Exam 15: Analysis of Variance

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A hotel chain has identically sized resorts in five locations.The data that follow resulted from analyzing the hotel occupancies on randomly selected days in the five locations. Analysis of Variance -What is the value that represents the between-group variation?

The total number of degrees of freedom is:

In an ANOVA analysis with K number of groups,H number of blocks,and m number of observations per cell,the degree of freedom for SSE is given by (K - 1)(H - 12).

The F distribution cannot be used with a two-way ANOVA.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The results of a two-factor ANOVA without replication are displayed below with missing values,identified by "A" through "G." ANOVA: Two-Factor Without Replication SUMMARY ANOVA -What value should replace "F"?

In a two-way ANOVA,interaction between groups and blocks occurs when differences in group efforts are not distributed uniformly across blocks.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Consider the following analysis of variance table: -Compute the F- ratio.

What is the total degrees of freedom for the test?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A production manager monitors the output per hour of four workers over the course of four hours.The results are reproduced below. Assume that the populations from which the sample drawn are normally distributed. -What are the appropriate null and alternative hypothesis using this information?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A consumer group wanted to examine how long different life bulbs last.They selected three different light bulbs (60 watt,75 watt and 100 watt)from four different manufacturers.They generated the following statistics from the data. -What is the value of "C"?

In a two-way ANOVA,the interpretations of the group effects make sense only when the interaction component is not significant.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A random sample of 10 observations was selected from each of four populations.A partial one-way ANOVA table is shown below: -At the .05 level of significance,can we reject the null hypothesis in the previous question?

When the F test is used for ANOVA,the rejection region is always in the right tail.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Random samples of two freshmen,two sophomores,two juniors,and two seniors each from four dormitories were asked to rate on a scale from 1 (poor)to 10 (excellent)the quality of the dormitory environment for studying.The results are shown in the table. -Test the null hypothesis of no interaction between student year and dormitory rating.

In ANOVA,if the calculated F statistic exceeds the critical F for a given test,the null hypothesis of equal population means is rejected.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The results of a two-factor ANOVA without replication are displayed below: ANOVA: Two-Factor Without Replication SUMMARY ANOVA -Is there sufficient evidence to reject H₀ that the average between programs A,B,and C regions is the same?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: In conducting the Kruskal-Wallis test,independent random samples of sizes 5,7,8,and 7 were drawn from four populations and the sum of ranks in each of the samples were 84,100,96,and 98,respectively. -How many degrees of freedom are associated with the Kruskal-Wallis test?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: An instructor in an economics class is considering three different texts.She is also considering three types of examinations-multiple choice,essays,and a mix of multiple choice and essays.During the year she teaches nine sections of the course and randomly assigns a text - examination type combination of each section.At the end of the course she obtained students' evaluations for each section.These ratings are shown in the accompanying table. -Test the null hypothesis of equality of population mean ratings for the three texts.Use α = 0.05.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Four different brokerage houses were asked for stocks' earnings forecasts for the next year for five different corporations.The brokerage houses asked the analysts on staff who had experience with the corporations in question.Four analysts were surveyed at each brokerage house.Some descriptive statistics are listed below: -Is there sufficient evidence to reject the null hypothesis that there is no interaction between brokerage houses and stocks' earning forecasts? Use α = 0.05.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A hotel chain has identically sized resorts in five locations.The data that follow resulted from analyzing the hotel occupancies on randomly selected days in the five locations. Analysis of Variance -What is the value of the element in the ANOVA table that always provides an estimate of the population variance?