DEFINITION of 'TwoTailed Test'
A statistical test in which the critical area of a distribution is two sided and tests whether a sample is either greater than or less than a certain range of values. If the sample that is being tested falls into either of the critical areas, the alternative hypothesis will be accepted instead of the null hypothesis. The twotailed test gets its name from testing the area under both of the tails (sides) of a normal distribution, although the test can be used in other nonnormal distributions.
INVESTOPEDIA EXPLAINS 'TwoTailed Test'
An example of when one would want to use a twotailed test is at a candy production/packaging plant. Let's say the candy plant wants to make sure that the number of candies per bag is around 50. The factory is willing to accept between 45 and 55 candies per bag. It would be too costly to have someone check every bag, so the factory selects random samples of the bags, and tests whether the average number of candies exceeds 55 or is less than 45 with whatever level of significance it chooses.

OneTailed Test
A statistical test in which the critical area of a distribution ... 
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Type II Error
A statistical term used within the context of hypothesis testing ...

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