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Elementary Statistics 8th Edition Neil A. Weiss - Solutions

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 equivalent to a procedure that you studied earlier.a.
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 from the existing t-table but must be provided
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 number of possible values for the two variables are a. Two and three. b. Four and three. c. m and n.
According to Dave Leip's Atlas of U.S. Presidential Elections, in the 2008 presidential election, 52.9% of those voting voted for the Democratic candidate (Barack H. Obama), whereas 61.9% of those voting who lived in Illinois did so. For that presidential election, does an association exist between
According to the document Physician Specialty Data, published by the Association of American Medical Colleges, in 2008, 12.9% of active male physicians specialized in internal medicine and 15.6% of active female physicians specialized in internal medicine. Does an association exist between the
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 distribution of gender.c. Determine the conditional
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 gender.c. Determine the conditional distribution
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 distribution of class level.c. Determine the
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 "class level" for this population of night-school
Refer to Table 12.12.a. If you have not done Exercise 12.47, 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 "political party affiliation" and "class level"
According to the Centers for Disease Control and Prevention publication HIV/AIDS Surveillance Report, Vol. 19, the number of AIDS cases in the United States in 2007, by gender and race, is as shown in the following contingency table.a. How many cells does this contingency table have?b. Fill in the
For a χ2-curve with 19 degrees of freedom, determine the χ2-value that has area a. 0.025 to its right. b. 0.95 to its right.
As reported by the Motor Vehicle Manufacturers Association of the United States in Motor Vehicle Facts and Figures, the number of cars and trucks in use by age are as shown in the following contingency table. Frequencies are in millions.a. How many cells does this contingency table have?b. Fill in
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 Table 1 of the article. 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 beds.In the following questions, the term
The U.S. Department of Agriculture, National Agricultural Statistics Service, 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 U.S. Census Bureau publishes information about housing units in American Housing Survey for the United States. The following table cross-classifies occupied housing units by number of persons and tenure of occupier. The frequencies are in thousands.a. How many occupied housing units are
Refer to Exercise 12.49. For AIDS cases in the United States in 2007, answer the following questions:a. Find and interpret the conditional distribution of gender by race.b. Find and interpret the marginal distribution of gender.c. Are the variables "gender" and "race" associated? Explain your
Refer to Exercise 12.50. Here, the term "vehicle" refers to either a U.S. car or truck currently in use.a. Determine the conditional distribution of age group for each type of vehicle.b. Determine the marginal distribution of age group for vehicles.c. Are the variables "type" and "age group" for
Refer to Exercise 12.51.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. Determine the marginal distribution of educational
Refer to Exercise 12.52.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 distribution of number of beds for U.S. hospitals.d.
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 CD.a. Group the bivariate data for these two
For a χ2-curve with 22 degrees of freedom, determine the χ2-value that has area a. 0.01 to its right. b. 0.995 to its right.
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-up), are as presented on the WeissStats CD.a.
The U.S. Congress, Joint Committee on Printing, provides information on the composition of Congress in Congressional Directory. On the WeissStats CD, we present data on party and class for the senators in the 111th Congress.a. Group the bivariate data for these two variables into a contingency
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? Explain your answer.b. Determine the marginal
The U.S. Census Bureau publishes census data on the resident population of the United States in Current Population Reports. 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 and gender, what percentage of the resident
In Example 12.9, we made the following statement: If no association exists between marital status and alcohol consumption, the proportion of married adults who abstain is the same as the proportion of all adults who abstain. Explain why that statement is true.
Studies have shown that a positive association exists between educational level and annual salary; in other words, people with more education tend to make more money.a. Does this finding mean that more education causes a person to make more money? Explain your answer.b. Do you think there is a
We stated earlier that, if two variables are not associated, there is no point in looking for a causal relationship. Why is that so?
For a χ2-curve with df = 10, determine a. χ2 0.05. b. χ20.975.
Identify three techniques that can be tried as a remedy when one or more of the expected-frequency assumptions for a chi-square independence test are violated.
