The mean height of a certain kind of plant is 172 centimeters. Suppose we want to carry out a hypothesis test to see if the mean height when these plants are treated with a certain chemical differs from 172. State the null hypothesis H, and the alternative hypothesis H, that we would use for this test. H: 0 O

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### Hypothesis Testing for Plant Mean Height

The mean height of a certain kind of plant is 172 centimeters. Suppose we want to carry out a hypothesis test to see if the mean height when these plants are treated with a certain chemical differs from 172. State the null hypothesis \(H_0\) and the alternative hypothesis \(H_1\) that we would use for this test.

#### Null Hypothesis ( \(H_0\) ):
\(H_0: \mu = 172\)

#### Alternative Hypothesis ( \(H_1\) ):
\(H_1: \mu \neq 172\)

##### Explanation:
- **Null Hypothesis ( \(H_0\) ):** This hypothesis assumes that there is no change in the mean height of the plants when treated with the certain chemical, i.e., the mean height is equal to 172 centimeters.
- **Alternative Hypothesis ( \(H_1\) ):** This hypothesis suggests that the mean height of the plants when treated with the chemical is different from 172 centimeters, indicating an effect of the chemical treatment.

#### Graphical Representation:
There are no specific graphs or diagrams provided in the image. The image is essentially focused on setting up the hypotheses for the hypothesis test.

**Continue Button:**
There is a 'Continue' button at the bottom left corner, indicating the option to proceed to the next step after setting up the hypotheses.

This setup is a standard approach in hypothesis testing where we compare the sample mean to the historical mean to determine if there is a significant difference, suggesting an effect due to treatment.
Transcribed Image Text:### Hypothesis Testing for Plant Mean Height The mean height of a certain kind of plant is 172 centimeters. Suppose we want to carry out a hypothesis test to see if the mean height when these plants are treated with a certain chemical differs from 172. State the null hypothesis \(H_0\) and the alternative hypothesis \(H_1\) that we would use for this test. #### Null Hypothesis ( \(H_0\) ): \(H_0: \mu = 172\) #### Alternative Hypothesis ( \(H_1\) ): \(H_1: \mu \neq 172\) ##### Explanation: - **Null Hypothesis ( \(H_0\) ):** This hypothesis assumes that there is no change in the mean height of the plants when treated with the certain chemical, i.e., the mean height is equal to 172 centimeters. - **Alternative Hypothesis ( \(H_1\) ):** This hypothesis suggests that the mean height of the plants when treated with the chemical is different from 172 centimeters, indicating an effect of the chemical treatment. #### Graphical Representation: There are no specific graphs or diagrams provided in the image. The image is essentially focused on setting up the hypotheses for the hypothesis test. **Continue Button:** There is a 'Continue' button at the bottom left corner, indicating the option to proceed to the next step after setting up the hypotheses. This setup is a standard approach in hypothesis testing where we compare the sample mean to the historical mean to determine if there is a significant difference, suggesting an effect due to treatment.
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