of 94 Nero matchboxes shows the average number of matches per box to be 43.1. Using a 1% level of signifi cance, can you say that the average number of matches per box is more than 40?
Statistical Literacy What are the values of the mean and standard deviation of a standard normal distribution?
Statistical Literacy According to the empirical rule, about what percentage of a normal distribution falls within 2 standard deviations of the mean?
Statistical Literacy Please give a careful but brief answer to each of the following questions.(a) What is a population? How do you get a simple random sample? Give examples.(b) What is a sample statistic? What is a sampling distribution? Give examples.(c) Give a careful and complete statement of
Normal Distribution Oxygen demand is a term biologists use to describe the oxygen needed by fi sh and other aquatic organisms for survival. The Environmental Protection Agency conducted a study of a wetland area in Marin County, California. In this wetland environment, the mean oxygen demand was m
Normal Approximation to the Binomial The majority of house burglars simply walk into a house that is unlocked! In fact, about 57% of all house burglars gain entrance through an unlocked window or door(Reference: The Book of Risks by Larry Laudan).Suppose that n 5 129 house burglaries will occur
Sampling Distribution x Workers at a large toxic cleanup project are concerned that their white blood cell counts may have been reduced. Let x be a random variable that represents white blood cell count per cubic millimeter of whole blood in a healthy adult.Then m 7500 and s < 1750 (Reference:
Sampling Distribution pˆ Do you have a great deal of confi dence in the advice given to you by your medical doctor? About 45% of all adult Americans claim they do have a great deal of confi dence in their MDs (Reference:National Opinion Research Center, University of Chicago). Suppose a random
Testing and Estimating m with s Known Let x be a random variable that represents micrograms of lead per liter of water (g/L). An industrial plant discharges water into a creek. The Environmental Protection Agency has studied the discharged water and found x to have a normal distribution, with s 5
Testing and Estimating m with s Unknown Carboxyhemoglobin is formed when hemoglobin is exposed to carbon monoxide. Heavy smokers tend to have a high percentage of carboxyhemoglobin in their blood(Reference: A Manual of Laboratory and Diagnostic Tests by F. Fischbach). Let x be a random variable
Testing and Estimating a Proportion p Although older Americans are most afraid of crime, it is young people who are more likely to be the actual victims of crime. It seems that older people are more cautious about the people with whom they associate. A national survey showed that 10% of all people
Essay and Project In Chapters 8 and 9 you studied estimation and hypothesis testing.(a) Write a brief essay in which you discuss using information from samples to infer information about populations. Be sure to include methods of estimation and hypothesis testing in your discussion.What two
Critical Thinking Explain hypothesis testing to a friend, using the following scenario as a model.Describe the hypotheses, the sample statistic, the P-value, the meanings of type I and type II errors, and the level of signifi cance. Discuss the signifi cance of the results. Formulas are not
Statistical Literacy Are data that can be paired independent or dependent?
Statistical Literacy Consider a set of data pairs. What is the fi rst step in processing the data for a paired differences test? What is the symbol for the sample test statistic? Describe the value of the sample test statistic.
Statistical Literacy When testing the difference of means for paired data, what is the null hypothesis?
Statistical Literacy When conducting a paired differences test, what is the value of n?
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?
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
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
At the 5% level of signifi cance, test the claim that the population mean of the differences is different from 0.(a) Check Requirements Is it appropriate to use a Student’s t distribution for the sample test statistic? Explain. What degrees of freedom are used?(b) State the hypotheses.(c) Compute
Basic Computation: Paired Differences Test For a random sample of 20 data pairs, the sample mean of the differences was
The sample standard deviation of the differences was
Assume that the distribution of the differences is mound-shaped and symmetrical. At the 1% level of signifi cance, test the claim that the population mean of the differences is positive.(a) Check Requirements Is it appropriate to use a Student’s t distribution for the sample test statistic?
