[SOLVED] We have provided a distribution and the

> Step 1 of Procedure 12.2 gives generic statements for the null and alternative hypotheses of a chi-square independence test. Use the terms statistically dependent and statistically independent, introduced on page 496, to restate those hypotheses.

> To decide whether two variables of a population are associated, we usually need to resort to inferential methods such as the chi-square independence test. Why?

> The U.S. Census Bureau publishes census data on the resident population of the United States in Current Population Survey. According to that document, 7.3% of male residents are in the age group 20–24 years. a. If no association exists between age group

> In this exercise, you are to consider two variables, x and y, defined on a hypothetical population. Following are the conditional distributions of the variable y corresponding to each value of the variable x. a. Are the variables x and y associated? Expl

> Use Table V to find the required χ2-values. Illustrate your work graphically. For a χ2-curve with 22 degrees of freedom, determine the χ2-value that has area a. 0.01 to its right. b. 0.005 to its right.

> The U.S. Congress, Joint Committee on Printing, provides information on the composition of Congress in Congressional Directory. On the WeissStats site, we present data on party and class for the senators in the 113th Congress. a. Group the bivariate data

> The Scottish Executive, Analytical Services Division Transport Statistics, compiles information on motorcycle accidents in Scotland. During one year, data on the number of motorcycle accidents, by day of the week and type of road (built-up or non–built-u

> The National Governors Association publishes information on U.S. governors in Governors’ Political Affiliations & Terms of Office. Based on that document, we obtained the data on region of residence and political party given on the WeissStats site. a. Gr

> A golf ball manufacturer has determined that a newly developed process results in a ball that lasts roughly twice as long as a ball produced by the current process. To illustrate this advance graphically, she designs a brochure showing a “new” ball havin

> Refer to Exercise 12.50. a. Determine the conditional distribution of number of beds within each facility type. b. Does an association exist between facility type and number of beds for U.S. hospitals? Explain your answer. c. Determine the marginal distr

> Refer to Exercise 12.49. a. Find the conditional distribution of educational attainment within each type of prison facility. b. Does an association exist between educational attainment and type of prison facility for prisoners? Explain your answer. c. De

> For students below postsecondary, solve the following problems. a. Determine the conditional distribution of level for each gender. b. Determine the marginal distribution of level. c. Are the variables “gender” and “level” associated? Explain your answer

> For AIDS cases in the United States in 2011, solve the following problems: a. Find and interpret the conditional distributions of region by race. b. Find and interpret the marginal distribution of region. c. Are the variables “region” and “race” associat

> The U.S. Census Bureau publishes information about housing units in American Housing Survey for the United States. The following table cross-classifies single-unit occupied housing units by foundation type and tenure of occupier. The frequencies are in t

> The U.S. Department of Agriculture publishes information about U.S. farms in Census of Agriculture. A joint frequency distribution for number of farms, by acreage and tenure of operator, is provided in the following contingency table. Frequencies are in

> The American Hospital Association publishes information about U.S. hospitals and nursing homes in Hospital Statistics. The following contingency table provides a cross classification of U.S. hospitals and nursing homes by type of facility and number of b

> Use Table V to find the required χ2-values. Illustrate your work graphically. For a χ2-curve with 19 degrees of freedom, determine the χ2-value that has area a. 0.025 to its right. b. 0.01 to its right.

> In the article “Education and Correctional Populations” (Bureau of Justice Statistics Special Report, NCJ 195670), C. Harlow examined the educational attainment of prisoners by type of prison facility. The following contingency table was adapted from Tab

> The Current Population Survey from the U.S. Census Bureau provides data on school enrollment. The following contingency table shows school enrollment below postsecondary, in thousands, by level and gender. a. How many cells does this contingency table ha

> Suggest a way in which the developer can accurately illustrate that twice as many homes will be built in the area this year as last.

