Practice — Hypothesis Testing & Statistical Inference (7 questions)

A support team trials a new ticket-triage tool. Resolution time in hours for two independent groups of tickets:

1. State the hypotheses and compute Welch's t statistic and the approximate degrees of freedom. Is the result significant at \alpha = 0.05 (two-sided)? (Use t_{0.975} \approx 2.00.)
2. Give a 95% confidence interval for the difference and Cohen's d. In one or two sentences, what should the team be told?
3. Why is Welch's version preferable to Student's pooled t here?

Monthly sales performance for your reps has a month-to-month correlation of about \rho = 0.5 (roughly half of any rep's deviation from the team average persists next month; the rest is noise). This month, you pull the 10 lowest performers — averaging 2 standard deviations below the team mean — into a mandatory coaching program.

Assume the coaching has zero true effect. On average, what z-score should you expect from those same 10 reps next month?