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Understandable Statistics Concepts And Methods 13th Edition Charles Henry Brase, Corrinne Pellillo Brase - Solutions

Interpretation: Test of Independence Consider Charlotte’s study of source of fraud/identity theft and residential setting (see Problem 6). She computed sample x 2 510.2.(a) How many degrees of freedom are used? Recall that there were 5 sources of fraud/identity theft and, of course, 2 residential
Interpretation: Test of Homogeneity Consider Zane’s study regarding products recycled and age group (see Problem 5). Suppose he found a sample x 2 516.83.(a) How many degrees of freedom are used? Recall that there were 4 age groups and 3 products specified. Approximate the P-value and conclude
Basic Computation: Expected Counts The following table shows the results from a random sample of 80 people on the relationship between pet preference and social behavior.Pet Preference Social Behavior Dog Cat Row Total Extrovert 30 17 47 Introvert 11 22 33 Column Total 41 39 80 Using the
Basic Computation: Expected Counts The following table shows the results from a random sample data of 50 people on the relationship between dietary preference and athletic status.Dietary Preference Athletic Status Vegetarian Non-Vegetarian Row Total Athlete 12 14 26 Non-Athlete 9 15 24 Column Total
Critical Thinking Charlotte is doing a study on fraud and identity theft based both on source (checks, credit cards, debit cards, online banking/finance sites, other) and on residential setting of the victim.Describe the sampling method appropriate for a test of independence regarding source of
Critical Thinking Zane is interested in the proportion of people who recycle each of three distinct products:paper, plastic, electronics. He wants to test the hypothesis that the proportion of people recycling each type of product differs by age group: 12–18 years old, 19–30 years old, 31–40
Critical Thinking In general, how do the hypotheses for chi-square tests of independence differ from those for chi-square tests of homogeneity? Explain.AppendixLO1
Statistical Literacy For chi-square tests of independence and of homogeneity, do we use a righttailed, left-tailed, or two-tailed test?AppendixLO1
Statistical Literacy For chi-square distributions, as the number of degrees of freedom increases, does any skewness increase or decrease? Do chi-square distributions become more symmetric (and normal)as the number of degrees of freedom becomes larger and larger?AppendixLO1
Statistical Literacy In general, are chi-square distributions symmetric or skewed? If skewed, are they skewed right or left?AppendixLO1
What is two-way ANOVA and where is it used?AppendixLO1
What is one-way ANOVA and where is it used? (SECTION 10.5)AppendixLO1
How do you test two variances s1 2 and s2 2 ? (SECTION 10.4)AppendixLO1
How do you compute confidence intervals and tests for s ?AppendixLO1
How do you decide if two distributions are not only dependent, but actually share the same distribution? (SECTION 10.2)AppendixLO1
How do you decide if different populations share the same proportions of specified characteristics? (SECTION 10.1)AppendixLO1
How do you decide if random variables are dependent or independent? (SECTION 10.1)AppendixLO1
Statistical Literacy For a binomial experiment with r successes out of n trials, what value do we use as a point estimate for the probability of success p on a single trial?AppendixLO1
Statistical Literacy In order to use a normal distribution to compute confidence intervals for p, what conditions on np and nq need to be satisfied?AppendixLO1
Critical Thinking Results of a poll of a random sample of 3003 American adults showed that 20% did not know that caffeine contributes to dehydration. The poll was conducted for the Nutrition Information Center and had a margin of error of 61.4%.(a) Does the margin of error take into account any
Critical Thinking You want to conduct a survey to determine the proportion of people who favor a proposed tax policy. How does increasing the sample size affect the size of the margin of error?AppendixLO1
Critical Thinking You want to conduct a survey to determine the proportion of people who favor a proposed tax policy. How does increasing the confidence level from 90% to 95% affect the size of the margin of error?AppendixLO1
Critical Thinking You and your friend, Felix, wanted to determine the proportion of students on campus who believe wearing a mask will slow down the spread of a virus. Each of you collected your own sample of 100 students. Felix created a 95% confidence interval of 0.73 , p , 0.78.Suppose you also
Critical Thinking Jerold tested 30 laptop computers owned by classmates enrolled in a large computer science class and discovered that 22 were infected with keystroke-tracking spyware. Is it appropriate for Jerold to use his data to estimate the proportion of all laptops infected with such spyware?
