Exam 12: Analysis of Variance

In ANOVA, when we do not reject the null hypothesis, ______ inference is made about the population means.

The statistical technique used to test the equality of three or more population means is ___________________.

When testing for differences between treatment means, the t statistic is based on ____________.

To test the hypothesis that two population variances are equal, a random sample of size 13 was selected from the first population, and a random sample of size 21 was selected from the second population. Given that the sample standard deviation from the first population is larger than the sample standard deviation from the second population, what is the F critical value using 0.01 as the significance level?

Given the following ANOVA table for three treatments each with six observations: What is the treatment mean square?

An ANOVA has three sources of variation. They are _____, _____, and _____.

Several employees have submitted different methods of assembling a subassembly. Sample data for each method are: How many treatments are there?

A random sample of 40 companies with assets over $10 million was surveyed and asked to indicate their industry and annual computer technology expense. The ANOVA comparing the average computer technology expense among three industries rejected the null hypothesis. The mean square error (MSE) was 195. The following table summarized the results: Based on the comparison between the mean annual computer technology expense for companies in the tax service and food service industries, the 95% confidence interval shows an interval of -5.85 to 14.85 for the difference. This result indicates that _______________.

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 alternate hypothesis?

A bottle cap manufacturer with four machines and six operators wants to see if variation in production is due to the machines and/or the operators. The ANOVA table follows. What is the critical value of F for the machine treatment effect at the 1% level of significance? B.6 at the 0.01 significance level, with a 3 degrees of freedom numerator and a 15 degrees of freedom denominator.

The test statistic used to compare two variances is the ___________ statistic.

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. To select a critical F-statistic, the number of degrees of freedom for the numerator is _____.

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: Based on the comparison between the mean annual incomes for executives with undergraduate and master's degrees or more, ________________.

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 are the degrees of freedom for the numerator of the F ratio?

Below is the information for a completely randomized experimental design involving four treatments, where 12 observations were recorded for each treatment for a total of 48 observations. SST = 210 (Sum of Squares Between Groups) SS Total = 840 (Sum of Squares Total) The computed value of F, or the test statistic, is ______.

Given the following ANOVA table for three treatments each with six observations: What is the critical value of F at the 5% level of significance?

When a blocking effect is included in an ANOVA, the result is a larger error sum of squares.

A company compared the variance of salaries for employees who have been employed for 5 years or less with employees who have been employed for 10 years or more. They randomly selected 21 employees with 5 years or less experience and 15 employees with 10 years or more experience. The standard deviation for the group with 5 years or less experience was $2,225; the standard deviation for the group with 10 years or more experience was $1,875. Using the 0.05 significance level, what is the F critical value for the hypothesis test?

A random sample of 20 female 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 250. The following table summarized the results: To compare the mean annual incomes of female executives with an undergraduate degree and female executives with a master's degree or more, compute the 99% confidence interval.

A random sample of 40 companies with assets over $10 million was surveyed and asked to indicate their industry and annual computer technology expense. The ANOVA comparing the average computer technology expense among three industries rejected the null hypothesis. The mean square error (MSE) was 195. The following table summarized the results: When comparing the mean annual computer technology expense for companies in the education and tax services industries, which of the following 95% confidence interval can be constructed?