Question

Please respond with at least 175 words. What are a one tail and a two tailed test. Why are they important and what are their differences?

Answer 1

Solution :-

One tailed test :-

A one-tailed test allows you to determine if one mean is greater or less than another mean, but not both. A direction must be chosen prior to testing.

In other words, a one-tailed test tells you the effect of a change in one direction and not the other.

Two tailed test :-

A two-tailed test allows you to determine if two means are different from one another. A direction does not have to be specified prior to testing.

In other words, a two-tailed test will taken into account the possibility of both a positive and a negative effect.

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importantance --

One-tailed tests are used for asymmetric distributions that have a single tail, such as the chi-squared distribution, which are common in measuring goodness-of-fit, or for one side of a distribution that has two tails, such as the normal distribution, which is common in estimating location; this corresponds to specifying a direction.

Two-tailed tests are only applicable when there are two tails, such as in the normal distribution, and correspond to considering either direction significant.

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Difference

1.One-tailed test, as the name suggest is the statistical hypothesis test, in which the alternative hypothesis has a single end.

for, two-tailed test implies the hypothesis test; wherein the alternative hypothesis has dual ends.

2.In a one-tailed test, the region of rejection is either on the left or right of the sampling distribution.

for,two tailed test, the region of rejection is on both the sides of the sampling distribution.

3.for One-tailed test,when an alternative hypothesis has ‘> or <‘ sign, then one-tailed test is carried out.

for,two tailed test,When an alternative hypothesis has ‘≠’ sign, then a two-tailed test is performed.