Exam 12: Analysis of Variance

In a study of protein breakfast bars,five bars from each of three brands were tested to see if the mean amount of protein per bar differs among the brands.If the sum of squares for the brands is 0.05 and the sum of squares for the error is 0.09,what is the decision rule if $\alpha$ = 0.05? ________________________

The F distribution is a ______________ distribution.

For the hypothesis test, ,with n₁ = 4 and n₂ = 4,the F-test statistic is 50.01.At the 0.01 level of significance,we would reject the null hypothesis.

In an ANOVA table,k represents the total number of sample observations and n represents the total number of treatments.

In a study of protein breakfast bars,five bars from each of three brands were tested to see if the mean amount of protein per bar differs among the brands.If F calculated is 4.75 what is the decision if $\alpha$ = 0.05? ___________

An experiment to determine the most effective way to teach safety principles applied four different teaching methods.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.A sample of five tests was selected from each group.The test grade results were: At the 0.01 level,what is the critical value?

To employ ANOVA,the populations should have approximately equal standard deviations.

Two accounting professors decided to compare the variance 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 regarding the null hypothesis?

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.

The alternate hypothesis for ANOVA states that not all the means are equal.

A random sample of 30 executives from companies with assets over $1 million was selected and asked for their annual income and level of education.The ANOVA comparing the average income among three levels of education rejected the null hypothesis.The Mean Square Error (MSE)was 243.7.The following table summarized the results: When comparing the mean annual incomes for executives with a High School education or less and Undergraduate Degree,the 95% confidence interval shows an interval of 11.7 to 42.7 for the difference.This result indicates that

A manufacturer of automobile transmissions uses three different processes.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 sum of squares for the treatment?

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.

The F-distribution is useful when testing a requirement of two-sample tests of hypothesis.What is the assumption? ________________

To employ ANOVA,the populations being studied must be approximately normally distributed.

Two accounting professors decided to compare the variance 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?

A manufacturer of automobile transmissions uses three different processes.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?

What is the null hypothesis for an ANOVA? ____________________

What is the shape of the F distribution? ______________________

If an ANOVA test is conducted and the null hypothesis is rejected,what does this indicate?