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) There is no significant difference between the two incomes.
B) The interval contains a difference of zero.
C) Executives with an Undergraduate Degree earn significantly more than executives with a High School education or less.
D) Executives with an Undergraduate Degree earn significantly less than executives with a High School education or less.

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 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) There is no significant difference between the two incomes. 
B) The interval contains a difference of zero. 
C) Executives with an Undergraduate Degree earn significantly more than executives with a High School education or less. 
D) Executives with an Undergraduate Degree earn significantly less than executives with a High School education or less.

Quizplus · Accepted Answer

The confidence interval for the difference between the mean annual incomes of executives with a High School education or less and Undergraduate Degree does not contain zero, which indicates that there is a significant difference between the two groups. Specifically, executives with an Undergraduate Degree earn significantly more than executives with a High School education or less. Therefore, the correct answer is C.

A Random Sample of 30 Executives from Companies with Assets