Mistake Master
Zero Inside Means Nothing Was Shown, Not That Nothing Happened
You'll learnhow to turn an interval for a mean into a verdict on a claimed value, why zero is the decisive value for a mean difference and what containing it does and does not establish, what the margin of error covers and cannot cover, and how to write the justification.
A manufacturer claims a mean lifetime of 128 hours, the sample mean comes out at 124.6, and the data still do not contradict the claim — because the interval reaches past it, and a verdict is a membership test rather than a comparison of two point values. This page runs every such test in code. For a mean difference the decisive member is zero, the no-change value: a paired study's interval clears it and shows improvement, while a hypothetical one straddles it, and the correct sentence there is that no change was detected — not that none occurred, since a gain of 4.8 points sits inside that interval too. Then the margin of error is taken apart lever by lever, each move priced by integration, and the two habits it cannot survive are executed: crediting it with covering a leading question, and buying a narrower interval at 80 percent confidence as if the missing capture rate were free. Twelve short steps; press Next for each one.