Question 1201174
**a) Interpretation of Power**

* **Power:** The power of a statistical test is the probability of correctly rejecting the null hypothesis when the alternative hypothesis is true. 

* **In this context:** The power of 0.69 means that if the true germination rate after spraying the chemical is actually 0.75 (the alternative hypothesis), there is a 69% chance that the test will correctly detect this difference and reject the null hypothesis (that the germination rate is 0.80).

**b) Ways to Increase Power**

1. **Increase Sample Size:**

    * **How:** Increase the number of seeds sprayed with the chemical.
    * **Disadvantage:** Increased cost and time associated with testing more seeds.

2. **Increase Significance Level (α):**

    * **How:** Increase α from 0.05 to a higher value (e.g., 0.10).
    * **Disadvantage:** Increases the probability of Type I error (rejecting the null hypothesis when it is actually true).

**c) Decision Based on Confidence Interval**

* **The 95% confidence interval for the true germination rate is (0.726, 0.809).**
* **The null hypothesis states that the true germination rate is 0.80.**

* **Since the value 0.80 (the hypothesized value) falls within the 95% confidence interval,** we **fail to reject the null hypothesis.** 

* **Reasoning:** The confidence interval suggests that the true germination rate could plausibly be 0.80. If the true rate were significantly different from 0.80, we would expect the confidence interval to not include 0.80.

**In summary:**

* The power of the test indicates the likelihood of correctly detecting a true difference in germination rates if it exists.
* Increasing sample size or significance level can increase power but also has potential drawbacks.
* The 95% confidence interval provides evidence that the true germination rate might not be significantly different from the hypothesized 0.80, leading to the failure to reject the null hypothesis.