> According to the Centers for Disease Control and Prevention publication HIV Surveillance Report, the number of AIDS cases in the United States in 2011, by region and race, is as shown in the following contingency table. a. How many cells does this contin

> Refer to Table 12.12. a. If you have not done Exercise 12.45, group the bivariate data for the two variables into a contingency table. b. Determine the conditional distribution of class level within each political party affiliation. c. Are the variables

> Refer to Table 12.12. a. Group the bivariate data for the two variables into a contingency table. b. Determine the conditional distribution of political party affiliation within each class level. c. Are the variables “political party affiliation” and “cl

> Refer to Table 12.11. Consider the variables “class level” and “college.” a. Group the bivariate data for these two variables into a contingency table. b. Determine the conditional distribution of class level within each college and the marginal distribu

> Refer to Table 12.11. Consider the variables “gender” and “college.” a. Group the bivariate data for these two variables into a contingency table. b. Determine the conditional distribution of gender within each college and the marginal distribution of ge

> Refer to Table 12.11. Consider the variables “gender” and “class level.” a. Group the bivariate data for these two variables into a contingency table. b. Determine the conditional distribution of gender within each class level and the marginal distributi

> According to the document Physician Specialty Data Book, published by the Association of American Medical Colleges, in 2010, 12.9% of active male physicians specialized in internal medicine and 15.3% of active female physicians specialized in internal me

> According to Dave Leip’s Atlas of U.S. Presidential Elections, in the 2012 presidential election, 51.01% of those voting voted for the Democratic candidate (Barack H. Obama), whereas 57.50% of those voting who lived in Illinois did so. For that president

> The t-table has entries for areas of 0.10, 0.05, 0.025, 0.01, and 0.005. In contrast, the χ2-table has entries for those areas and for 0.995, 0.99, 0.975, 0.95, and 0.90. Explain why the t-values corresponding to these additional areas can be obtained fr

> Identify three ways in which the total number of observations of bivariate data can be obtained from the frequencies in a contingency table.

> An article, titled “We’re Happiest at 74; It’s All Downhill till 40, Then Life Gets Better, Say Scientists,” included a graph, similar to the following one, of a happiness scale versus age. The article argues that happiness decreases until the age of 46

> Suppose that bivariate data are to be grouped into a contingency table. Determine the number of cells that the contingency table will have if the numbers of possible values for the two variables are a. two and three. b. four and three. c. m and n.

> What are the small boxes inside the heavy lines of a contingency table called?

> Identify the type of table that is used to group bivariate data.

> The chi-square goodness-of-fit test provides a method for performing a hypothesis test about the distribution of a variable that has c possible values. If the number of possible values is 2, that is, c = 2, the chi-square goodness-of-fit test is equivale

> Table showed the calculated sums of the observed frequencies, the expected frequencies, and their differences. Strictly speaking, those sums are not needed. However, they serve as a check for computational errors. a. In general, what common value should

> One probability model for child gender is that a boy or a girl is equally likely to be born. If that model is correct, then, for a two-child family, the probabilities are 0.25, 0.50, and 0.25 of two girls, one girl and one boy, and two boys, respectively

> Arabidopsis is a genus of flowering plant related to cabbage. A variegated mutant of the Arabidopsis has yellow streaks or marks. E. Miura et al. studied the origin of this variegated mutant in the article “The Balance between Protein Synthesis and Degra

> The World Series in baseball is won by the first team to win four games (ignoring the 1903 and 1919–1921 World Series, when it was a best of nine). Thus it takes at least four games and no more than seven games to establish a winner. If two teams are eve

> A project exploring the bottled-water phenomenon and preference of water types was conducted by researchers M. Lunsford and A. Fink in the article “Water Taste Test Data” (Journal of Statistics Education, Vol. 18, No. 1). One hundred nine subjects partic

> Consider two χ2-curves with degrees of freedom 12 and 20, respectively. Which one more closely resembles a normal curve? Explain your answer.

> Drunk-driving fatalities represent the total number of people (occupants and non-occupants) killed in motor vehicle traffic crashes in which at least one driver had a blood alcohol content (BAC) of 0.08 or higher. The following graph is based on data pub

> A gambler thinks a die may be loaded, that is, that the six numbers are not equally likely. To test his suspicion, he rolled the die 150 times and obtained the data shown in the following table. Do the data provide sufficient evidence to conclude that th

> An American roulette wheel contains 18 red numbers, 18 black numbers, and 2 green numbers. The following table shows the frequency with which the ball landed on each color in 200 trials. At the 5% significance level, do the data suggest that the wheel is

> Observing that the proportion of blue M&Ms in his bowl of candy appeared to be less than that of the other colors, R. Fricker, Jr., decided to compare the color distribution in randomly chosen bags of M&Ms to the theoretical distribution reported by M&M/

