Two-Tailed Hypothesis Test

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A Two-Tailed Hypothesis Test is a statistical hypothesis test where the region of rejection lies on both sides of the sampling distribution.

Set Null Hypothesis Alternative Hypothesis
1 [math]\displaystyle{ H_0: \quad \mu=M }[/math] [math]\displaystyle{ H_A: \quad \mu \neq M }[/math]
2 [math]\displaystyle{ H_0: \quad \mu=M }[/math] [math]\displaystyle{ H_A: \quad \mu \gt M \; or\; \quad \mu \lt M }[/math]
Set 1 is the most used expression for the null and alternative two-tailed hypothesis test while Set 2 is less used.


References

2022

2017a

2017b

2017c

  • (Stattrek,2017) ⇒ http://stattrek.com/statistics/dictionary.aspx?definition=Two_tailed_test
    • Two-Tailed Test - A test of a statistical hypothesis , where the region of rejection is on both sides of the sampling distribution , is called a two-tailed test.

      For example, suppose the null hypothesis states that the mean is equal to 10. The alternative hypothesis would be that the mean is less than 10 or greater than 10. The region of rejection would consist of a range of numbers located on both sides of sampling distribution; that is, the region of rejection would consist partly of numbers that were less than 10 and partly of numbers that were greater than 10.

2017D

  • (Stattrek, 2017) ⇒ http://stattrek.com/hypothesis-test/region-of-acceptance.aspx
    • One-Tailed and Two-Tailed Hypothesis Tests - The steps taken to define the region of acceptance will vary, depending on whether the null hypothesis and the alternative hypothesis call for one- or two-tailed hypothesis tests. So we begin with a brief review.
The table below shows three sets of hypotheses. Each makes a statement about how the population mean μ is related to a specified value M. (In the table, the symbol ≠ means " not equal to ".)
Set Null Hypothesis Alternative Hypothesis Number of tails
1 [math]\displaystyle{ \mu=M }[/math] [math]\displaystyle{ \mu \neq M }[/math] [math]\displaystyle{ 2 }[/math]
2 [math]\displaystyle{ \mu\geq M }[/math] [math]\displaystyle{ \mu \lt M }[/math] [math]\displaystyle{ 1 }[/math]
2 [math]\displaystyle{ \mu\leq M }[/math] [math]\displaystyle{ \mu \gt M }[/math] [math]\displaystyle{ 1 }[/math]
The first set of hypotheses (Set 1) is an example of a two-tailed test, since an extreme value on either side of the sampling distribution would cause a researcher to reject the null hypothesis. The other two sets of hypotheses (Sets 2 and 3) are one-tailed tests, since an extreme value on only one side of the sampling distribution would cause a researcher to reject the null hypothesis.

2017E