Let's break down and solve each step, explaining the reasoning and method before moving on. --- ## **Вопрос 1: Calculate Mean Normalized Acres Burnt** **Step 1: Create `acrespersqmile`** - Formula: \[ \text{acrespersqmile} = \frac{\text{acres}}{\text{landarea}} \] For each state-year, divide the number of acres burnt by the land area (in square miles) of the state. **Step 2: Calculate the Mean** - Add up all the values of `acrespersqmile` and divide by the number of observations (years × states). **Explanation:** This gives the average number of acres burnt per square mile, which is called "mean normalized acres burnt." Use Excel's `=AVERAGE(<range>)` to calculate this. --- ## **Вопрос 2: Sample Standard Deviation** **Step 1: Find the Standard Deviation of `acrespersqmile`** - Use Excel's `=STDEV.S(<range>)` function. **Explanation:** This tells you how much the normalized acres burnt values deviate from the mean, across all state-year observations. --- ## **Вопрос 3: State Hypotheses** **Step 1: State the Null and Alternative Hypotheses** - The **EPA claim**: mean = 1.32 acres/sq mile. - We are testing if the actual mean is different from 1.32 (two-sided test). **Correct Answer:** \[ H_: \mu = 1.32 \qquad H_A: \mu \neq 1.32 \] **Explanation:** We want to check if the mean normalized acres burnt is equal to 1.32 or not. --- ## **Вопрос 4: T-Test in Excel** **Step 1: Conduct a One-Sample t-Test** - In Excel, use `=T.TEST(<range>, <mean>, 2, 1)` `<range>`: your normalized acres burnt data `<mean>`: 1.32 `2`: two-tailed test `1`: one-sample test - Alternatively, use `=T.TEST(<range>, <mean>, 2, 1)` directly or calculate t-statistic as: \[ t = \frac{\bar{x} - 1.32}{s/\sqrt{n}} \] where \(\bar{x}\) = sample mean, \(s\) = sample std dev, \(n\) = sample size. **Explanation:** This test checks if the mean normalized acres burnt is statistically different from 1.32. --- ## **Вопрос 5: Report the p-value** **Step 1: Find the p-value from your t-test** - Excel's `T.TEST` or output from Data Analysis Toolpak gives the p-value. **Explanation:** If p-value < .05, reject \( H_ \); otherwise, fail to reject \( H_ \). --- ## **Final Conclusion** 1. **Calculated the mean normalized acres burnt** to summarize wildfire exposure per square mile. 2. **Calculated the sample standard deviation** to measure variability. 3. **Correctly formulated hypotheses** for a two-sided test of the EPA's claim. 4. **Conducted a one-sample t-test** in Excel to compare the observed mean to the EPA value. 5. **Reported the p-value** from the test to make a decision regarding the hypothesis. **Interpretation:** - If p-value < .05: There is evidence that the true mean normalized acres burnt is different from 1.32. - If p-value ≥ .05: There is not enough evidence to say it is different from 1.32. > **Note:** You must use your actual data values in Excel to get numeric answers for mean, standard deviation, t-statistic, and p-value. The process above is how you solve the problem step by step. If you provide the data, I can help with calculations.

## **Вопрос 1: Calculate Mean Normalized Acres Burnt** ### **Step 1: Create `acrespersqmile`** - **Formula:** \[ \text{acrespersqmile} = \frac{\text{acres}}{\text{landarea}} \] For each state-year, divide the number of acres burnt by the land area (in square miles) of the state. ### **Step 2: Calculate the Mean** - **Method:** Use Excel's formula: \[ \text{Mean} = \text{AVERAGE}(<range>) \] Replace `<range>` with the range of your calculated `acrespersqmile`. ### **Explanation:** This gives the average number of acres burnt per square mile, termed "mean normalized acres burnt." --- ## **Вопрос 2: Sample Standard Deviation** ### **Step 1: Calculate Standard Deviation** - **Method:** Use Excel's standard deviation function: \[ \text{Standard Deviation} = \text{STDEV.S}(<range>) \] ### **Explanation:** This value indicates how much the normalized acres burnt vary from the mean across all observations. --- ## **Вопрос 3: State Hypotheses** ### **Step 1: Formulate Hypotheses** - **Hypotheses:** - Null Hypothesis \(H_0\): \[ \mu = 1.32 \] - Alternative Hypothesis \(H_A\): \[ \mu \neq 1.32 \] ### **Explanation:** This sets up a two-tailed test to determine if the mean normalized acres burnt differs from the EPA's claim. --- ## **Вопрос 4: T-Test in Excel** ### **Step 1: Running the T-Test** - **Method:** Use Excel's `T.TEST` function: \[ =T.TEST(<range>, 1.32, 2, 1) \] Alternatively, calculate the t-statistic manually as: \[ t = \frac{\bar{x} - 1.32}{s/\sqrt{n}} \] where \(\bar{x}\) is the sample mean, \(s\) is the sample standard deviation, and \(n\) is the sample size. ### **Explanation:** This statistical test assesses whether the mean normalized acres burnt is significantly different from 1.32 acres/sq mile. --- ## **Вопрос 5: Report the p-value** ### **Step 1: Obtain the p-value** - **Method:** The output from the `T.TEST` function provides the p-value. ### **Explanation:** The p-value indicates the probability of observing the data under the null hypothesis. Compare this value to 0.05 to make a decision. --- ## **Final Conclusion** 1. **Mean Normalized Acres Burnt:** Indicates average wildfire exposure. 2. **Sample Standard Deviation:** Reflects variability in wildfire impact across states and years. 3. **Hypotheses Formulated:** Set up to test the EPA's mean claim. 4. **T-Test Conducted:** Evaluates the claim statistically. 5. **p-value Reported:** Determines if the null hypothesis can be rejected or not. ### **Interpretation of Results:** - If **p-value < 0.05**: Significant evidence against \(H_0\); the mean normalized acres burnt is different from 1.32. - If **p-value ≥ 0.05**: No significant evidence against \(H_0\); the mean normalized acres burnt is not different from 1.32. > **Note:** Execute the above steps in Excel with your dataset to derive specific numeric results for mean, standard deviation, t-statistic, and p-value. If you need assistance with specific values, please provide the dataset.

Yes, the solution addresses all the requirements outlined in the questions. Here’s a recap of how each question was handled: ## **Overview of Questions and Solutions** 1. **Mean Normalized Acres Burnt (Вопрос 1):** - Created a new variable `acrespersqmile` by dividing acres burnt by land area. - Explained how to calculate the mean using Excel's `AVERAGE` function. 2. **Sample Standard Deviation (Вопрос 2):** - Provided a method to calculate the sample standard deviation using Excel's `STDEV.S` function. - Explained what the standard deviation indicates regarding the data's variability. 3. **Hypotheses Formulation (Вопрос 3):** - Clearly stated the null and alternative hypotheses regarding the EPA's claim of 1.32 acres/sq mile. - Explained the significance of these hypotheses in the context of the analysis. 4. **T-Test Execution (Вопрос 4):** - Described how to perform a one-sample t-test in Excel, including both the `T.TEST` function and the manual t-statistic calculation. - Explained the purpose of the t-test in determining the validity of the hypotheses. 5. **Reporting the p-value (Вопрос 5):** - Explained how to extract the p-value from the t-test results. - Provided guidance on interpreting the p-value in relation to the null hypothesis. ## **Conclusion** - Each component of the problem was broken down into clear, actionable steps. - Explanations were provided after each solution to clarify the reasoning and methodology. - The structure followed a logical flow to ensure that all aspects of the questions were addressed. If you have any further questions or need more specific computations, please let me know!