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Understandable Statistics Concepts And Methods 13th Edition Charles Henry Brase, Corrinne Pellillo Brase - Solutions
Statistical Literacy: Physical Therapy Does talking while walking slow you down? A study reported in the journal Physical Therapy (Vol. 72, No. 4) considered mean cadence (steps per minute) for subjects using no walking device, a standard walker, and a rolling walker. In addition, the cadence was
Summarize experimental design features using a completely randomized design flow chart.AppendixLO1
Conclude the test for a two-way ANOVA.AppendixLO1
Estimate P-values using the F distribution.AppendixLO1
Compute different sample F statistics using mean-square values.AppendixLO1
Identify the three main types of deviations and how they break into additional effects.AppendixLO1
Identify the notation and setup for two-way ANOVA tests.AppendixLO1
Sociology: Ethnic Groups A sociologist studying New York City ethnic groups wants to determine if there is a difference in income for immigrants from four different countries during their first year in the city. She obtained the data in the following table from a random sample of immigrants from
Ecology: Pollution The quantity of dissolved oxygen is a measure of water pollution in lakes, rivers, and streams. Water samples were taken at four different locations in a river in an effort to determine if water pollution varied from location to location. Location I was 500 meters above an
Insurance: Sales An executive at the home office of Big Rock Life Insurance is considering three branch managers as candidates for promotion to vice president. The branch reports include records showing sales volume for each salesperson in the branch (in hundreds of thousands of dollars). A random
Ecology: Vegetation Wild irises are beautiful flowers found throughout the United States, Canada, and northern Europe. This problem concerns the length of the sepal (leaf-like part covering the flower) of different species of wild iris. Data are based on information taken from an article by R. A.
Ecology: Deer Where are the deer? Random samples of square-kilometer plots were taken in different ecological locations of Mesa Verde National Park.The deer counts per square kilometer were recorded and are shown in the following table (Source: The Mule Deer of Mesa Verde National Park, edited by
Economics: Profits per Employee A random sample of companies in electric utilities (I), financial services(II), and food processing (III) gave the following information regarding annual profits per employee(units in thousands of dollars). (See reference in Problem 11.)I II III 49.1 55.6 39.0 43.4
Economics: Profits per Employee How productive are U.S. workers? One way to answer this question is to study annual profits per employee. A random sample of companies in computers (I), aerospace (II), heavy equipment (III), and broadcasting (IV) gave the following data regarding annual profits per
Archaeology: Ceramics Another type of painted ceramic vessel is called three-circle red-on-white(see reference in Problem 9). At four different sites in the Wind Mountain archaeological region, the number of such sherds was counted in local dwelling excavations.Site I Site II Site III Site IV 17 18
Archaeology: Ceramics Wind Mountain is an archaeological study area located in southwestern New Mexico. Pot sherds are broken pieces of prehistoric Native American clay vessels. One type of painted ceramic vessel is called Mimbres classic black-on-white. At three different sites, the number of such
Education: Study Time Is there a significant difference between how people study in college?College students tend to have different ways of studying for their classes. A sociology student, Linus, decided to investigate three common study methods:alone, with friends, and with a tutor. To do this,
Social Media: Posts Do people post more on certain social media platforms compared to others? Three of the most popular social media platforms in the United States are Facebook, Twitter, and Instagram.To investigate the activity of users on each platform, a random sample of user data was collected
Basic Computation ANOVA Table Using the information provided, fill in the missing parts of the ANOVA table.Source of Variation Sum of Squares Degrees of Freedom Mean Square(Variance)F Ratio Between Groups 56 Within Groups 43 21 Total 24 In each problem, please provide the following information.(a)
Basic Computation ANOVA Table Using the information provided, fill in the missing parts of the ANOVA table.Source of Variation Sum of Squares Degrees of Freedom Mean Square(Variance)F Ratio Between Groups 135 4 Within Groups Total 310 35 AppendixLO1
