To solve this problem, we need to examine the average time on hold for each week and compare specific intervals to see if there has been an increase in the average time from the starting week to the ending week of the interval.
Here is the table for reference:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Week} & \text{Average Time on Hold (Minutes)} \\
\hline
1 & 7 \\
\hline
2 & 5 \\
\hline
3 & 3 \\
\hline
4 & 2 \\
\hline
5 & 3 \\
\hline
6 & 5 \\
\hline
\end{array}
\][/tex]
Now, let's analyze each given interval:
1. Week 1 to Week 3:
- Starting Week 1: 7 minutes
- Ending Week 3: 3 minutes
- Comparison: 7 (start) > 3 (end) – Time decreased.
2. Week 1 to Week 4:
- Starting Week 1: 7 minutes
- Ending Week 4: 2 minutes
- Comparison: 7 (start) > 2 (end) – Time decreased.
3. Week 4 to Week 6:
- Starting Week 4: 2 minutes
- Ending Week 6: 5 minutes
- Comparison: 2 (start) < 5 (end) – Time increased.
4. Week 3 to Week 5:
- Starting Week 3: 3 minutes
- Ending Week 5: 3 minutes
- Comparison: 3 (start) = 3 (end) – Time remained the same.
After comparing all the intervals, the only interval where the average time on hold increased is from Week 4 to Week 6.
Thus, the interval during which the average time spent on hold increased is:
[tex]\[
\boxed{\text{week 4 to week 6}}
\][/tex]
