Suppose that the true proportion of success in some population is 0.1 . The figure below shows the distribution of the sample proportion when the sample size n is 20, 100, and 500.What does each point (observation) in each of the plots represent?Describe what happens to the sampling distribution of p hat as n becomes larger. What stays the same? What changes? The image consists of three histogram graphs stacked vertically, each representing a distribution with varying bin sizes.### Top Graph:- **Description:** This histogram displays a sparse distribution with several distinct, tall bins and gaps between them. - **XAxis Range:** 0.0 to 0.4- **Feature:** The data points are concentrated around certain values indicating a more discrete or clustered distribution.### Middle Graph:- **Description:** This histogram shows a more continuous distribution compared to the top graph. The bins are smaller, and there is a clearer bell-shaped curve, suggesting a normal distribution.- **XAxis Range:** 0.0 to 0.4- **Feature:** The data appears more evenly spread across the range with a peak around the center, showing less clustering than the top graph.### Bottom Graph:- **Description:** The histogram exhibits a very smooth and dense distribution with tiny bins, forming a nearly perfect symmetrical bell curve.- **XAxis Range:** 0.0 to 0.4- **Feature:** This graph portrays the most refined distribution among the three, indicating a highly consistent data spread typical of a normal distribution.These graphs demonstrate how adjustments in bin size can impact the visualization of data distribution, from sparse to more refined representations.

1. Each of the point on the plots represent represents the proportion of success for the sample.…

Answered: Suppose that the true proportion of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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Suppose that the true proportion of success in some population is 0.1 . The figure below shows the distribution of the sample proportion when the sample size n is 20, 100, and 500.
1. What does each point (observation) in each of the plots represent?
2. Describe what happens to the sampling distribution of p hat as n becomes larger. What stays the same? What changes?

The image consists of three histogram graphs stacked vertically, each representing a distribution with varying bin sizes.

### Top Graph:
- **Description:** This histogram displays a sparse distribution with several distinct, tall bins and gaps between them.
- **XAxis Range:** 0.0 to 0.4
- **Feature:** The data points are concentrated around certain values indicating a more discrete or clustered distribution.

### Middle Graph:
- **Description:** This histogram shows a more continuous distribution compared to the top graph. The bins are smaller, and there is a clearer bell-shaped curve, suggesting a normal distribution.
- **XAxis Range:** 0.0 to 0.4
- **Feature:** The data appears more evenly spread across the range with a peak around the center, showing less clustering than the top graph.

### Bottom Graph:
- **Description:** The histogram exhibits a very smooth and dense distribution with tiny bins, forming a nearly perfect symmetrical bell curve.
- **XAxis Range:** 0.0 to 0.4
- **Feature:** This graph portrays the most refined distribution among the three, indicating a highly consistent data spread typical of a normal distribution.

These graphs demonstrate how adjustments in bin size can impact the visualization of data distribution, from sparse to more refined representations.

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