Critical Thinking Ainsley was conducting a study to determine whether the average number of video games a person owned differs based on the type of format(i.e., console, PC, and mobile). When conducting an ANOVA analysis, Ainsley noticed that the sample standard deviations amongst the different
Critical Thinking Haven was trying to study whether the average amount of time adults spend eating during meal times (i.e., breakfast, lunch, and dinner) differs.After collecting a random sample of three different meal times from several adults, Haven noticed that the sample means are very
Statistical Literacy For a One-Way ANOVA test, what is being measured by the between-group variability and the within-group variability?AppendixLO1
Statistical Literacy For a One-Way ANOVA test, how are the degrees of freedom computed for the F distribution?AppendixLO1
Conclude the test for a one-way ANOVA.AppendixLO1
Compute the sample F statistic.AppendixLO1
Compute mean squares between groups and within groups.AppendixLO1
Identify the notation and setup for a one-way ANOVA test.AppendixLO1
Identify the risk a of a Type I error when testing several means at once.AppendixLO1
Engineering: Thermostats A new thermostat has been engineered for the frozen food cases in large supermarkets. Both the old and the new thermostats hold temperatures at an average of 258F. However, it is hoped that the new thermostat might be more dependable in the sense that it will hold
Engineering: Fuel Injection A new fuel injection system has been engineered for pickup trucks. The new system and the old system both produce about the same average miles per gallon. However, engineers question which system (old or new) will give better consistency in fuel consumption (miles per
Investing: Mutual Funds How reliable are mutual funds that invest in bonds? Again, this depends on the bond fund you buy (see reference in Problem 11). A random sample of annual percentage returns for mutual funds holding short-term U.S. government bonds is shown next.4.6 4.7 1.9 9.3 −0.8 4.1
Investing: Mutual Funds You don’t need to be rich to buy a few shares in a mutual fund. The question is,“How reliable are mutual funds as investments?” That depends on the type of fund you buy. The following data are based on information taken from Morningstar, a mutual fund guide available
Economics: Productivity A random sample of leading companies in South Korea gave the following percentage yields based on assets (see reference in Problem 9):2.5 2.0 4.5 1.8 0.5 3.6 2.4 0.2 1.7 1.8 1.4 5.4 1.1 Use a calculator to verify that s2 5 2.247 for these South Korean companies.Another
Economics: Productivity An economist wonders if corporate productivity in some countries is more volatile than that in other countries. One measure of a company’s productivity is annual percentage yield based on total company assets. Data for this problem are based on information taken from
Agriculture: Wheat Two plots at Rothamsted Experimental Station (see reference in Problem 7) were studied for production of wheat straw. For a random sample of years, the annual wheat straw production (in pounds) from one plot was as follows:6.17 6.05 5.89 5.94 7.31 7.18 7.06 5.79 6.24 5.91 6.14
Agriculture: Wheat Rothamsted Experimental Station(England) has studied wheat production since 1852.Each year, many small plots of equal size but different soil/fertilizer conditions are planted with wheat. At the end of the growing season, the yield (in pounds) of the wheat on the plot is
Education: Time Are students as consistent with their study time as they are with leisure time? Many researchers worry that the amount of time students spend studying varies dramatically compared with the amount of time an individual spends doing leisure activities (playing games, watching movies,
School: SAT Scores Do students perform differently on the math versus the reading and writing portion of the SAT? Some educators believe that this might be the case. To study this phenomenon a study was conducted with two independent student groups. The first group consisted of a random sample of
Statistical Literacy To use the F distribution, what degrees of freedom need to be calculated?AppendixLO1
Statistical Literacy In general, is the F distribution symmetric? Can values of F be negative?AppendixLO1
Statistical Literacy When using the F distribution to test two variances, is it essential that each of the two populations be normally distributed? Would it be all right if the populations had distributions that were mound-shaped and more or less symmetric?AppendixLO1
