Question

A hypothesis test is a "two-tailed" if the alternative hypothesis contains a _______ sign.

1) greater than
2) less than
3) equal to
4) not equal to

Answer 1

A hypothesis test is considered 'two-tailed' if the alternative hypothesis includes 'not equal to' (≠) as its sign, which is option 4.

Step-by-step explanation:

A hypothesis test is a 'two-tailed' if the alternative hypothesis contains a 'not equal to' sign. The correct answer is 4) not equal to. When we conduct a two-tailed test, we are considering both directions of a possible effect or difference, not just one. If the null hypothesis (H₀) states that the mean is a specific value, and the alternative hypothesis (H₁ or Ha) states that the mean is not equal to this value, we are dealing with a two-tailed test. For example, if the null hypothesis is H₀: μ = 88, and the alternative hypothesis is H₁: μ ≠ 88, this is indeed a two-tailed test, as we're looking for evidence that the mean is either less than or greater than 88.