Exam 11: Analysis of Variance

A manufacturer of automobile transmissions uses three different processes. The management ordered a study of the production costs to see if there is a difference among the three processes. A summary of the findings is shown below. What is the critical value of F at the 1% level of significance?

i. One characteristic of the F distribution is that computed F can only range between -1 and +1. ii. The F distribution's curve is positively skewed. Iii) Like Student's t distribution, a change in the degrees of freedom causes a change in the shape of the F distribution.

Two accounting professors decided to compare the variation of their grading procedures. To accomplish this they each graded the same 10 exams with the following results: What is the critical value of F at the 0.05 level of significance?

i. The F distribution is positively skewed and its values may range from 0 to plus infinity. ii. The F distribution's curve is positively skewed. Iii) There is one, unique F distribution for a F-statistic with 29 degrees of freedom in the numerator and 28 degrees of freedom in the denominator.

ii. The calculated F value must be equal to or greater than zero (0) iii. The shape of the F distribution is symmetrical i. The test statistic used in ANOVA is F

Two accounting professors decided to compare the variation of their grading procedures. To accomplish this they each graded the same 10 exams with the following results: At the 1% level of significance, what is the decision?

i. If we want to determine which treatment means differ, one method is confidence intervals. ii. If the confidence interval includes 0, there is no difference in the pair of treatment means. Iii) If both end points of a confidence interval are of the same sign, it indicates that the treatment means are not different.

i. To employ ANOVA, the populations need not have equal standard deviations. ii. To employ ANOVA, the populations being studied need not be normally distributed. Iii) A technique that is efficient when simultaneously comparing more than two population means is known as analysis of deviation.

i. One characteristic of the F distribution is that computed F can only range between -1 and +1. ii. The shape of the F distribution is determined by the degrees of freedom for the F-statistic, one for the numerator and one for the denominator. Iii) The F distribution's curve is positively skewed.

Based on the comparison between the mean annual incomes for executives with Undergraduate and Master's Degree or more,

i. The rejection region for analysis of variance is in the upper tail of the F distribution ii. In ANOVA, k -1 degrees of freedom are associated with the numerator of the F ratio. Iii) In ANOVA, k-1 degrees of freedom are associated with the denominator of the F ratio.

A manufacturer of automobile transmissions uses three different processes. The management ordered a study of the production costs to see if there is a difference among the three processes. A summary of the findings is shown below. What are the degrees of freedom for the denominator?

In an effort to determine the most effective way to teach safety principles to a group of employees, four different methods were tried. Some employees were given programmed instruction booklets and worked through the course at their own pace. Other employees attended lectures. A third group watched a television presentation, and a fourth group was divided into small discussion groups. A high of 10 was possible. Samples of five tests were selected from each group. The test grade results were: At the 0.01 level, what is the critical value?

i. For an ANOVA test, rejection of the null hypothesis does not identify which populations differ significantly. Ii) Not rejecting the null hypothesis in ANOVA indicates that the population means are equal. iii. The null hypothesis for an ANOVA is µ1 - µ2 = µ3

i. If the computed value of F is 0.99 and the critical value is 3.89, we would not reject the null hypothesis. Ii) When comparing two population variances we use the F distribution. iii. A one way ANOVA is use to compare several treatment means.

Two accounting professors decided to compare the variation of their grading procedures. To accomplish this they each graded the same 10 exams with the following results: At the 5% level of significance, what is the decision?

Given the following Analysis of Variance table for three treatments each with six observations. What is the computed value of F?

Which statement is correct about the F distribution?

i. If the computed value of F is 4.01 and the critical value is 2.67, we would conclude that all the population means are equal. Ii) Not rejecting the null hypothesis in ANOVA indicates that the population means are equal. iii. The null hypothesis for an ANOVA is µ1 - µ2 = µ3

i. The alternate hypothesis for ANOVA states that not all the means are equal. ii. Not rejecting the null hypothesis in ANOVA indicates that the population means are equal. iii. The null hypothesis for an ANOVA is µ1 - µ2 = µ3