Exam 15: Analysis of Variance

Analysis of variance models test hypotheses about the population standard deviation.

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 are the appropriate null and alternative hypotheses?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Four stock analysts were asked to predict earnings for three different stocks for the next year.The following ANOVA table with missing values identified by "A" through "H" summarizes the responses. -What is the value of "F"?

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 "E"?

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 -The test statistic F is the ratio of two elements of the ANOVA table.Of these elements,what is the value of the one that provides an estimate of the population variance only when the null hypothesis is true?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Independent random samples of seven assistant professors,five associate professors,and six full professors were asked to estimate the amount of time outside the classroom spent on teaching responsibilities in the last week.Results,in hours,are shown in the accompanying table. -Employ the ANOVA test on the data in the table above.

Blocking variables cannot be used in a two-way ANOVA having randomized blocks.

When conducting sample variance using the Kruskal-Wallis test,the sample values are pooled together randomly.

In a one-way ANOVA with randomized blocks,the additional blocks are also known as blocking variables.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Independent random samples of seven assistant professors,five associate professors,and six full professors were asked to estimate the amount of time outside the classroom spent on teaching responsibilities in the last week.Results,in hours,are shown in the accompanying table. -Test the null hypothesis that the three population mean times are equal.Use α = 0.05.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A firm is considering adopting an employee screening exam and has three to choose from.The exams are administered to 10 different people,and their responses are recorded. -Is there sufficient evidence to reject the null hypothesis that there is no difference between the three exam forms? Use α = 0.05.

In a one-way ANOVA,if the ratio F =MSG / MSW is quite close to 1.0,there is little cause to doubt the null hypothesis of equality of population mean.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Random samples of eight freshmen,eight sophomores,and eight juniors taking a business statistics class were drawn.The accompanying table shows scores on the final examination. -Carry out a nonparametric test of the null hypothesis of equality of population mean examination scores for freshman,sophomore,and juniors.Use α = 0.05.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A sales manager is interested in evaluating the effectiveness of product literature.There are five different types of brochures currently in use.He asks four salespeople in each of the four regions of the country to evaluate the effectiveness of each of the brochures.The results of a two-way ANOVA are presented below. -Is there sufficient evidence to reject the null hypothesis that there is no interaction between region of the country and brochure type? Use α = 0.05.

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. -Is there sufficient evidence to reject H₀ that there is no difference in the output per hour of the four workers?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A sales manager is interested in evaluating the effectiveness of product literature.There are five different types of brochures currently in use.He asks four salespeople in each of the four regions of the country to evaluate the effectiveness of each of the brochures.The results of a two-way ANOVA are presented below. -Is there sufficient evidence to reject the null hypothesis that there is no difference between different types of brochures? Use α = 0.05.

The Kruskal-Wallis test assumes the parent populations are normally distributed.

In a one-way ANOVA,all the populations may or may not be normally distributed.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Consider the following analysis of variance table: -Test the null hypothesis at the 5% level of significance.

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 "B"?