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 salaries to test for differences between treatment means, the t statistic is based on:
A) the treatment degrees of freedom.
B) the total degrees of freedom.
C) the error degrees of freedom.
D) the ratio of treatment and error degrees of freedom.

Question

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 salaries to test for differences between treatment means, the t statistic is based on:
A) the treatment degrees of freedom. 
B) the total degrees of freedom. 
C) the error degrees of freedom. 
D) the ratio of treatment and error degrees of freedom.

Quizplus · Accepted Answer

The t statistic is based on the error degrees of freedom, which represent the variability within the groups after accounting for the differences caused by the treatment (in this case, the level of education). The error degrees of freedom are used to estimate the standard error of the difference between treatment means, which is critical for calculating the t statistic and determining whether the differences between means are statistically significant. Therefore, the correct choice is C.

A Random Sample of 30 Executives from Companies with Assets