In the TV show Sneak Preview by the late Gene Siskel and Roger Ebert, the two Chicago movie critics reviewed the week's new movie releases and then rated them thumbs up (positive), mixed, or thumbs down (negative). These two critics often saw the merits of a movie differently. In general, however,
Preventable chronic diseases are increasing rapidly in Native American populations, particularly diabetes. F. Gilliland et al. examined the diabetes issue in the paper "Preventative Health Care among Rural American Indians in New Mexico" (Preventative Medicine, Vol. 28, pp. 194-202). Following is a
M. Stuart et al. studied various aspects of grade-school children and their mothers and reported their findings in the article "Learning to Read at Home and at School" (British Journal of Educational Psychology, 68(1), pp. 3-14). The researchers gave a questionnaire to parents of 66 children in
A study reported by D. Goldberg in The Detection of Psychiatric Illness by Questionnaire (Oxford University Press, London, 1972, p. 126) examined the relationship between mental-health classification and thoughts of suicide.The mental health of each person in a sample of 295 was classified as
The American Bar Foundation publishes information on the characteristics of lawyers in The Lawyer Statistical Report. The following contingency table cross-classifies 307 randomly selected U.S. lawyers by status in practice and the size of the city in which they practice. At the 5% significance
Exit polls are surveys of a small percentage of voters taken after they leave their voting place. Pollsters use these data to project the positions of all voters or segments of voters on a particular race or ballot measure. From Election Center 2008 on the Cable News Network Web site, we found an
In the paper "Depression and Bone Mineral Density: Is There a Relationship in Elderly Asian Men?" (Osteoporosis International, Vol. 16, pp. 610-615), S. Wong et al. published results of their study on bone mineral density (BMD) and depression for 1999 Hong Kong men aged 65 to 92 years. Here are the
In Issue 338 of the Amstat News, thenpresident of the American Statistical Association Fritz Scheuren reported the results of a survey on how members would prefer to receive ballots in annual elections.a. Following are the results of the survey, cross-classified by gender. At the 5% significance
A CNN/USA TODAY poll conducted by Gallup asked a sample of employed Americans the following question: "Which do you enjoy more, the hours when you are on your job, or the hours when you are not on your job?" The responses to this question were cross-tabulated against several characteristics, among
For a χ2-curve with df = 4, determine a. χ2 0.005. b. χ2 0.99.
In Exercise 12.75, you couldn't perform the chi-square independence test because the assumptions regarding expected frequencies were not met. As mentioned in the text, three approaches are available for remedying the situation: (1) combine rows or columns; (2) eliminate rows or columns; or (3)
In part (c) of Exercise 12.78, you couldn't perform the chi-square independence test because the assumptions regarding expected frequencies were not met. Combine the MA and Other categories and then attempt to perform the hypothesis test again.
Consider a variable of several populations. Define the terms homogeneous and nonhomogeneous in this context.
State the null and alternative hypotheses for a chi-square homogeneity test a. Without using the terms homogeneous and nonhomogeneous. b. Using the terms homogeneous and nonhomogeneous.
The U.S. Census Bureau compiles data on the U.S. population by region and race and publishes its findings in Current Population Reports. Independent simple random samples of residents in the four U.S. regions gave the following data on race.At the 1% significance level, do the data provide
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 taken in May 2008. Independent simple random samples of 300 residents each in red (predominantly Republican), blue (predominantly Democratic), and
The Bureau of Justice Statistics surveys jail inmates on various issues and reports its findings in Profile of Jail Inmates. Independent simple random samples of jail inmates in two different years gave the following information on age.At the 5% significance level, do the data provide sufficient
Prior to the 2008 election, the Quinnipiac University Poll asked a sample of U.S. residents, "If Barack Obama is elected President, do you think the economy will get better, get worse or stay about the same?" This problem is based on the results of that poll. Independent simple random samples of
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 of observation only (129 patients), an
A newspaper article titled "On Race in America" reported the results of a New York Times/CBS News poll of 1338 whites and 297 blacks on several race issues. One question was whether race relations in the United States are generally good or bad. The results are presented in the following table.At
From the Web site of Gallup, Inc., we found polls regarding Americans' approval of how the president is handling foreign affairs. In two particular polls, the question asked was, "Do you approve of the way Barack Obama is handling foreign affairs?" In a February 2009 poll of 1007 national adults,
From two USA Today/Gallup polls, we found information about Americans' approval of government bailouts to two of the Big Three U.S. automakers. The question asked was, "Do you approve or disapprove of the federal loans given to General Motors and Chrysler last year to help them avoid bankruptcy?"
