Question: We have presented a contingency table that
We have presented a contingency table that gives a cross-classification of a random sample of values for two variables, x and y, of a population. For each exercise, perform the following tasks.
a. Find the expected frequencies. Note: You will first need to compute the row totals, column totals, and grand total.
b. Determine the value of the chi-square statistic.
c. Decide at the 5% significance level whether the data provide sufficient evidence to conclude that the two variables are associated.
> In each part, specify what type of analysis you might use. a. To study the effect of one factor on the mean of a response variable b. To study the effect of two factors on the mean of a response variable.
> Consider a variable of several populations. Define the terms homogeneous and nonhomogeneous in this context.
> True or false: If you know any two of the three sums of squares, SST, SSTR, and SSE, you can determine the remaining one. Explain your answer.
> For what purpose is a chi-square homogeneity test used?
> The following table presents information on the Kelley Blue Book’s “10 Best Green Cars of 2013.” Note that mpg and mpge are abbreviations for miles per gallon and miles per gallon equivalent, respectively. Identify the type of data provided by the inform
> State the one-way ANOVA identity, and interpret its meaning with regard to partitioning the total variation in the data.
> Although the chi-square homogeneity test and the chi-square independence test use essentially the same basic procedure, the context of the two tests are quite different. Explain the difference.
> 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
> 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-tabu
> 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?
> 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-tabu
> Suppose that a one-way ANOVA is being performed to compare the means of three populations and that the sample sizes are 10, 12, and 15. Determine the degrees of freedom for the F-statistic.
> 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-tabu
> Suppose that the variable under consideration is normally distributed on each of two populations and that the population standard deviations are equal. Further suppose that you want to perform a hypothesis test to decide whether the populations have diff
> Why is the phrase “goodness of fit” used to describe the type of hypothesis test considered in this section?
> The U.S. government’s flagship international educational exchange program, the Fulbright program, is sponsored by the Bureau of Educational and Cultural Affairs. Fulbright’s are awarded based on “academic and leadership potential, providing the opportuni
> Show that, for two populations, MSE = s2p, where s2p is the pooled variance defined in Section 10.2 on page 407. Conclude that √MSE is the pooled sample standard deviation, sp.
> 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-tabu
> What symbol is used to denote the F-value having area 0.05 to its right? 0.025 to its right? α to its right?
> 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-tabu
> we have provided data from independent simple random samples from several populations. Determine the following items. a. SSTR b. MSTR c. SSE d. MSE e. F
> 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-tabu
> we have provided data from independent simple random samples from several populations. Determine the following items. a. SSTR b. MSTR c. SSE d. MSE e. F
> 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 Ho
> we have provided data from independent simple random samples from several populations. Determine the following items. a. SSTR b. MSTR c. SSE d. MSE e. F
> A worldwide poll on religion was conducted by WIN-Gallup International and published as the document Global Index of Religiosity and Atheism. One question involved religious belief and educational attainment. The following data is based on the answers to
> As reported in Primetime Broadcast Programs, a publication of The Nielsen Company, the top three prime broadcast network television shows for the week of August 5, 2013, are as presented in the following table. Ratings are the percentage of TV homes in t
> we have provided data from independent simple random samples from several populations. Determine the following items. a. SSTR b. MSTR c. SSE d. MSE e. F
> In the article “Correlates for Completion of 3-dose Regimen of HPV Vaccine in Female Members of a Managed Care Organization” (Mayo Clinical Proceedings, Vol. 84, pp. 864– 870), C. Chao et al. examined factors that may influence whether young female patie
> we have provided data from independent simple random samples from several populations. Determine the following items. a. SSTR b. MSTR c. SSE d. MSE e. F
> In the article “Growing Pains and Fear of Gangs” (Applied Psychology in Criminal Justice, Vol. 5, No. 2, pp. 139–164), B. Brown and W. Benedict examined the relationship between worry about a gang attack and actually being a victim of a gang attack. Inte
> we have provided data from independent simple random samples from several populations. Determine the following items. a. SSTR b. MSTR c. SSE d. MSE e. F
> In the article “When News Reporters Deceive: The Production of Stereotypes” (Journalism & Mass Communication Quarterly, Vol. 84, No. 2, pp. 281–298), researchers D. Lasorsa and J. Dai investigated the relationship between authenticity and tone for news s
> In one-way ANOVA, what is the residual of an observation?
> 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 q
> 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 Me
> Discuss two methods for checking the assumptions of normal populations and equal standard deviations for a one-way ANOVA.
> As reported on MLB.com, the five players with the highest runs batted in (RBI) during the 2012 Major League Baseball season are listed in the following table. Also included are the teams for which they played, their positions, and their weights. Identify
> Use Table V to find the required χ2-values. Illustrate your work graphically. For a χ2-curve with df = 4, determine a. χ20.005. b. χ20.01.
