Does the coaching cut average handle time below 6 minutes?

Question

A call center's average handle time is 6.0 minutes with a known standard deviation of $\sigma = 1.5$ . After coaching, a sample of 100 calls averages 5.72 minutes. Management claims the coaching lowers handle time.

Run a one-sided z-test at the 5% level (does time decrease?): report the z-statistic and the decision.

Accepted Answer

Directional claim (time goes down), \sigma known, so use a lower-tail z-test. Hypotheses: H0: \mu = 6.0 versus H1: \mu < 6.0. Standard error: 	ext{SE} = \frac{1.5}{\sqrt{100}} = \frac{1.5}{10} = 0.15. Test statistic: z = \frac{5.72 - 6.0}{0.15} = \frac{-0.28}{0.15} = -1.87. For a lower-tail test the critical value is -z{0.05} = -1.645. Since -1.87 < -1.645, reject H0. The one-sided p-value is \Phi(-1.87) \approx 0.031. Conclusion: there is evidence the coaching reduced average handle time. Takeaway. A modest 0.28-minute drop becomes significant because the large sample (n = 100) makes the st…

Does the coaching cut average handle time below 6 minutes?

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