Critical Thinking: Brain Teaser A requirement for using the normal distribution to approximate the pˆdistribution is that both np . 5 and nq . 5. Since we usually do not know p, we estimate p by pˆ and q by qˆ 512pˆ. Then we require that npˆ . 5 and nqˆ . 5. Show that the conditions npˆ . 5
Basic Computation: Confidence Interval for p Consider n 5100 binomial trials with r 5 30 successes.(a) Check Requirements Is it appropriate to use a normal distribution to approximate the pˆdistribution?(b) Find a 90% confidence interval for the population proportion of successes p.(c)
Basic Computation: Confidence Interval for p Consider n 5 200 binomial trials with r 5 80 successes.(a) Check Requirements Is it appropriate to use a normal distribution to approximate the pˆdistribution?(b) Find a 95% confidence interval for the population proportion of successes p.(c)
Basic Computation: Sample Size What is the minimal sample size needed for a 95% confidence interval to have a maximal margin of error of 0.1(a) if a preliminary estimate for p is 0.25?(b) if there is no preliminary estimate for p?AppendixLO1
Basic Computation: Sample Size What is the minimal sample size needed for a 99% confidence interval to have a maximal margin of error of 0.06(a) if a preliminary estimate for p is 0.8?(b) if there is no preliminary estimate for p?AppendixLO1
Myers–Briggs: Actors Isabel Myers was a pioneer in the study of personality types. The following information is taken from A Guide to the Development and Use of the Myers–Briggs Type Indicator by Myers and McCaulley (Consulting Psychologists Press). In a random sample of 62 professional actors,
Myers–Briggs: Judges In a random sample of 519 judges, it was found that 285 were introverts. (See reference in Problem 13.)(a) Let p represent the proportion of all judges who are introverts. Find a point estimate for p.(b) Find a 99% confidence interval for p. Give a brief interpretation of the
Navajo Lifestyle: Traditional Hogans A random sample of 5222 permanent dwellings on the entire Navajo Indian Reservation showed that 1619 were traditional Navajo hogans (Navajo Architecture: Forms, History, Distributions by Jett and Spencer, University of Arizona Press).(a) Let p be the proportion
Archaeology: Pottery Santa Fe black-on-white is a type of pottery commonly found at archaeological excavations in Bandelier National Monument. At one excavation site a sample of 592 potsherds was found, of which 360 were identified as Santa Fe black-onwhite(Bandelier Archaeological Excavation
Health Care: Colorado Physicians A random sample of 5792 physicians in Colorado showed that 3139 provide at least some charity care (i.e., treat people at no cost). These data are based on information from State Health Care Data: Utilization, Spending, and Characteristics (American Medical
Law Enforcement: Escaped Convicts Case studies showed that out of 10,351 convicts who escaped from U.S. prisons, only 7867 were recaptured (The Book of Odds by Shook and Shook, Signet).(a) Let p represent the proportion of all escaped convicts who will eventually be recaptured. Find a point
Fishing: Barbless Hooks In a combined study of northern pike, cutthroat trout, rainbow trout, and lake trout, it was found that 26 out of 855 fish died when they were caught using barbless hooks on flies or lures and then released. All hooks were removed from the fish (Source: A National Symposium
Social Media: Dating and Relationships How often do we use social media to talk about our love life? In 2020, a study by the Pew Research Center released a report on data and relationships in the digital age from 4,860 respondents. In their study, they found that 53% of social media shared or
Physicians: Solo Practice A random sample of 328 medical doctors showed that 171 have a solo practice(Source: Practice Patterns of General Internal Medicine, American Medical Association).(a) Let p represent the proportion of all medical doctors who have a solo practice. Find a point estimate for
Marketing: Customer Loyalty In a marketing survey, a random sample of 730 shoppers revealed that 628 remained loyal to their favorite supermarket during the past year (i.e., did not switch stores) (Source:Trends in the United States: Consumer Attitudes and the Supermarket, The Research Department,
Marketing: Bargain Hunters In a marketing survey, a random sample of 1001 supermarket shoppers revealed that 273 always stock up on an item when they find that item at a real bargain price. (See reference in Problem 22.)(a) Let p represent the proportion of all supermarket shoppers who always stock
Lifestyle: Smoking In a survey of 1000 large corporations, 250 said that, given a choice between a job candidate who smokes and an equally qualified nonsmoker, the nonsmoker would get the job (USA Today).(a) Let p represent the proportion of all corporations preferring a nonsmoking candidate. Find
Opinion Poll: Crime and Violence A New York Times/CBS poll asked the question, “What do you think is the most important problem facing this country today?” Nineteen percent of the respondents answered,“Crime and violence.” The margin of sampling error was plus or minus 3 percentage points.
