StatisticsdrillConfidence interval for a difference of means
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 = 8, x̄ = 104.3, s = 11.3. Machine B: n = 20, x̄ = 105.2, s = 11.3 (units per day). Assuming equal population variances, find the lower limit of a 90% confidence interval for μ1 - μ2 (Machine A minus Machine B) using the pooled t procedure. Round to 2 decimal places.
What this problem teaches
If the interval contains 0, the two means are not distinguishable at this confidence level. The sign of the limits follows the order of subtraction, so state which group comes first.
A hint if you get stuck
(x̄1 - x̄2) ± t* × sp √(1/n1 + 1/n2), with t* from n1 + n2 - 2 degrees of freedom and sp the pooled standard deviation.
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