8. A state's Department of Natural Resources (DNR) is required to estimate the number of whitetail deer in the state. The DNR suspects that whitetail deer spend more time moving around a forest during cooler weather. More movement makes it easier to count the deer. On a 50-acre plot, it is known that there are 45 deer. On a warm day, 24 deer are observed. On a cool day on the same plot, 36 deer are observed. Let P1 = the true proportion of all deer observed on a cool day and P2 = the true proportion of all deer observed on a warm day. Which of the following correctly states the hypotheses and checks conditions for conducting a significance test of p1 -p2? a. Ho: P1- p2 = 0, Ha: P1- p2 # 0 and both the Random and Large Counts conditions are met. %3D %3D b. Ho: pi - p2 = 0, Ha: p1-p2 > 0 and both the Random and Large Counts conditions are met. C. Ho: Pr-p2 = 0, Ha: P1- p2 > 0 and the Random condition is not met and the Large Counts condition is met. d. None of these is correct. %3D %3D

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### Statistical Significance Testing in Wildlife Research

**Problem Scenario:**

A state's Department of Natural Resources (DNR) is tasked with estimating the number of whitetail deer in the state. The DNR hypothesizes that whitetail deer are more active and therefore easier to count during cooler weather conditions. This hypothesis arises from the assumption that deer spend more time moving around the forest in cool weather compared to warm weather.

**Dataset:**

- The count of deer is observed on a 50-acre plot of forest land.
- The total number of deer on the plot is confirmed to be 45.
- On a warm day, 24 deer are observed.
- On a cool day, 36 deer are observed.

**Variables:**

- \( p_1 \): True proportion of all deer observed on a cool day.
- \( p_2 \): True proportion of all deer observed on a warm day.

**Objective:**

To correctly state the hypotheses and check the conditions for conducting a significance test of \( p_1 \) - \( p_2 \).

**Which of the following correctly states the hypotheses and checks conditions for conducting a significance test of \( p_1 \) - \( p_2 \)?**

A. \( H_0: p_1 - p_2 = 0 \), \( H_a: p_1 - p_2 \ne 0 \) and both the Random and Large Counts conditions are met.

B. \( H_0: p_1 - p_2 = 0 \), \( H_a: p_1 - p_2 \ne 0 \) and the Random condition is met and the Large Counts condition is not met.

C. \( H_0: p_1 - p_2 = 0 \), \( H_a: p_1 - p_2 > 0 \) and both the Random and Large Counts conditions are met.

D. \( H_0: p_1 - p_2 = 0 \), \( H_a: p_1 - p_2 > 0 \) and the Random condition is not met and the Large Counts condition is met.

E. None of the above.

### Explanation of Conditions:

- **Random Condition:** This condition is verified to ensure that the sample data is randomly selected from the population, which helps in generalizing the results.
- **Large Counts Condition:** This specifies that the number of observed
Transcribed Image Text:### Statistical Significance Testing in Wildlife Research **Problem Scenario:** A state's Department of Natural Resources (DNR) is tasked with estimating the number of whitetail deer in the state. The DNR hypothesizes that whitetail deer are more active and therefore easier to count during cooler weather conditions. This hypothesis arises from the assumption that deer spend more time moving around the forest in cool weather compared to warm weather. **Dataset:** - The count of deer is observed on a 50-acre plot of forest land. - The total number of deer on the plot is confirmed to be 45. - On a warm day, 24 deer are observed. - On a cool day, 36 deer are observed. **Variables:** - \( p_1 \): True proportion of all deer observed on a cool day. - \( p_2 \): True proportion of all deer observed on a warm day. **Objective:** To correctly state the hypotheses and check the conditions for conducting a significance test of \( p_1 \) - \( p_2 \). **Which of the following correctly states the hypotheses and checks conditions for conducting a significance test of \( p_1 \) - \( p_2 \)?** A. \( H_0: p_1 - p_2 = 0 \), \( H_a: p_1 - p_2 \ne 0 \) and both the Random and Large Counts conditions are met. B. \( H_0: p_1 - p_2 = 0 \), \( H_a: p_1 - p_2 \ne 0 \) and the Random condition is met and the Large Counts condition is not met. C. \( H_0: p_1 - p_2 = 0 \), \( H_a: p_1 - p_2 > 0 \) and both the Random and Large Counts conditions are met. D. \( H_0: p_1 - p_2 = 0 \), \( H_a: p_1 - p_2 > 0 \) and the Random condition is not met and the Large Counts condition is met. E. None of the above. ### Explanation of Conditions: - **Random Condition:** This condition is verified to ensure that the sample data is randomly selected from the population, which helps in generalizing the results. - **Large Counts Condition:** This specifies that the number of observed
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