Final answer:
The null hypothesis, denoted as H₀, contains a form of equality and states no effect or difference, while the alternative hypothesis, denoted H₁ or Hᵢ, contains an inequality and is what's being tested.
The type of test (left-tailed, right-tailed, two-tailed) is determined by the alternative hypothesis symbol.
Step-by-step explanation:
The null hypothesis is often stated as the assumption that there is no change, no difference between two groups, or no relationship between two variables, and it often contains a form of equality (=, ≤, or ≥).
For instance, if a null hypothesis states that the mean is at least 18, it is written as H₀: μ ≥ 18. The alternative hypothesis, denoted as H₁ or Hᵢ, is the statement that is being tested against the null hypothesis and typically involves inequalities like <, >, or ≠ (not equal to).
For example, if the alternative hypothesis claims that the mean is more than 15, it would be Ha: μ > 15. When the alternative hypothesis includes a not equal to symbol (≠), a two-tailed test is used.
The choice of whether a hypothesis test is left-tailed, right-tailed, or two-tailed depends on the alternative hypothesis.
A hypothesis with a ">" symbol indicates a right-tailed test, while a "<" symbol indicates a left-tailed test. If the alternative hypothesis includes a "≠" (not equal to), it implies a two-tailed test.