Explain thedifference between a left-tailed, two-tailed, and right-tailedtest. W

Question

Explain thedifference between a left-tailed, two-tailed, and right-tailedtest. When would we choose a two-tailed test? How can we tell thedirection of the test by looking at a pair of hypothesis? How canwe tell which direction (or no direction) to make the hypothesis bylooking at the problem statement (research question)?

Explanation / Answer

Use a one-sided hypothesis test if there is a reason to believe(before data collection) that the true population mean lies to oneside of some particular value. That is, if the test is one-sided,e.g. H_a: mu > 3 or H_a: mu < 3 (3 is just used as anexample), then it is a left tail or right tail test, respectively.That is, in the first hypothesis test, we think our test statisticwill be on the right side of 3 (above 3), so we would be looking inthe right tail. If there isn't a particular direction that you are checking for butyou are just looking for some difference, then a two-sided test isin order. The null hypothesis can usually be thought of as the traditional orconventional belief. For instance, if we want to run a test on theprobability of getting heads while flipping a coin, then thetraditional value would be 1/2, thus H_0: p=0.5. The alternative hypothesis is usually what the researchers aretrying to show. For instance, perhaps we have reason to believethat the probability of flipping tails is greater than that offlipping heads, then H_a: p > 0.5. That is, we think theprobability of tails is greater than 0.5 (in this made-up example).If the researchers are uncertain of whether it is more or lessthan, perhaps they are just interested in whether it is not 1/2,then a two-sided test would be in order: H_0: p not= 0.5. Source:http://answers.yahoo.com/question

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