The Internal Revenue Service wishes to study the time required to process tax returns in three regional centers. A random sample of three tax returns is chosen from each of three centers. The time (in days) required to process each return is recorded as shown below. $$\begin{array} { | c | c | c | }
\hline \text { East } & \text { West } & \text { Midwest } \
\hline 49 & 47 & 54 \
39 & 52 & 49 \
45 & 51 & 56 \
\hline
\end{array}$$ The test to use to compare the means for all three groups would require:
A)three-factor ANOVA.
B)one-factor ANOVA.
C)repeated two-sample test of means.
D)two-factor ANOVA with replication.

Question

The Internal Revenue Service wishes to study the time required to process tax returns in three regional centers. A random sample of three tax returns is chosen from each of three centers. The time (in days) required to process each return is recorded as shown below. $$\begin{array} { | c | c | c | } 
\hline \text { East } & \text { West } & \text { Midwest } \
\hline 49 & 47 & 54 \
39 & 52 & 49 \
45 & 51 & 56 \
\hline
\end{array}$$ The test to use to compare the means for all three groups would require:
A)three-factor ANOVA.
B)one-factor ANOVA.
C)repeated two-sample test of means.
D)two-factor ANOVA with replication.

Quizplus · Accepted Answer

One-factor ANOVA is appropriate for comparing the means of more than two groups when the data meet assumptions such as normality and equal variances. In this case, we have three groups (East, West, Midwest), and the data appear to meet the assumptions based on the information given. Therefore, we can use a one-factor ANOVA to compare the means of the three groups. The other options (three-factor ANOVA, repeated two-sample test of means, two-factor ANOVA with replication) are not appropriate for this scenario.

The Internal Revenue Service Wishes to Study the Time Required