Medical: Blood Type A random sample of medical files is used to estimate the proportion p of all people who have blood type B.(a) If you have no preliminary estimate for p, how many medical files should you include in a random sample in order to be 85% sure that the point estimate pˆ will be
Social Media: Brand Recommendations How often do we trust a brand recommended online?Let p represent the proportion of the time a consumer trusts a brand that showed up on their social media feed.(a) If you have no preliminary estimate for p, how many participants should you include in a random
Campus Life: Majors What percentage of your campus student body majors in business? Let p be the proportion of business majors on your campus.(a) If no preliminary study is made to estimate p, how large a sample is needed to be 99% sure that a point estimate pˆ will be within a distance of 0.05
Small Business: Bankruptcy The National Council of Small Businesses is interested in the proportion of small businesses that declared Chapter 11 bankruptcy last year. Since there are so many small businesses, the National Council intends to estimate the proportion from a random sample. Let p be the
Brain Teaser: Algebra Why do we use 1/4 in place of p(12p) in formula (22) for sample size when the probability of success p is unknown?(a) Show that p(12p) 51/4 2(p 21/2)2.(b) Why is p(12p) never greater than 1/4?AppendixLO1
Expand Your Knowledge: Plus Four Confidence Interval for a Single Proportion One of the technical difficulties that arises in the computation of confidence intervals for a single proportion is that the exact formula for the maximal margin of error requires knowledge of the population proportion of
Distinguish between independent and dependent samples.AppendixLO1
Compute confidence intervals for m1 2m2 when s1 and s2 are known.AppendixLO1
Compute confidence intervals for m1 −m2 when s1 and s2 are unknown.AppendixLO1
Compute confidence intervals for p1 2 p2 using the normal approximation.AppendixLO1
nterpret the meaning and implications of an all-positive, all-negative, or mixed confidence interval.AppendixLO1
Statistical Literacy When are two random samples independent?AppendixLO1
Statistical Literacy When are two random samples dependent?AppendixLO1
Critical Thinking Josh and Kendra each calculated a 90% confidence interval for the difference of means using a Student’s t distribution for random samples of size n1 5 20 and n2 5 31. Kendra followed the convention of using the smaller sample size to computed. f . 519. Josh used his calculator
Critical Thinking If a 90% confidence interval for the difference of means m1 2m2 contains all positive values, what can we conclude about the relationship between m1 and m2 at the 90% confidence level?AppendixLO1
Critical Thinking If a 90% confidence interval for the difference of means m1 2m2 contains all negative values, what can we conclude about the relationship between m1 and m2 at the 90%confidence level?AppendixLO1
Critical Thinking If a 90% confidence 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% confidence level?AppendixLO1
Basic Computation: Confidence Interval for m1 2m2 Consider two independent normal distributions. A random sample of size n1 5 20 from the first distribution showed x1 512 and a random sample of size n2 5 25 from the second distribution showed x2 514.(a) Check Requirements If s1 and s2 are known,
Basic Computation: Confidence Interval for m1 2m2 Consider two independent distributions that are mound-shaped. A random sample of size n1 5 36 from the first distribution showed x1 515, and a random sample of size n2 5 40 from the second distribution showed x2 514.(a) Check Requirements If s1 and
Basic Computation: Confidence Interval for p1 2 p2 Consider two independent binomial experiments. In the first 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 pˆ pˆ 1 2 2
Basic Computation: Confidence Interval for p1 2 p2 Consider two independent binomial experiments. In the first 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 pˆ pˆ 1 2 2
Video Games: Costs The two biggest markets for people to purchase online video games for consoles is the Xbox Marketplace and PlayStation Store. Each online store sells video games at various prices.Suppose a random sample of 50 different games and their prices were independently selected from both
Internet: Online Viewing Most individuals now get most of their content online through streaming services. Two of the top streaming services are Netflix and Hulu with viewers logging in a number of hours a day watching the service. Suppose a random sample of 100 adults were independently surveyed
Internet: YouTube One of the most popular online platforms for people to post video content is YouTube.Whenever a new video is posted, viewers have the option to “Like” or “Dislike” the video based on the content being shown. Suppose a content creator posted two videos. The first was a
