Final answer:
An invalid alternative hypothesis is H₁ : Mu = 18, because alternative hypotheses should express a change from the null hypothesis using inequality signs, not an equals sign.
Step-by-step explanation:
The invalid alternative hypothesis is H₁ : Mu = 18. Alternative hypotheses should be statements that express a difference from the null hypothesis, and they are typically formulated with not equals (\(≠\)), greater than (\(>\)), or less than (\(<\)) signs. An alternative hypothesis should not contain an equals sign as it is meant to show that the parameter is different from the null hypothesis value. In statistical hypothesis testing, we aim to determine if there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis.
When the alternative hypothesis includes a not equals symbol, this indicates the need for a two-tailed test. A null hypothesis that states the mean is at least a certain value, such as 18, would be associated with a right-tailed test, while a null hypothesis stating the mean is at most a certain value would call for a left-tailed test. If the null hypothesis states equality and the alternative hypothesis states the mean is not equal, then again a two-tailed test is appropriate.