### Analyzing Sample Size and Standard Error**Objective:**Understand how to calculate the standard error of the mean for different sample sizes, assuming a normal population.#### (a) Calculating the Standard ErrorFor each sampling scenario, find the standard error of the mean. Round your answers to two decimal places.- **Standard Error Formula:** \[ \text{Standard Error (SE)} = \frac{\sigma}{\sqrt{n}} \] where $\sigma$ is the standard deviation and $n$ is the sample size.**Scenarios:**1. **(a)** $\sigma = 20, n = 25$ 2. **(b)** $\sigma = 20, n = 100$ 3. **(c)** $\sigma = 20, n = 400$ **Standard Error Table:**| | Standard Error ||----------------|----------------|| (a) $\sigma = 20, n = 25$ | || (b) $\sigma = 20, n = 100$ | || (c) $\sigma = 20, n = 400$ | |#### (b) Understanding the Effect of Increasing Sample Size**Question:**What happens to the standard error each time you quadruple the sample size?- The standard error is $[ \text{Click to select} ]$ by half.**Explanation:**When you quadruple the sample size, the standard error is divided by two, as the standard error is inversely proportional to the square root of the sample size.

Given, The variance and sample size. σ=20, n=25σ=20, n=100σ=20, n=400

(a) Find the standard error of the mean for each sampling situation (assuming a normal population). (Round your answers to 2 decimal places.) Standard Error (a) o = 20, n = 25 (b) o = 20, n = 100 (c) o = 20, n = 400 (b) What happens to the standard error each time you quadruple the sample size? The standard error is (Click to select) v by half.

(a) Find the standard error of the mean for each sampling situation (assuming a normal population). (Round your answers to 2 decimal places.) Standard Error (a) o = 20, n = 25 (b) o = 20, n = 100 (c) o = 20, n = 400 (b) What happens to the standard error each time you quadruple the sample size? The standard error is (Click to select) v by half.

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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Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

### Analyzing Sample Size and Standard Error

**Objective:**
Understand how to calculate the standard error of the mean for different sample sizes, assuming a normal population.

#### (a) Calculating the Standard Error

For each sampling scenario, find the standard error of the mean. Round your answers to two decimal places.

- **Standard Error Formula:**
\[
\text{Standard Error (SE)} = \frac{\sigma}{\sqrt{n}}
\]
where $\sigma$ is the standard deviation and $n$ is the sample size.

**Scenarios:**

1. **(a)** $\sigma = 20, n = 25$
2. **(b)** $\sigma = 20, n = 100$
3. **(c)** $\sigma = 20, n = 400$

**Standard Error Table:**

| | Standard Error |
|----------------|----------------|
| (a) $\sigma = 20, n = 25$ | |
| (b) $\sigma = 20, n = 100$ | |
| (c) $\sigma = 20, n = 400$ | |

#### (b) Understanding the Effect of Increasing Sample Size

**Question:**
What happens to the standard error each time you quadruple the sample size?

- The standard error is $[ \text{Click to select} ]$ by half.

**Explanation:**
When you quadruple the sample size, the standard error is divided by two, as the standard error is inversely proportional to the square root of the sample size.

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