Statistical Literacy When using the F distribution to test variances from two populations, should the random variables from each population be independent or dependent?AppendixLO1
Conclude a test for two variances.AppendixLO1
Estimate a P-value using the F distribution.AppendixLO1
Compute the sample F statistic using sample variances.AppendixLO1
Set up a test for two variances 1 s2 and 2 s2.AppendixLO1
Engineering: Solar Batteries A set of solar batteries is used in a research satellite. The satellite can run on only one battery, but it runs best if more than one battery is used. The variance s 2 of lifetimes of these batteries affects the useful lifetime of the satellite before it goes dead. If
Law: Bar Exam A factor in determining the usefulness of an examination as a measure of demonstrated ability is the amount of spread that occurs in the grades. If the spread or variation of examination scores is very small, it usually means that the examination was either too hard or too
Engineering: Jet Engines The fan blades on commercial jet engines must be replaced when wear on these parts indicates too much variability to pass inspection. If a single fan blade broke during operation, it could severely endanger a flight. A large engine contains thousands of fan blades, and
Veterinary Science: Tranquilizer Morgan is a veterinarian who visits a Vermont farm to examine prize bulls. In order to examine a bull, Morgan first gives the animal a tranquilizer shot. The effect of the shot is supposed to last an average of 65 minutes, and it usually does. However, Morgan
Medical: Clinical Test A new kind of typhoid shot is being developed by a medical research team. The old typhoid shot was known to protect the population for a mean time of 36 months, with a standard deviation of 3 months. To test the time variability of the new shot, a random sample of 23 people
Professors: Salaries The following problem is based on information taken from Academe, Bulletin of the American Association of University Professors. Let x represent the average annual salary of college and university professors (in thousands of dollars) in the United States. For all colleges and
Mountain Climbing: Accidents The following problem is based on information taken from Accidents in North American Mountaineering (jointly published by The American Alpine Club and The Alpine Club of Canada). Let x represent the number of mountain climbers killed each year. The long-term variance of
Food: Calories Let x 5 the amount of calories per meal of a healthy adult. Studies show that the population variance of x was approximately s 2 5 5776.Suppose a recent study on the diets of adult athletes from a random sample of 41 participants gave a sample variance of s2 5 3025. Use a 5% level to
Archaeology: Chaco Canyon The following problem is based on information from Archaeological Surveys of Chaco Canyon, New Mexico, by A. Hayes, D. Brugge, and W. Judge, University of New Mexico Press. A transect is an archaeological study area that is 1/5 mile wide and 1 mile long. A site in a
Psychology: Sleep Hours Studying for exams can lead college students to have severe anxiety.Some researchers believe that increased anxiety can lead to more varied sleep patterns in individuals. Let x represent the amount of hours a college student gets regularly. Suppose that students normally
Technology: Smartphones With more advanced applications being developed on mobile devices, some researchers claim that there has been a significant variation in the amount of daily smartphone usage by adult users. Let x represent the amount of hours an adult spends using their smartphone. Suppose,
Critical Thinking The x distribution must be normal in order to use a chi-square distribution to test the variance. What are some methods you can use to assess whether the x distribution is normal? Hint: See Chapter 6 and Section 10.2.AppendixLO1
Statistical Literacy Does the x distribution need to be normal in order to use the chi-square distribution to test the variance? Is it acceptable to use the chi-square distribution to test the variance if the x distribution is simply mound-shaped and more or less symmetric?AppendixLO1
Compute confidence intervals for s2 or s .AppendixLO1
Conclude the test of a single variance or standard deviation.AppendixLO1
Estimate the P-value for a test of a single variance or standard deviation using the x 2 distribution.AppendixLO1
Compute the sample x 2 statistic.AppendixLO1
Set up a test for a single variance s2.AppendixLO1
