Answer :
To test whether the mean height of a certain kind of plant differs when treated with a certain chemical, we need to define our hypotheses for a hypothesis test.
1. Null Hypothesis (H₀): The null hypothesis represents the statement of no effect or no difference. For this problem, it is the statement that the mean height of the plants remains the same even after being treated with the chemical. Therefore, the null hypothesis is:
- [tex]\( H_0: \mu = 126 \)[/tex]
This means that the mean height of the plants treated with the chemical is equal to 126 centimeters.
2. Alternative Hypothesis (H₁): The alternative hypothesis is what you are trying to provide evidence for, indicating a change or effect. In this scenario, it suggests that the treatment with the chemical causes the mean height to be different from 126 centimeters. Thus, the alternative hypothesis is:
- [tex]\( H_1: \mu \neq 126 \)[/tex]
This indicates that the mean height of the plants treated with the chemical is not equal to 126 centimeters.
By setting up these hypotheses, you'll be able to conduct a statistical test to determine if there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis.
1. Null Hypothesis (H₀): The null hypothesis represents the statement of no effect or no difference. For this problem, it is the statement that the mean height of the plants remains the same even after being treated with the chemical. Therefore, the null hypothesis is:
- [tex]\( H_0: \mu = 126 \)[/tex]
This means that the mean height of the plants treated with the chemical is equal to 126 centimeters.
2. Alternative Hypothesis (H₁): The alternative hypothesis is what you are trying to provide evidence for, indicating a change or effect. In this scenario, it suggests that the treatment with the chemical causes the mean height to be different from 126 centimeters. Thus, the alternative hypothesis is:
- [tex]\( H_1: \mu \neq 126 \)[/tex]
This indicates that the mean height of the plants treated with the chemical is not equal to 126 centimeters.
By setting up these hypotheses, you'll be able to conduct a statistical test to determine if there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis.