Refer to Exercise 12.95 and show that the value of the χ2-statistic equals the square of the value of the z-statistic. (Note: You may observe slight differences due to roundoff error.)
Refer to Exercise 12.96 and show that the value of the χ2-statistic equals the square of the value of the z-statistic. (Note: You may observe slight differences due to roundoff error.)
From Exercises 12.97 and 12.98, we conjecture that, for a comparison of two population proportions, the value of the χ2-statistic of a chi-square homogeneity test equals the square of the value of the z-statistic of a two-proportions z-test. Establish that fact.
Consider a χ2-curve with 17 degrees of freedom. Use Table V to determine a. χ2 0.99. b. χ2 0.01. c. The χ2-value that has area 0.05 to its right. d. The χ2-value that has area 0.05 to its left. e. The two χ2-values that divide the area under the curve into a middle 0.95 area and two outside
The U.S. Census Bureau compiles census data on educational attainment of Americans. From the document Current Population Reports, we obtained the 2000 distribution of educational attainment for U.S. adults 25 years old and older. Here is that distribution. Highest level PercentageNot HS
From the Information Please Almanac, we compiled the following table on U.S. region of birth and political party of the first 44 U.S. presidents. The table uses these abbreviations: F = Federalist, DR = Democratic-Republican, D = Democratic, W= Whig, R = Republican, U = Union; NE = Northeast, MW =
Refer to Problem 12.a. Find the conditional distributions of birth region by party and the marginal distribution of birth region.b. Find the conditional distributions of party by birth region and the marginal distribution of party.c. Does an association exist between the variables "birth region"
From data in Hospital Statistics, published by the American Hospital Association, we obtained the following contingency table for U.S. hospitals and nursing homes by type of facility and type of control. We used the abbreviations Gov for Government, Prop for Proprietary, and NP for nonprofit.In the
Refer to Problem 14.a. Obtain the conditional distribution of control type within each facility type.b. Does an association exist between facility type and control type for U.S. hospitals? Explain your answer.c. Determine the marginal distribution of control type for U.S. hospitals.d. Construct a
Hodgkin's disease is a malignant, progressive, sometimes fatal disease of unknown cause characterized by enlargement of the lymph nodes, spleen, and liver. The following contingency table summarizes data collected during a study of 538 patients with Hodgkin's disease. The table cross-classifies the
The U.S. Census Bureau compiles information on money income of people by type of residence and publishes its finding in Current Population Reports. Independent simple random samples of people residing inside principal cities (IPC), outside principal cities but within metropolitan areas (OPC), and
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 conducted in May 2008. Independent simple random samples of registered Democrats, Republicans, and Independents were asked, "Do you think the United
The document Arizona Residential Property Valuation System, published by the Arizona Department of Revenue, describes how county assessors use computerized systems to value single-family residential properties for property tax purposes. On the WeissStats CD are data on lot size (in acres) and house
Several years ago, a Gallup Poll asked 1528 adults the following question: "The New Jersey Supreme Court recently ruled that all life-sustaining medical treatment may be withheld or withdrawn from terminally ill patients, provided that is what the patients want or would want if they were able to
a. Explain what it would mean for an association to exist between eye color and hair color.b. Do you think that an association exists between eye color and hair color? Explain your answer.c. Use the data provided in the contingency table to decide, at the 5% significance level, whether an
a. Sex and classificationb. Sex and residencyc. Sex and colleged. Classification and residencye. Classification and collegef. College and residencyRecall from Chapter 1 (refer to page 30) that the Focus database and Focus sample contain information on the undergraduate students at the University of
Recall that the number of degrees of freedom for the t-distribution used in a one-mean t-test depends on the sample size. Is that true for the chi-square distribution used in a chisquarea. Goodness-of-fit test?b. Independence test?c. Homogeneity test? Explain your answers.