Business: CEO Raises Are America’s top chief executive offi cers (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:
Fishing: Shore or Boat? Is fi shing better from a boat or from the shore?Pyramid Lake is located on the Paiute Indian Nation in Nevada. Presidents, movie stars, and people who just want to catch fi sh go to Pyramid Lake for really large cutthroat trout. Let row B represent hours per fi sh caught fi
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 fi ve weather stations on Trail Ridge Road in Rocky Mountain National Park, the peak wind gusts(in
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
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 U.S. and foreign countries. Sex ratios for eight study sites in northern Europe are shown on the next page (based on The Wolf by
Demographics: Birth Rate and Death Rate In the following data pairs, A represents birth rate 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,
Golf: Tournaments Do professional golfers play better in their fi rst round?Let row B represent the score in the fourth (and fi nal) round, and let row A represent the score in the fi rst round of a professional golf tournament. A random sample of fi nalists in the British Open 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
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
Expand Your Knowledge: Confi dence Intervals for md Using techniques from Section 8.2, we can fi nd a confi dence interval for md. Consider a random sample of n matched data pairs A, B. Let d 5 B A be a random variable representing the difference between the values in a matched data pair. Compute
Critical Region Method: Student’s t Solve Problem 9 using the critical region method of testing. Compare your conclusions with the conclusion obtained by using the P-value method. Are they the same?
Critical Region Method: Student’s t Solve Problem 11 using the critical region method of testing. Compare your conclusions with the conclusion obtained by using the P-value method. Are they the same?
Statistical Literacy Consider a hypothesis test of difference of means for two independent populations x1 and x2. What is the sample test statistic?
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?
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?
Critical Thinking When conducting a test of 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.
Critical Thinking Josh and Kendra each calculated a 90% confi dence interval for the difference of means using a Student’s t distribution for random samples of size n1 5 20 and n2 5
Kendra followed the convention of using the smaller sample size to compute d.f. 5
Josh used his calculator and Satterthwaite’s approximation and obtained d.f. < 36.3. Which confi dence interval is shorter? Which confi dence interval is more conservative in the sense that the margin of error is larger?
Critical Thinking If a 90% confi dence interval for the difference of means m1 m2 contains all positive values, what can we conclude about the relationship between m1 and m2 at the 90% confi dence level?
Basic Computation: Testing m1 m2 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
Test the claim that the population means are different. Use level of signifi cance 0.01.(a) Check Requirements What distribution does the sample test statistic follow?Explain.(b) State the hypotheses.(c) Compute x1 x2 and the corresponding sample test statistic.(d) Estimate the P-value of the
Basic Computation: Testing m1 m2 Two populations have mound-shaped, symmetrical distributions. A random sample of 16 measurements from the fi rst 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 m1 m2 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 claim
Basic Computation: Testing m1 m2 Two populations have normal distributions.The fi rst has population standard deviation 2 and the second has population standard deviation 3.A random sample of 16 measurements from the fi rst population had a sample mean of 20.An independent random sample of 9
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. Borbély). Assume that REM sleep time is normally
Enviroment: Pollution Index Based on information from the Rocky Mountain News, a random sample of n1 5 12 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 5 14 winter days gave a sample
Survey: Outdoor Activities A Michigan study concerning preference for outdoor activities used a questionnaire with a six-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 fi shing as an
Generation Gap: Education Education infl uences 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
Crime Rate: FBI A random sample of n1 5 10 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 5 12 regions in the Rocky Mountain states gave the following violent crime
Medicine: Hay Fever A random sample of n1 5 16 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 5 14 regions in
Education: Tutoring In the journal American Journal on Intellectual and Developmental Disabilities, an article reported the results of a peer tutoring program to help mildly mentally retarded children learn to read. In the experiment, the mildly retarded children were randomly divided into two
Education: Tutoring In the article cited in Problem 17, the results of the following experiment were reported: Form 2 of the Gates-MacGintie Reading Test was administered to both an experimental group and a control group after 6 weeks of instruction during which the experimental group received peer
Wildlife: Fox Rabies A study of fox rabies in southern Germany gave 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 2:11–34). Based on information from
Agriculture: Bell Peppers The pathogen Phytophthora capsici causes bell peppers to wilt and die. Because bell peppers are an important commercial crop, this organism has undergone a great deal of agricultural research. It is thought that too much water aids the spread of the pathogen. Two fi elds
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 variable x1 measures manager’s
Management: Intimidators and Stressors This problem is based on information regarding productivity in leading Silicon Valley companies (see reference in Problem 21). In large corporations, an “intimidator” is an employee who tries to stop communication, sometimes sabotages others, and, above
Expand Your Knowledge: Software Approximation for Degrees of Freedom Given x1 and x2 distributions that are normal or approximately normal with unknown s1 and s2, the value of t corresponding to x1 x2 has a distribution that is approximated by a Student’s t distribution. We use the convention
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 30.Then, if s1 and s2 are unknown but we have reason to believe that s1 5 s2, we can pool the
Critical Region Method: Testing m1 m2; s1, s2 Unknown Redo Problem 15(a) using the critical region method, and compare your results to those obtained using the P-value method.