> The report Controlling Road Rage: A Literature Review and Pilot Study was prepared for the AAA Foundation for Traffic Safety by D. Rathbone and J. Huckabee. The authors discussed the results of a literature review and pilot study on how to prevent aggres

> The Higher Education Research Institute of the University of California, Los Angeles, publishes information on characteristics of incoming college freshmen in The American Freshman. In 2000, 27.7% of incoming freshmen characterized their political views

> According to the U.S. Census Bureau publication Demographic Profiles, a relative-frequency distribution of the U.S. resident population by region in 2000 was as follows. A simple random sample of this year’s U.S. residents gave the following frequency di

> We have provided a distribution and the observed frequencies of the values of a variable from a simple random sample of a population. In each case, use the chi-square goodness-of-fit test to decide, at the specified significance level, whether the distri

> Of the quantities p1, p2, x1, x2, pˆ1, pˆ2, and pˆp, a. which represent parameters and which represent statistics? b. which are fixed numbers and which are variables?

> We have provided a distribution and the observed frequencies of the values of a variable from a simple random sample of a population. In each case, use the chi-square goodness-of-fit test to decide, at the specified significance level, whether the distri

> The Federal Reserve System publishes weekly figures of M2 money supply in the document Money Stock Measures. M2 includes such things as cash in circulation, deposits in checking accounts, nonbank traveler’s checks, accounts such as savings deposits, and

> Consider a hypothesis test for two population proportions with the null hypothesis H0: p1 = p2. What parameter is being estimated by the a. sample proportion pˆ1? b. sample proportion pˆ2? c. pooled sample proportion pˆp?

> We have provided a distribution and the observed frequencies of the values of a variable from a simple random sample of a population. In each case, use the chi-square goodness-of-fit test to decide, at the specified significance level, whether the distri

> Industry Research polled teenagers on sunscreen use. The survey revealed that 46% of teenage girls and 30% of teenage boys regularly use sunscreen before going out in the sun. a. Identify the specified attribute. b. Identify the two populations. c. Are t

> How do you identify different chi-square distributions?

> In an ABC Global Kids Study, conducted by Roper Starch Worldwide, Inc., estimates were made in various countries of the percentage of children who attend church at least once a week. Two of the countries in the survey were the United States and Germany.

> We have provided a distribution and the observed frequencies of the values of a variable from a simple random sample of a population. In each case, use the chi-square goodness-of-fit test to decide, at the specified significance level, whether the distri

> Explain the basic idea for performing a hypothesis test, based on independent samples, to compare two population proportions.

> We have provided a distribution and the observed frequencies of the values of a variable from a simple random sample of a population. In each case, use the chi-square goodness-of-fit test to decide, at the specified significance level, whether the distri

> In the article “Drowning Deaths of Zero to Five Year Old Children in Victorian Dams, 1989–2001” (Australian Journal of Rural Health, Vol. 13, Issue 5, pp. 300–308), L. Bugeja and R. Franklin examined drowning deaths of young children in Victorian dams to

> According to Current Housing Reports, published by the U.S. Census Bureau, the primary heating fuel for all occupied housing units is distributed as follows. Suppose that you want to determine whether the distribution of primary heating fuel for occupied

> The U.S. Census Bureau publishes data on the population of the United States by race and Hispanic origin in American Community Survey. From that document, we constructed the following bar chart. Note that people who are Hispanic may be of any race, and p

> We have given the relative frequencies for the null hypothesis of a chi-square goodness-of-fit test and the sample size. Decide whether Assumptions 1 and 2 for using that test are satisfied. Sample size: n = 100. Relative frequencies: 0.44, 0.25, 0.30,

> A Harris Interactive survey found that 92.0%of 1001 American adults said they always wash up after using the bathroom. a. At the 5% significance level, do the data provide sufficient evidence to conclude that more than 9 of 10 Americans always wash up af

> We have given the relative frequencies for the null hypothesis of a chi-square goodness-of-fit test and the sample size. Decide whether Assumptions 1 and 2 for using that test are satisfied. Sample size: n = 50. Relative frequencies: 0.22, 0.22, 0.25, 0

