To determine during which intervals the average time spent on hold increased, let's analyze the given data step-by-step.
First, we need to calculate the week-to-week changes in the average time on hold. Here are the average times for each week:
- Week 1: 7 minutes
- Week 2: 5 minutes
- Week 3: 3 minutes
- Week 4: 2 minutes
- Week 5: 3 minutes
- Week 6: 5 minutes
Next, let's calculate the changes in average times from one week to the next:
1. Change from Week 1 to Week 2: [tex]\( 5 - 7 = -2 \)[/tex]
2. Change from Week 2 to Week 3: [tex]\( 3 - 5 = -2 \)[/tex]
3. Change from Week 3 to Week 4: [tex]\( 2 - 3 = -1 \)[/tex]
4. Change from Week 4 to Week 5: [tex]\( 3 - 2 = 1 \)[/tex]
5. Change from Week 5 to Week 6: [tex]\( 5 - 3 = 2 \)[/tex]
The changes week by week are: [tex]\([-2, -2, -1, 1, 2]\)[/tex].
We now examine if the average time spent on hold increased in the specified intervals.
1. Week 1 to Week 3:
The total change from Week 1 to Week 3 is [tex]\((-2) + (-2) = -4\)[/tex]. Since the change is negative, the average time did not increase in this interval.
2. Week 1 to Week 4:
The total change from Week 1 to Week 4 is [tex]\((-2) + (-2) + (-1) = -5\)[/tex]. Since the change is negative, the average time did not increase in this interval.
3. Week 4 to Week 6:
The total change from Week 4 to Week 6 is [tex]\(1 + 2 = 3\)[/tex]. Since the change is positive, the average time increased in this interval.
4. Week 3 to Week 5:
The total change from Week 3 to Week 5 is [tex]\((-1) + 1 = 0\)[/tex]. Since the change is zero, the average time did not increase in this interval.
Summarizing the findings:
- The average time spent on hold did not increase from Week 1 to Week 3.
- The average time spent on hold did not increase from Week 1 to Week 4.
- The average time spent on hold increased from Week 4 to Week 6.
- The average time spent on hold did not increase from Week 3 to Week 5.
Therefore, the interval during which the average time spent on hold increased is Week 4 to Week 6.
