We’ve all heard some talking head on TV spout some statistic we feel just has to be wrong. Stuff like, “75% of small businesses fail within the first year”...which obviously can’t be correct, because that seems like a crazy-high percentage.
A two-tailed test is a way to determine if there’s actually evidence to support the idea that the value is something other than the 75% that the talking head quoted.
Two-tailed tests are a specific kind of hypothesis test that we run when we believe that a proportion (percentage) or mean (average) or some other value we’ve heard or read about has a value different from what we’ve been quoted. We take a random sample, calculate a statistic from that sample, run it through a couple of formulas, and come up with a probability that indicates how likely it is that the actual value is different from the quoted one. Most people use a graphing calculator, spreadsheet, or website to do all the mathematical heavy lifting.
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