Archaeology: Ireland Inorganic phosphorous is a naturally occurring element in all plants and animals, with concentrations increasing progressively up the food chain (fruit < vegetables < cereals < nuts
Archaeology: Ireland Please see the setting and reference in Problem 14. Independent random samples from two regions (not those cited in Problem 14) gave the following phosphorous measurements (in ppm). Assume the distribution of phosphorous is mound-shaped and symmetric for these two
Large U.S. Companies: Foreign Revenue For large U.S. companies, what percentage of their total income comes from foreign sales? A random sample of technology companies (IBM, Hewlett-Packard, Intel, and others) gave the following information.Technology companies, % foreign revenue: x1; n1 5 16 62.8
Pro Football and Basketball: Weights of Players Independent random samples of professional football and basketball players gave the following information(References: Sports Encyclopedia of Pro Football and Official NBA Basketball Encyclopedia). Note: These data are also available for download at
Pro Football and Basketball: Heights of Players Independent random samples of professional football and basketball players gave the following information(References: Sports Encyclopedia of Pro Football and Official NBA Basketball Encyclopedia). Note: These data are also available for download at
Botany: Iris The following data represent petal lengths (in cm) for independent random samples of two species of iris (Reference: E. Anderson, Bulletin American Iris Society). Note: These data are also available for download at the Companion Sites for this text.Petal length (in cm) of Iris
Myers–Briggs: Marriage Counseling Isabel Myers was a pioneer in the study of personality types. She identified four basic personality preferences, which are described at length in the book A Guide to the Development and Use of the Myers–Briggs Type Indicator by Myers and McCaulley (Consulting
Myers–Briggs: Marriage Counseling Most married couples have two or three personality preferences in common (see reference in Problem 20). 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
Yellowstone National Park: Old Faithful Geyser The U.S. Geological Survey compiled historical data about Old Faithful Geyser (Yellowstone National Park) from 1870 to 1987. Some of these data are published in the book The Story of Old Faithful, by G. D. Marler (Yellowstone Association Press). Let x1
Psychology: Parental Sensitivity A study was conducted on parental empathy for sensitivity cues and baby temperament (higher scores mean more empathy). Let x1 be a random variable that represents the score of a mother on an empathy test (as regards her baby). Let x2 be the empathy score of a
Navajo Culture: Traditional Hogans The following information is taken from the book Navajo Architecture: Forms, History, Distributions (University of Arizona Press). On the Navajo Reservation, a random sample of 210 permanent dwellings in the Fort Defiance region showed that 65 were traditional
Archaeology: Cultural Affiliation “Unknown cultural affiliations and loss of identity at high elevations.”These words are used to propose the hypothesis that archaeological sites tend to lose their identity as altitude extremes are reached. This idea is based on the notion that prehistoric
Wildlife: Wolves In the book The Wolf in the Southwest: The Making of an Endangered Species(University of Arizona Press), the following weights of adult gray wolves from two regions in Old Mexico are listed.Chihuahua region: x1 variable in pounds 86 75 91 70 79 80 68 71 74 64 Durango region: x2
Medical: Plasma Compress At Community Hospital, the burn center is experimenting with a new plasma compress treatment. A random sample of n1 5 316 patients with minor burns received the plasma compress treatment. Of these patients, it was found that 259 had no visible scars after treatment. Another
Psychology: Sleep Many studies in the past have reported connections between sleep and cognitive functions. One such study analyzed how the amount of sleep a student gets might affect their exam score.Students were divided into three randomized groups categorized by the amount of sleep and then
Focus Problem: Wood Duck Nests In the Focus Problem at the beginning of this chapter, a study was described comparing the hatch ratios of wood duck nesting boxes. Group I nesting boxes were well separated from each other and well hidden by available brush. There were a total of 474 eggs in group I
Critical Thinking: Different Confidence Levels(a) Suppose a 95% confidence interval for the difference of means contains both positive and negative numbers. Will a 99% confidence interval based on the same data necessarily contain both positive and negative numbers? Explain. What about a 90%
