(d) What is the p-value from the simulated distribution of sample statistics? .0857 O.2238 O.0091 O.007 (e) What is the p-value from the theory-based distribution of sample statistics? .2238 O.0857 0.007 0.0091 (f) The conclusion we should make is... O It is plausible that the true population parameter is = 0.15. O It is plausible that the true population parameter is π = 0.0857. O We have strong evidence that the true population parameter is different than π = 0.15. O We have strong evidence that the true population parameter is different than π = 0.0857.

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**Simulation Tool for Understanding Binomial Distributions**

This tool is designed to help students grasp the concept of binomial distributions through simulations. 

**Parameters:**

- **Probability of success (π):** 0.15
- **Sample size (n):** 210
- **Number of samples:** 1000

**Features:**

- **Animate:** Check this box to see an animation of the sampling process.
- **Draw Samples:** Click this button to generate samples.

**Options:**

- **Number of successes:** Toggle to view results in terms of the number of successes.
- **Proportion of successes:** Toggle to view results in terms of the proportion of successes.

**Settings:**

- **As extreme as ≤ :** Field is set to 0.0857. Use this to find samples with proportions as extreme.
- **Count:** Click to count occurrences.

- **Proportion of samples:** `(6 + 1) / 1000 = 0.0070`

**Graph Explanation:**

The graph displays a histogram of the proportion of successes in the samples, with a smooth curve overlay representing the distribution. 

- **X-axis:** Proportion of successes
- **Y-axis:** Frequency of each proportion
- **Red lines:** Indicate critical values (≤ 0.0857 and ≥ 0.2238)
- **Highlighted Area:** Proportion of samples with values as extreme as specified.

**Additional Settings:**

- **Two-sided (between):** Calculates two-sided probabilities.
- **Exact Binomial:** Uses the exact binomial distribution for calculations.
- **Normal Approximation:** Utilizes normal approximation methods.
- **Summary Stats:** Option to view summary statistics.
- **Show previous/Show sliders:** Toggles to view previous settings or to display parameter sliders for adjustments.

This interactive tool provides a visual and practical approach to understanding probability distributions and statistical significance.
Transcribed Image Text:**Simulation Tool for Understanding Binomial Distributions** This tool is designed to help students grasp the concept of binomial distributions through simulations. **Parameters:** - **Probability of success (π):** 0.15 - **Sample size (n):** 210 - **Number of samples:** 1000 **Features:** - **Animate:** Check this box to see an animation of the sampling process. - **Draw Samples:** Click this button to generate samples. **Options:** - **Number of successes:** Toggle to view results in terms of the number of successes. - **Proportion of successes:** Toggle to view results in terms of the proportion of successes. **Settings:** - **As extreme as ≤ :** Field is set to 0.0857. Use this to find samples with proportions as extreme. - **Count:** Click to count occurrences. - **Proportion of samples:** `(6 + 1) / 1000 = 0.0070` **Graph Explanation:** The graph displays a histogram of the proportion of successes in the samples, with a smooth curve overlay representing the distribution. - **X-axis:** Proportion of successes - **Y-axis:** Frequency of each proportion - **Red lines:** Indicate critical values (≤ 0.0857 and ≥ 0.2238) - **Highlighted Area:** Proportion of samples with values as extreme as specified. **Additional Settings:** - **Two-sided (between):** Calculates two-sided probabilities. - **Exact Binomial:** Uses the exact binomial distribution for calculations. - **Normal Approximation:** Utilizes normal approximation methods. - **Summary Stats:** Option to view summary statistics. - **Show previous/Show sliders:** Toggles to view previous settings or to display parameter sliders for adjustments. This interactive tool provides a visual and practical approach to understanding probability distributions and statistical significance.
### Statistical Analysis Exercise

**(d) What is the p-value from the simulated distribution of sample statistics?**

- ○ .0857
- ○ .2238
- ○ .0091
- ○ .007

**(e) What is the p-value from the theory-based distribution of sample statistics?**

- ○ .2238
- ○ .0857
- ○ .007
- ○ .0091

**(f) The conclusion we should make is…**

- ○ It is plausible that the true population parameter is π = 0.15.
- ○ It is plausible that the true population parameter is π = 0.0857.
- ○ We have strong evidence that the true population parameter is different than π = 0.15.
- ○ We have strong evidence that the true population parameter is different than π = 0.0857.
Transcribed Image Text:### Statistical Analysis Exercise **(d) What is the p-value from the simulated distribution of sample statistics?** - ○ .0857 - ○ .2238 - ○ .0091 - ○ .007 **(e) What is the p-value from the theory-based distribution of sample statistics?** - ○ .2238 - ○ .0857 - ○ .007 - ○ .0091 **(f) The conclusion we should make is…** - ○ It is plausible that the true population parameter is π = 0.15. - ○ It is plausible that the true population parameter is π = 0.0857. - ○ We have strong evidence that the true population parameter is different than π = 0.15. - ○ We have strong evidence that the true population parameter is different than π = 0.0857.
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