Fair Dice: Uniform Distribution A gambler complained about the dice. They seemed to be weighted! The dice were taken off the table and tested one at a time. One die was rolled 300 times and the following frequencies were recorded.Outcome 1 2 3 4 5 6 Observed frequency O 62 45 63 32 47 51 Do these
Accounting Records: Benford’s Law Benford’s Law states that the first nonzero digits of numbers drawn at random from a large complex data file have the following probability distribution (Reference:American Statistical Association, Chance, Vol. 12, No. 3, pp. 27–31; see also the Focus Problem
Marketing: Music Snoop Incorporated is a firm that does market surveys. The Rollum Sound Company hired Snoop to study the age distribution of people who stream music. To check the Snoop report, Rollum used a random sample of 519 customers and obtained the following data:Customer Age(years)Percent
Census: California The accuracy of a census report on a city in southern California was questioned by some government officials. A random sample of 1215 people living in the city was used to check the report, and the results are shown here:Ethnic Origin Census Percent Sample Result Black 10% 127
Library: Book Circulation The director of library services at Fairmont College did a survey of types of books (by subject) in the circulation library. Then she used library records to take a random sample of 888 books checked out last term and classified the books in the sample by subject. The
Census: Political Affiliation A study by a political web site reported that the distribution of voters in the United States is broken up into 36% independent, 34% Democrat, and 30% Republican. This is not always the case for metropolitan cities. The following data shows the results of a random
Technology: Gaming Preference In the past, some video game web sites believed the preference of the top video gaming consoles (Sony PlayStation, Microsoft XBOX, and Nintendo Switch) amongst gamers is equally distributed. The following data shows results of a random sample of 200 gamers who were
Ecology: Fish The Fish and Game Department stocked Lake Lulu with fish in the following proportions: 30% catfish, 15% bass, 40% bluegill, and 15% pike. Five years later it sampled the lake to see if the distribution of fish had changed. It found that the 500 fish in the sample were distributed as
Meteorology: Normal Distribution Let x be a random variable that represents the average daily temperature (in degrees Fahrenheit) in January for the town of Hana, Maui. The x variable has a mean m of approximately 688F and standard deviation s of approximately 48F (see reference in Problem 13). A
Meteorology: Normal Distribution The following problem is based on information from the National Oceanic and Atmospheric Administration (NOAA)Environmental Data Service. Let x be a random variable that represents the average daily temperature(in degrees Fahrenheit) in July in the town of Kit
Ecology: Deer The types of browse (leaves, twigs, and berries) favored by deer are shown in the following table (The Mule Deer of Mesa Verde National Park, edited by Mierau and Schmidt). Using binoculars, volunteers observed the feeding habits of a random sample of 320 deer.Type of Browse Plant
Archaeology: Stone Tools The types of raw materials used to construct stone tools found at the archaeological site Casa del Rito are shown below(Bandelier Archaeological Excavation Project, edited by Kohler and Root). A random sample of 1486 stone tools was obtained from a current excavation
Census: Type of Household The following lists the type of household for the U.S. population and for a random sample of 411 households from a metropolitan city in the United States.Type of Household Percent of U.S.Households Observed Number of Households Married with children 26% 102 Married, no
Census: Age The age distribution of the Canadian population and the age distribution of a random sample of 455 residents in the community of Red Lake Village (Northwest Territories) are shown below(based on U.S. Bureau of the Census, International Data Base).Age (years)Percent of Canadian
Basic Computation: Expected Counts A gaming web site claimed that the distribution of video game console owners follows the following proportion: 40% PlayStation, 35% Xbox, and 25% Switch. Suppose a random sample of 80 gamers were surveyed. Create a table of expected counts for each of the
Basic Computation: Expected Counts Suppose a “fair” die is rolled 100 times. Create a table of expected counts for each outcome of the die roll.AppendixLO1
Critical Thinking When the sample evidence is sufficient to justify rejecting the null hypothesis in a goodness-of-fit test, can we tell exactly how the distribution of observed values over the specified categories differs from the expected distribution?Explain.AppendixLO1