Critical Region Method: Testing m1 m2; s1, s2 Known Redo Problem 11(a) using the critical region method, and compare your results to those obtained using the P-value method.
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 fi rst population and r2 successes out of n2 trials for the second population. What is the sample test statistic 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 fi rst population and r2 successes out of n2 trials for the second population. What is the best pooled estimate p for
Critical Thinking Consider two independent populations for which the proportion of successes in the fi rst population is p1 and the proportion of successes in the second population is p2. What alternate hypothesis would indicate that the proportion of successes p1 in the fi rst population is larger
Critical Thinking If a 90% confi dence interval for the difference of proportions contains some positive and some negative values, what can we conclude about the relationship between p1 and p2 at the 90% confi dence level?
Basic Computation: Testing p1 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 p1 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 signifi cance, test the claim that the probability of success for the second
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
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
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
Political Science: Voters This problem is based on information taken from The Rating Guide to Life in America’s Fifty States, by G. S. Thomas. 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
Extraterrestrials: Believe It? Based on information from Harper’s Index, r1 5 37 out of a random sample of n1 5 100 adult Americans who did not attend college believe in extraterrestrials. However, out of a random sample of n2 5 100 adult Americans who did attend college, r2 5 47 claim that they
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 7). A random sample of n1 5 59 people who are conservative voters showed that r1 5 45 said yes.Another
Critical Region Method: Testing p1 p2 Redo Problem 7 using the critical region method, and compare your results to those obtained using the P-value method.
Critical Region Method: Testing p1 p2 Redo Problem 8 using the critical region method, and compare your results to those obtained using the P-value method.
Basic Computation: Confi dence Interval for p1 p2 Consider two independent binomial experiments. In the fi rst one, 40 trials had 10 successes. In the second one, 50 trials had 15 successes.(a) Check Requirements Is it appropriate to use a normal distribution to approximate the pˆ1 pˆ2
Basic Computation: Confi dence Interval for p1 p2 Consider two independent binomial experiments. In the fi rst one, 40 trials had 15 successes. In the second one, 60 trials had 6 successes.(a) Check Requirements Is it appropriate to use a normal distribution to approximate the pˆ1 pˆ2
Myers-Briggs: Marriage Counseling Isabel Myers was a pioneer in the study of personality types. She identifi ed four basic personality preferences that are described at length in the book Manual: A Guide to the Development and Use of the Myers-Briggs Type Indicator, by Myers and McCaulley
Myers-Briggs: Marriage Counseling Most married couples have two or three personality preferences in common (see reference in Problem 17). Myers used a random sample of 375 married couples and found that 132 had three preferences in common. Another random sample of 571 couples showed that 217 had
Navajo Culture: Traditional Hogans S. C. Jett is a professor of geography at the University of California, Davis. He and a colleague, V. E. Spencer, are experts on modern Navajo culture and geography. The following information is taken from their book Navajo Architecture: Forms, History,

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