Final answer:
The correct null hypothesis (H₀) is that the mean amount of juice μ is equal to 18 ounces, and the alternative hypothesis (Hᵢ) is that the mean amount μ is not equal to 18 ounces, representing a claim of an actual difference from the labeled content, requiring a two-tailed test.
Step-by-step explanation:
To formulate the null and alternative hypotheses for a hypothesis test about a mean amount of juice in an 18-ounce bottled drink, let's consider what the consumer advocacy group is claiming. The group claims that the mean amount is not 18 ounces, which suggests a two-tailed test because they are considering the possibility that the mean may be less than or greater than the stated amount. Therefore, the correct null and alternative hypotheses from the choices given would be:
- Null hypothesis (H₀): μ = 18 ounces
- Alternative hypothesis (Hᵢ): μ ≠ 18 ounces
In hypothesis testing, the null hypothesis is assumed to be true and represents a statement of no effect or no difference. It is tested against the alternative hypothesis, which is what we are trying to find evidence for. If the test results lead us to reject the null hypothesis, then we have reason to believe the alternative hypothesis may be true.