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Question: Suppose that the variable under consideration is


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 different means, that is, whether μ1 ≠ μ2. If independent simple random samples are used, identify two hypothesis-testing procedures that you can use to carry out the hypothesis test.


> The National Association of Colleges and Employers(NACE) conducts surveys on salary offers to college graduates by field and degree. Results are published in Salary Survey. The following table provides summary statistics for starting salaries, in thousan

> Entanglement of marine mammals in fishing gear is a global issue and a significant threat to minke whales, in particular. In the article “Fishing Gears Involved in Entanglements of Minke Whales (Balaenoptera acutorostrata) in the East Sea of Korea” (Mari

> A clinical study was conducted to see whether an antibody called denosumab is effective in treatment of osteoporosis of postmenopausal women, as reported in the article “Denosumab in Postmenopausal Women with Low Bone Mineral Density (New England Journal

> Considerable controversy exists over whether long-term neurodevelopment is affected by nutritional factors in early life. A. Lucas and R. Morley summarized their findings on that question for preterm babies in the publication “Breast Milk and Subsequent

> An F-curve has df = (8, 19). What is the number of degrees of freedom for the: a. denominator? b. numerator?

> In a study by J. Zeng et al., three materials for making artificial teeth—Endura, Duradent, and Duracross—were tested for hardness. Their results were published as the paper “In Vitro Wear Resistance of Three Types of Composite Resin Denture Teeth” (Jour

> In a study by J. Zeng et al., three materials for making artificial teeth—Endura, Duradent, and Duracross—were tested for wear. Their results were published as the paper “In Vitro Wear Resistance of Three Types of Composite Resin Denture Teeth” (Journal

> Explain the difference between a. frequency and relative frequency. b. percentage and relative frequency.

> Rock Sparrows breeding in northern Italy are the subject of a long-term ecology and conservation study due to their wide variety of breeding patterns. Both males and females have a yellow patch on their breasts that is thought to play a significant role

> The U.S. Geological Survey, in cooperation with the Florida Department of Environmental Protection, investigated the effects of waste disposal practices on ground water quality at five poultry farms in north-central Florida. At one site, they drilled fou

> The U.S. Census Bureau collects data on monthly rents of newly completed apartments and publishes the results in Current Housing Reports. Independent random samples of newly completed apartments in the four U.S. regions yielded the data on monthly rents,

> In the publication “How Often Do Fishes ‘Run on Empty’?” (Ecology, Vol. 83, No 8, pp. 2145–2151), D. Arrington et al. examined almost 37,000 fish of 254 species from the waters of Africa, South and Central America, and North America to determine the perc

> Consumer Reports publishes reviews and comparisons of products based on results from its laboratory. Data from their website gave the following table for battery lives, in hours, for samples of laptops made by four different computer companies. The four

> Permeation sampling is a method of sampling air in buildings for pollutants. It can be used over a long period of time and is not affected by humidity, air currents, or temperature. In the paper “Calibration of Permeation Passive Samplers With Silicone M

> In the article “Using EDE, ANOVA and Regression to Optimize Some Microbiology Data” (Journal of Statistics Education, Vol. 12, No. 2, online), N. Binnie analyzed bacteria culture data collected by G. Cooper at the Auckland University of Technology. Five

> We considered two hypothetical examples to explain the logic behind one-way ANOVA. Now, you are to further examine those examples. a. Perform a one-way ANOVA on the data and compare your conclusion to that stated in the corresponding “What Does it Mean?”

> An F-curve has df = (12, 7). What is the number of degrees of freedom for the: a. numerator? b. denominator?

> Copepods are tiny crustaceans that are an essential link in the estuarine food web. Marine scientists G. Weiss et al. at the Chesapeake Biological Laboratory in Maryland designed an experiment to determine whether dietary lipid (fat) content is important

> What is a frequency distribution of qualitative data and why is it useful?

> Movie fans use the annual Leonard Maltin Movie Guide for facts, cast members, and reviews of more than 21,000 films. The movies are rated from 4 stars (4*), indicating a very good movie, to 1 star (1*), which Leonard Maltin refers to as a BOMB. The follo

> We provide data from independent simple random samples from several populations. a. compute SST, SSTR, and SSE by using the computing formulas. b. compare your results in part (a) for SSTR and SSE where you employed the defining formulas. c. construct a

> We provide data from independent simple random samples from several populations. a. compute SST, SSTR, and SSE by using the computing formulas. b. compare your results in part (a) for SSTR and SSE where you employed the defining formulas. c. construct a

> We provide data from independent simple random samples from several populations. a. compute SST, SSTR, and SSE by using the computing formulas. b. compare your results in part (a) for SSTR and SSE where you employed the defining formulas. c. construct a

> We provide data from independent simple random samples from several populations. a. compute SST, SSTR, and SSE by using the computing formulas. b. compare your results in part (a) for SSTR and SSE where you employed the defining formulas. c. construct a

> We provide data from independent simple random samples from several populations. a. compute SST, SSTR, and SSE by using the computing formulas. b. compare your results in part (a) for SSTR and SSE where you employed the defining formulas. c. construct a

> We provide data from independent simple random samples from several populations. a. compute SST, SSTR, and SSE by using the computing formulas. b. compare your results in part (a) for SSTR and SSE where you employed the defining formulas. c. construct a

> 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 chi-square homogeneity test is to be conducted to decide whether a difference exists among the distributions of a variable of six populations. The variable has five possible values. What are the degrees of freedom for the χ2-statistic?

> Another important type of data is ordinal data, which are data about order or rank given on a scale such as 1, 2, 3, . . . or A, B, C, . . . . Following are several variables. Which, if any, yield ordinal data? Explain your answer. a. Height b. Weight c.

> Using the Fα-notation, identify the F-value having area 0.975 to its left.

> If a variable of two populations has only two possible values, the chi-square homogeneity test is equivalent to a two-tailed test that we discussed in an earlier chapter. What test is that?

> Fill in the missing entries in the partially completed one-way ANOVA tables.

> Fill in the blank: If a variable has only two possible values, the chi-square homogeneity test provides a procedure for comparing several population?

> Fill in the missing entries in the partially completed one-way ANOVA tables.

> 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.

> 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

> 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

> 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 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

2.99

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