(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.
(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.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question

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.

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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