To determine the intervals during which the average time spent on hold increased, let's analyze the data week by week.
Here is the table for reference:
[tex]\[
\begin{tabular}{|c|c|}
\hline \multicolumn{2}{|c|}{ Average Time on Hold with Help Desk } \\
\hline Week & \begin{tabular}{c}
Average Time on Hold \\
(Minutes)
\end{tabular} \\
\hline 1 & 7 \\
\hline 2 & 5 \\
\hline 3 & 3 \\
\hline 4 & 2 \\
\hline 5 & 3 \\
\hline 6 & 5 \\
\hline
\end{tabular}
\][/tex]
Given the intervals we are checking for increases:
1. Week 1 to week 3
2. Week 1 to week 4
3. Week 4 to week 6
4. Week 3 to week 5
First, let’s find the weekly differences in hold times:
- Week 2 - Week 1: [tex]\(5 - 7 = -2\)[/tex]
- Week 3 - Week 2: [tex]\(3 - 5 = -2\)[/tex]
- Week 4 - Week 3: [tex]\(2 - 3 = -1\)[/tex]
- Week 5 - Week 4: [tex]\(3 - 2 = 1\)[/tex]
- Week 6 - Week 5: [tex]\(5 - 3 = 2\)[/tex]
Now, let's analyze the intervals:
1. Week 1 to week 3:
- Week 2 - Week 1: -2
- Week 3 - Week 2: -2
- Since both differences are negative, the average time did not increase in this interval.
2. Week 1 to week 4:
- Week 2 - Week 1: -2
- Week 3 - Week 2: -2
- Week 4 - Week 3: -1
- Since all differences are negative, the average time did not increase in this interval.
3. Week 4 to week 6:
- Week 5 - Week 4: 1
- Week 6 - Week 5: 2
- Both differences are positive, indicating that the average time increased during this interval.
4. Week 3 to week 5:
- Week 4 - Week 3: -1
- Week 5 - Week 4: 1
- Since there is at least one positive difference (week 5 to week 4), the average time increased during this interval.
Thus, during the intervals where the average time on hold increased are:
- Week 4 to week 6
- Week 3 to week 5
Hence, the intervals during which the average time spent on hold increased are:
- Week 4 to week 6
- Week 3 to week 5
