StatisticsdrillTwo-sample t test (pooled)
A statistics problem from Statisticsdrill. Solve it with one answer box, with a fresh sample on every attempt and the worked steps and spreadsheet function in the answer, and it is checked the moment you submit.
The task
A plant compares the daily output of two machines. Machine A: n = 18, x̄ = 105.5, s = 6.5. Machine B: n = 8, x̄ = 113.8, s = 6.2 (units per day). Assume equal population variances. Find the pooled two-sample t statistic (Machine A minus Machine B) for H0: μ1 = μ2 against H1: μ1 ≠ μ2, then decide at α = 0.01. Round to 2 decimal places.
What this problem teaches
The pooled test assumes both groups share one variance. When the sample standard deviations differ a lot, use the Welch version instead.
A hint if you get stuck
Pool the variances: sp² = [(n1 - 1)s1² + (n2 - 1)s2²] / (n1 + n2 - 2). Then t = (x̄1 - x̄2) / (sp √(1/n1 + 1/n2)) with n1 + n2 - 2 degrees of freedom.
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