Explain why a chi-square goodness-of-fit test, a chi-square independence test, or a chi-square homogeneity test is always right tailed.
Regarding the expected-frequency assumptions for a chisquare goodness-of-fit test, a chi-square independence test, or a chi-square homogeneity test,a. State them.b. How important are they?
T. G. Exter's book Regional Markets, Vol. 2/Households (Ithaca, NY: New Strategist Publications, Inc.) provides information on U.S. households by region of the country. This problem gives data current at the time of the book's publication. One table in the book cross-classifies households by race
Suppose that you have bivariate data for an entire population.a. How would you decide whether an association exists between the two variables under consideration?b. Assuming that you make no calculation mistakes, could your conclusion be in error? Explain your answer.
Suppose that you have bivariate data for a sample of a population. a. How would you decide whether an association exists between the two variables under consideration? b. Assuming that you make no calculation mistakes, could your conclusion be in error? Explain your answer.
For an F-curve with df = (6, 10), finda. F0.05.b. F0.01.c. F0.025.
Refer to Table VI in Appendix A. Because of space restrictions, the numbers of degrees of freedom are not consecutive. For instance, the degrees of freedom for the numerator skips from 24 to 30. If you had only Table VI and you needed to find F0.05 for df = (25, 20), how would you do it?
State the four assumptions required for one-way ANOVA. How crucial are these assumptions?
If we define s = √MSE, of which parameter is s an estimate?
The null and alternative hypotheses for a one-way ANOVA test are, respectively, H0: μ1 = μ2 = · · · = μk Ha: Not all means are equal. Suppose that, in reality, the null hypothesis is false. Does that mean that no two of the populations have the same mean? If not, what does it mean?
In one-way ANOVA, identify the statistic used a. As a measure of variation among the sample means. b. As a measure of variation within the samples. c. To compare the variation among the sample means to the variation within the samples.
Explain the logic behind one-way ANOVA.
Discuss two methods for checking the assumptions of normal populations and equal standard deviations for a one-way ANOVA.
Determine the following items.a. SSTR b. MSTR c. SSE d. MSE e. F
Determine the following items.a. SSTR b. MSTR c. SSE d. MSE e. F
Determine the following items.a. SSTR b. MSTR c. SSE d. MSE e. F
Determine the following items.a. SSTR b. MSTR c. SSE d. MSE e. F
Determine the following items.a. SSTR b. MSTR c. SSE d. MSE e. F
Determine the following items.a. SSTR b. MSTR c. SSE d. MSE e. F
Show that, for two populations, MSE = s2p, where s2p is the pooled variance defined in Section 10.2 on page 397. Conclude that ˆš MSE is the pooled sample standard deviation, sp. Suppose that x is a normally distributed variable on each of two populations and that the population standard
We stated earlier that a one-way ANOVA test is always right tailed because the null hypothesis is rejected only when the test statistic, F, is too large. Why is the null hypothesis rejected only when F is too large?
Following are the notations for the three sums of squares. State the name of each sum of squares and the source of variation each sum of squares represents. a. SSE b. SSTR c. SST
Fill in the missing entries in the partially completed one-way ANOVA tables.
Fill in the missing entries in the partially completed one-way ANOVA tables.
Fill in the missing entries in the partially completed one-way ANOVA tables.
Fill in the missing entries in the partially completed one-way ANOVA tables.
a. Compute SST, SSTR, and SSE by using the computing formulas given in Formula 13.1 b. Compare your results in part (a) for SSTR and SSE with those in Exercises 13.24–13.29, where you employed the defining formulas. c. Construct a one-way ANOVA table. d. Decide, at the 5%
a. Compute SST, SSTR, and SSE by using the computing formulas given in Formula 13.1b. Compare your results in part (a) for SSTR and SSE with those in Exercises 13.24€“13.29, where you employed the defining formulas.c. Construct a one-way ANOVA table.d. Decide, at the 5% significance level,
a. Compute SST, SSTR, and SSE by using the computing formulas given in Formula 13.1b. Compare your results in part (a) for SSTR and SSE with those in Exercises 13.24€“13.29, where you employed the defining formulas.c. Construct a one-way ANOVA table.d. Decide, at the 5% significance

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