Customer Support Resolution Time - 90% Confidence Interval

Statistical Summary

Sample Statistics:

• Sample size (n): 28
• Mean resolution time: 18.5 minutes
• Standard deviation: 6.2 minutes
• Standard error: 1.17 minutes

90% Confidence Interval: (16.50, 20.50) minutes

Interpretation

Based on 28 customer support interactions, the average resolution time is 18.5 minutes. We are 90% confident that the true average resolution time for all customer support interactions lies between 16.50 and 20.50 minutes.

What This Means:

• Central estimate: Most support issues are resolved in approximately 18-19 minutes
• Precision: The margin of error is ±2.0 minutes, indicating reasonable precision for this sample size
• Range: If we set staffing and SLA expectations, we should plan for resolution times in the 16.5-20.5 minute range

What This Doesn’t Mean:

• ❌ This is NOT a guarantee that 90% of individual tickets are resolved within this range
• ❌ This is NOT the time range for individual ticket resolution (some tickets may take much longer)
• ❌ The CI tells us about the average, not about the variability in individual cases

Significance Testing

Using a t-distribution with 27 degrees of freedom:

• t-critical value: 1.703 (for 90% confidence)
• Margin of error: ±2.00 minutes

The relatively narrow confidence interval suggests consistent performance across the sample.

Business Recommendations

1. Service Level Agreements (SLAs)

• Set average resolution time target at 18-19 minutes
• Account for the upper bound (20.5 min) when setting customer expectations
• Current performance appears stable and predictable

2. Staffing Implications

• Plan capacity assuming ~18.5 minutes per interaction on average
• The narrow CI indicates consistent agent performance
• Monitor for trends that might shift the average outside this range

3. Performance Benchmarking

• If industry standard is 20+ minutes: You’re performing above average
• If industry standard is 15 minutes: There’s room for improvement (though you’d need to reduce average by ~3.5 minutes to reach that target)
• Consider tracking resolution time over time to identify improvement opportunities

4. Sample Size Consideration

• With n=28, the margin of error is ±2.0 minutes
• If you need more precision (narrower CI), collect more data
• To halve the margin of error (±1.0 min), you’d need roughly 4× the sample size (~112 interactions)

5. Next Steps

• ✓ Use 16.5-20.5 minutes as the expected range for planning purposes
• ✓ Monitor whether future samples fall within this range
• ✓ Investigate any systematic changes that push averages outside this interval
• ✓ Consider segmenting by issue type to identify areas for improvement

Technical Notes

Method: t-distribution confidence interval for a single mean

• Assumptions: Resolution times are approximately normally distributed (reasonable for n=28 due to Central Limit Theorem)
• Confidence Level: 90% (chosen per request)
• Formula: CI = x̄ ± t₀.₀₅,₂₇ × (s/√n) where x̄=18.5, s=6.2, n=28

Degrees of Freedom: 27 (n-1)

When to Re-evaluate:

• If you observe systematic changes in average resolution time
• If sample size increases significantly (tighter CI)
• If you change support processes or staffing