Expand Your Knowledge: Sample Size, Difference of Means What about sample size? If we want a confidence interval with maximal margin of error E and level of confidencec, then Section 7.1 shows us which formulas to apply for a single mean m and Section 7.3 shows us formulas for a single proportion
Expand Your Knowledge: Sample Size, Difference of Proportions What about the sample size n for confidence intervals for the difference of proportions p1 2p2? Let us make the following assumptions: equal sample sizes n 5n1 5n2 and all four quantities ˆ n1p1,ˆ n1q1, ˆ n2 p2, and ˆ n2q2 are
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 2x2 has a distribution that is approximated by a Student’s t distribution. We use the convention
Expand Your Knowledge: Pooled Two-Sample Procedures Under the condition that both populations have equal standard deviations(s1 5s2 ), we can pool the standard deviations and use a Student’s t distribution with degrees of freedomd. f . 5n1 1n2 2 2 to find the margin of error of a c confidence
Statistical Literacy In your own words, carefully explain the meanings of the following terms: point estimate, critical value, maximal margin of error, confidence level, and confidence interval.AppendixLO1
Critical Thinking Suppose you are told that a 95%confidence interval for the average price of a gallon of regular gasoline in your state is from $3.15 to $3.45.Use the fact that the confidence interval for the mean has the form x 2E to x 1E to compute the sample mean and the maximal margin of error
Critical Thinking If you have a 99% confidence interval for m based on a simple random sample,(a) is it correct to say that the probability that m is in the specified interval is 99%? Explain.(b) is it correct to say that in the long run, if you computed many, many confidence intervals using the
Auto Insurance: Claims Anystate Auto Insurance Company took a random sample of 370 insurance claims paid out during a 1-year period. The average claim paid was $1570. Assume s 5$250. Find 0.90 and 0.99 confidence intervals for the mean claim payment.For Problems 4–19, categorize each problem
Psychology: Closure Three experiments investigating the relationship between need for cognitive closure and persuasion were reported in “Motivated Resistance and Openness to Persuasion in the Presence or Absence of Prior Information” by A. W. Kruglanski (Journal of Personality and Social
Psychology: Closure How large a sample is needed in Problem 5 if we wish to be 99% confident that the sample mean score is within 2 points of the population mean score for students who are high on the need for closure?For Problems 4–19, categorize each problem according to the parameter being
Archaeology: Excavations The Wind Mountain archaeological site is located in southwestern New Mexico. Wind Mountain was home to an ancient culture of prehistoric Native Americans called Anasazi.A random sample of excavations at Wind Mountain gave the following depths (in centimeters) from
Archaeology: Pottery Shards of clay vessels were put together to reconstruct rim diameters of the original ceramic vessels found at the Wind Mountain archaeological site (see source in Problem 7). A random sample of ceramic vessels gave the following rim diameters (in centimeters):15.9 13.4 22.1
Interviews: Survey The National Study of the Changing Work Force conducted an extensive survey of 2958 wage and salaried workers on issues ranging from relationships with their bosses to household chores.The data were gathered through hour-long telephone interviews with a nationally representative
Interviews: Survey How large a sample is needed in Problem 9 if we wish to be 95% confident that the sample percentage of those equating success with personal satisfaction is within 1% of the population percentage?Hint: Use p < 0.52 as a preliminary estimate.AppendixLO1
Archaeology: Pottery Three-circle, red-on-white is one distinctive pattern painted on ceramic vessels of the Anasazi period found at the Wind Mountain archaeological site (see source for Problem 7). At one excavation, a sample of 167 potsherds indicated that 68 were of the three-circle,
Archaeology: Pottery Consider the three-circle, red-on-white pattern discussed in Problem 11.How many ceramic potsherds must be found and identified if we are to be 95% confident that the sample proportion ˆp of such potsherds is within 6% of the population proportion of three-circle, red-on-white
Agriculture: Bell Peppers The following data represent soil water content (percent water by volume) for independent random samples of soil taken from two experimental fields growing bell peppers (Reference: Journal of Agricultural, Biological, and Environmental Statistics). Note:These data are also

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