Final answer:
The null hypothesis (H0) for this test is that the mean height of the plants is 191 cm (H0: μ = 191 cm), and the alternative hypothesis (H1) is that the mean height is not equal to 191 cm (H1: μ ≠ 191 cm). A p-value is used to determine the likelihood of the sample mean being as extreme as it is, given that H0 is true. If this p-value is small enough, it suggests that the chemical does affect plant height.
Step-by-step explanation:
When we conduct a hypothesis test to determine if the mean height of plants treated with a chemical differs from 191 centimeters, we use two opposing hypotheses.
The null hypothesis (H0) represents the idea that there is no effect, and for this case would state that the mean height of the plants is equal to 191 centimeters (H0: μ = 191).
The alternative hypothesis (H1) represents the idea that there is an effect, meaning the mean height after treatment does differ from 191 centimeters. This hypothesis can be two-sided or one-sided depending on what we want to test for specifically (greater than, less than, or simply not equal to).
If we're checking if the mean height is different in either direction, our hypotheses would be:
- Null Hypothesis (H0): μ = 191 cm
- Alternative Hypothesis (H1): μ ≠ 191 cm
If we're specifically checking if the treatment increases or decreases plant height, the alternative hypothesis might be H1: μ > 191 cm for increase or H1: μ < 191 cm for a decrease.
In hypothesis testing, we use a calculated p-value to decide whether to reject the null hypothesis. If the p-value is less than our predetermined significance level (commonly 0.05), we have evidence to reject H0 and accept H1, indicating that the chemical treatment does have an effect on the mean height of the plants, different from 191 centimeters.