Statistical Literacy If observed data closely resembles the distribution mentioned in the null hypothesis for a goodness-of-fit test, would you expect the P-value to be large or small?AppendixLO1
Statistical Literacy If observed data closely resembles the distribution mentioned in the null hypothesis for a goodness-of-fit test, would you expect the sample test statistic x 2 to be large or small?AppendixLO1
Statistical Literacy Explain why goodness-of-fit tests are always right-tailed tests.AppendixLO1
Statistical Literacy How are expected frequencies computed for goodness-of-fit tests?AppendixLO1
Statistical Literacy For a chi-square goodness-of-fit test, how are the degrees of freedom computed?AppendixLO1
Sociology: Methods of Communication Random samples of people ages 15–24 and 25–34 were asked about their preferred method of (remote)communication with friends. The respondents were asked to select one of the methods from the following list: Video call, text message, e-mail, other.(i) Make a
Political Affiliation: Spending Two random samples were drawn from members of the U.S. Congress. One sample was taken from members who are Democrats and the other from members who are Republicans. For each sample, the number of dollars spent on federal projects in each congressperson’s home
Focus Problem: Archaeology The Focus Problem at the beginning of the chapter refers to excavations at Burnt Mesa Pueblo in Bandelier National Monument.One question the archaeologists asked was: Is raw material used by prehistoric people for stone tool manufacture independent of the archaeological
Sociology: Ethnic Groups After a large fund drive to help the Boston City Library, the following information was obtained from a random sample of contributors to the library fund. Using a 1%level of significance, test the claim that the amount contributed to the library fund is independent of
Sociology: Movie Preference Mr. Acosta, a sociologist, is doing a study to see if there is a relationship between the age of a young adult (18 to 35 years old) and the type of movie preferred. A random sample of 93 young adults revealed the following data. Test whether age and type of movie
Psychology: Myers–Briggs The following table shows the Myers–Briggs personality preference and area of study for a random sample of 519 college students(Applications of the Myers–Briggs Type Indicator in Higher Education, edited by Provost and Anchors). In the table, IN refers to introvert,
Ecology: Buffalo The following table shows age distribution and location of a random sample of 166 buffalo in Yellowstone National Park (based on information from The Bison of Yellowstone National Park, National Park Service Scientific Monograph Series).Age Lamar District Nez Perce District
Archaeology: Pottery The following table shows ceremonial ranking and type of pottery sherd for a random sample of 434 sherds at a location in the Sand Canyon Archaeological Project, Colorado (The Architecture of Social Integration in Prehistoric Pueblos, edited by Lipe and Hegmon).Ceremonial
Archaeology: Pottery The following table shows site type and type of pottery for a random sample of 628 sherds at a location in Sand Canyon Archaeological Project, Colorado (The Sand Canyon Archaeological Project, edited by Lipe).Site Type Pottery Type Row Total Blackon-White Mesa Verde
Psychology: Myers–Briggs The following table shows the Myers–Briggs personality preferences for a random sample of 519 people in the listed professions (Atlas of Type Tables by Macdaid, McCaulley, and Kainz). T refers to thinking and F refers to feeling.Occupation Personality Preference Type T
Psychology: Myers–Briggs The following table shows the Myers–Briggs personality preferences for a random sample of 406 people in the listed professions (Atlas of Type Tables by Macdaid, McCaulley, and Kainz).E refers to extroverted and I refers to introverted.Occupation Personality Preference
Sociology: Social Media Preference The following table shows the results of a study from a random sample of 400 people showing social media app preferences and age group.Person’s Age Social Media 18–23 yrs 24–29 yrs 30–35 yrs Row Total Facebook 12 26 88 126 Instagram 27 31 20 78 YouTube 35
Sociology: Dating The following table shows results from a general survey conducted by a dating web site from a random sample of 100 people on the type of dating activity and whether a person’s enjoyed their date.Results of Date Type of Activity Good Date Bad Date Neutral Row Total Indoor
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