> Figure 13.7 shows side-by-side boxplots of independent samples from three normally distributed populations having equal standard deviations. Based on these boxplots, would you be inclined to reject the null hypothesis of equal population means? Why?
> In the classic TV show Sneak Previews, originally hosted 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 c
> Figure 13.6 shows side-by-side boxplots of independent samples from three normally distributed populations having equal standard deviations. Based on these boxplots, would you be inclined to reject the null hypothesis of equal population means? Why?
> We have presented a contingency table that gives a cross-classification of a random sample of values for two variables, x and y, of a population. For each exercise, perform the following tasks. a. Find the expected frequencies. Note: You will first need
> How many degrees of freedom does an F-curve have? What are those degrees of freedom called?
> We have presented a contingency table that gives a cross-classification of a random sample of values for two variables, x and y, of a population. For each exercise, perform the following tasks. a. Find the expected frequencies. Note: You will first need
> What does the term one-way signify in the phrase one-way ANOVA?
> We have presented a contingency table that gives a cross-classification of a random sample of values for two variables, x and y, of a population. For each exercise, perform the following tasks. a. Find the expected frequencies. Note: You will first need
> Explain the logic behind one-way ANOVA.
> The Recording Industry Association of America (RIAA) reports annual statistics on shipments and revenues. For the year 2012, RIAA reported the following data on physical shipments. Identify the type of data provided by the information in each of the foll
> To compare the variation among the sample means to the variation within the samples, we use the ratio of MSTR to _____? This ratio is called the _____?
> We have given the number of possible values for two variables of a population. For each exercise, determine the maximum number of expected frequencies that can be less than 5 in order that Assumption 2 of Procedure 12.2 on page 506 be satisfied. Note: Th
> A measure of variation within the samples is called the ____? The mathematical abbreviation for it is _____?
> We have given the number of possible values for two variables of a population. For each exercise, determine the maximum number of expected frequencies that can be less than 5 in order that Assumption 2 of Procedure 12.2 on page 506 be satisfied. Note: Th
> A measure of variation among the sample means is called the ____ ? The mathematical abbreviation for it is ____ ?
> We have given the number of possible values for two variables of a population. For each exercise, determine the maximum number of expected frequencies that can be less than 5 in order that Assumption 2 of Procedure 12.2 on page 506 be satisfied. Note: Th
> For a one-way ANOVA test, 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?
> We have given the number of possible values for two variables of a population. For each exercise, determine the maximum number of expected frequencies that can be less than 5 in order that Assumption 2 of Procedure 12.2 on page 506 be satisfied. Note: Th
> Explain the reason for the word variance in the phrase analysis of variance.
> From the Baseball Almanac website, we found the heights, in inches, of the players on the 2012 World Series runner-up Detroit Tigers baseball team. a. Construct a stem-and-leaf diagram of these data with five lines per stem. b. Why is it better to use fi
> We have given the number of possible values for two variables of a population. For each exercise, determine the maximum number of expected frequencies that can be less than 5 in order that Assumption 2 of Procedure 12.2 on page 506 be satisfied. Note: Th
> If we define s = √MSE, of which parameter is s an estimate?
> Use Table V to find the required χ2-values. Illustrate your work graphically. For a χ2-curve with df = 10, determine a. χ20.05. b. χ20.025.
> One-way ANOVA is a procedure for comparing the means of several populations. It is the generalization of what procedure for comparing the means of two populations?
> We have given the number of possible values for two variables of a population. For each exercise, determine the maximum number of expected frequencies that can be less than 5 in order that Assumption 2 of Procedure 12.2 on page 506 be satisfied. Note: Th
> Find the required F -values. For an F-curve with df = (6, 10), find a. F0.05. b. F0.01. c. F0.025.
> 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.
> How do we identify an F-distribution and its corresponding F-curve?
> 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? Expla
> We stated earlier that, if two variables are not associated, there is no point in looking for a causal relationship. Why is that so?
> From the Baseball Almanac website, we found the heights, in inches, of the players on the 2012 World Series–winning San Francisco Giants baseball team. a. Construct a stem-and-leaf diagram of these data with five lines per stem. b. Why is it better to us
> In the article, “One’s Sex, Sleep, and Posttraumatic Stress Disorder” (Biology of Sex Differences, Vol. 3, No. 29, pp. 1–7), I. Kobayashi et al. study the relationship between one’s sex, sleep patterns, and posttraumatic stress disorder (PTSD) after trau
> A chi-square independence test is to be conducted to decide whether an association exists between two variables of a population. One variable has six possible values, and the other variable has four. What is the degrees of freedom for the χ2-statistic?
> 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.
> 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
