Question

The null and alternative hypotheses are given. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed and indicate the parameter(s) being tested.

a.) ?0: ?1 = ?2 ?? ?1: ?1 > ?2
  
b.) ?0: ? = 8.6 ?? ?1: ? > 8.6

Answer 1

Solution :

The hypothesis test is said to be two-tailed test, if direction of the test is not specified i.e. there is "not equal to" sign in the alternative hypothesis.

And the hypothesis test is said to be righ-tailed test or left-tailed test, if direction of the test is specified. If there is "greater than" sign in the alternative hypothesis, then the hypothesis test is said to be right-tailed test. If there is "less than" sign in the alternative hypothesis, then the hypothesis test is said to be left-tailed test.

a) H​​​​​​0 : P​​​​​​1 = P​​​​​​2  vs  H​​​​​​0 : P​​​​​​1 > P​​​​​​2

The hypothesis test is right-tailed test, because the alternative hypothesis has "greater than" sign.

b)  ​​​​​​H​​​​​​0 : σ = 8.6  vs  H​​​​​​0 : σ > 8.6

The hypothesis test is right-tailed test, because the alternative hypothesis has "greater than" sign.

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