> In the article “Prothrombotic Factors in Children With Stroke or Porencephaly” (Pediatrics Journal, Vol. 116, Issue 2, pp. 447–453), J. Lynch et al. compared differences and similarities in children with arterial ischemic stroke and porencephaly. Three c

> We have given the relative frequencies for the null hypothesis of a chi-square goodness-of-fit test and the sample size. Decide whether Assumptions 1 and 2 for using that test are satisfied. Sample size: n = 50. Relative frequencies: 0.22, 0.21, 0.25, 0

> In a national poll, 1053 U.S. adults were asked, “As you may know, Congress is considering a new economic stimulus package of at least 800 billion dollars. Do you favor or oppose Congress passing this legislation?” Of those sampled, 548 favored passage.

> We have given the relative frequencies for the null hypothesis of a chi-square goodness-of-fit test and the sample size. Decide whether Assumptions 1 and 2 for using that test are satisfied. Sample size: n = 50. Relative frequencies: 0.20, 0.20, 0.25, 0

> Of the 38 numbers on an American roulette wheel, 18 are red, 18 are black, and 2 are green. If the wheel is balanced, the probability of the ball landing on red is 18/38 = 0.474. A gambler has been studying a roulette wheel. If the wheel is out of balanc

> We have given the relative frequencies for the null hypothesis of a chi-square goodness-of-fit test and the sample size. Decide whether Assumptions 1 and 2 for using that test are satisfied. Sample size: n = 50. Relative frequencies: 0.65, 0.30, 0.05.

> This exercise involves the use of an unrealistically small population to provide a concrete illustration for the exact distribution of a sample proportion. A population consists of three men and two women. The first names of the men are Jose, Pete, and C

> Each year the director of the reading program in a school district administers a standard test of reading skills. Then the director compares the average score for his district with the national average. Figure 2.20 was presented to the school board in th

> We have given the relative frequencies for the null hypothesis of a chi-square goodness-of-fit test and the sample size. Decide whether Assumptions 1 and 2 for using that test are satisfied. Sample size: n = 100. Relative frequencies: 0.65, 0.30, 0.05.

> Labor Day was created by the U.S. labor movement over 100 years ago. It was subsequently adopted by most states as an official holiday. In a poll by Gallup, 1003 randomly selected adults were asked whether they approve of labor unions; 65% said yes. a. I

> In 2012, 15.9% of all U.S. families had incomes below the poverty level, as reported by the U.S. Census Bureau in American Community Survey. During that same year, of 400 randomly selected Wyoming families, 50 had incomes below the poverty level. At the

> P. Noakes et al. researched the effects of fatty acids found in oily fish on lowering the risk of allergic disease in the article “Increased Intake of Oily Fish in Pregnancy: Effects on Neonatal Immune Responses and on Clinical Outcomes in Infants at 6 M

> In 2010, shortly before that year’s midterm elections, when Americans were dissatisfied with government and the Tea Party movement was emerging as a political force, 58% of American adults thought that a third major party was needed. In a recent Gallup p

> A poll conducted by Gallup asked American adults about vegetarianism. This problem is based on that poll. Of independent random samples of 500 men and 512 women, 20 of the men and 36 of the women said they were vegetarians. At the 5% significance level d

> The Arizona Republic conducted a telephone poll of 758 Arizona adults who celebrate Christmas. The question asked was, “In your family, do you open presents on Christmas Eve or Christmas Day?” Of those surveyed, 394 said they wait until Christmas Day. a.

> Scoliosis is a condition involving curvature of the spine. In a study by A. Nachemson and L. Peterson, reported in the Journal of Bone and Joint Surgery (Vol. 77, Issue 6, pp. 815–822), 286 girls aged 10 to 15 years were followed to determine the effects

> Gallup conducted a national survey of 1008 American adults, asking “As you may know, as part of its efforts to investigate terrorism, a federal government agency obtained records from larger U.S. telephone and Internet companies in order to compile telep

> The Quinnipiac University Poll conducts nationwide surveys as a public service and for research. This problem is based on the results of one such poll that asked independent random samples of American adults in urban, suburban, and rural regions, “Do you

> The Times Higher Education “World University Rankings” presents global university performance tables to judge world class universities on the basis of teaching, research, knowledge transfer, and international outlook. The rankings employ 13 carefully cal