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# Educational Exercise: Sampling Distribution of the Sample Mean In this exercise, we explore the sampling distribution of the sample mean \( \bar{x} \) by considering a random sample of size \( n \) taken from a population with a known mean \( \mu \) and standard deviation \( \sigma \). For each scenario provided, calculate the mean, variance, and standard deviation of the sampling distribution of \( \bar{x} \). Ensure that all answers are rounded to four decimal places. ### Scenario A - **Population Mean (\( \mu \)):** 7 - **Population Standard Deviation (\( \sigma \)):** 4 - **Sample Size (\( n \)):** 39 | Statistic | Value | |-------------|----------| | Mean of \( \bar{x} \) | | | Variance of \( \bar{x} \) | | | Standard Deviation of \( \bar{x} \) | | ### Scenario B - **Population Mean (\( \mu \)):** 559 - **Population Standard Deviation (\( \sigma \)):** 3 - **Sample Size (\( n \)):** 119 | Statistic | Value | |-------------|----------| | Mean of \( \bar{x} \) | | | Variance of \( \bar{x} \) | | | Standard Deviation of \( \bar{x} \) | | ### Scenario C - **Population Mean (\( \mu \)):** 3 - **Population Standard Deviation (\( \sigma \)):** 6 - **Sample Size (\( n \)):** 8 | Statistic | Value | |-------------|----------| | Mean of \( \bar{x} \) | | | Variance of \( \bar{x} \) | | | Standard Deviation of \( \bar{x} \) | | ### Instructions 1. **Mean of \( \bar{x} \):** The mean of the sampling distribution is equal to the population mean \( \mu \). 2. **Variance of \( \bar{x} \):** Calculate using the formula \(\sigma^2 / n\). 3. **Standard Deviation of \( \bar{x} \):** Calculate using the formula \(\sigma / \sqrt{n}\). This exercise provides practice in understanding

# Educational Exercise: Sampling Distribution of the Sample Mean In this exercise, we explore the sampling distribution of the sample mean \( \bar{x} \) by considering a random sample of size \( n \) taken from a population with a known mean \( \mu \) and standard deviation \( \sigma \). For each scenario provided, calculate the mean, variance, and standard deviation of the sampling distribution of \( \bar{x} \). Ensure that all answers are rounded to four decimal places. ### Scenario A - **Population Mean (\( \mu \)):** 7 - **Population Standard Deviation (\( \sigma \)):** 4 - **Sample Size (\( n \)):** 39 | Statistic | Value | |-------------|----------| | Mean of \( \bar{x} \) | | | Variance of \( \bar{x} \) | | | Standard Deviation of \( \bar{x} \) | | ### Scenario B - **Population Mean (\( \mu \)):** 559 - **Population Standard Deviation (\( \sigma \)):** 3 - **Sample Size (\( n \)):** 119 | Statistic | Value | |-------------|----------| | Mean of \( \bar{x} \) | | | Variance of \( \bar{x} \) | | | Standard Deviation of \( \bar{x} \) | | ### Scenario C - **Population Mean (\( \mu \)):** 3 - **Population Standard Deviation (\( \sigma \)):** 6 - **Sample Size (\( n \)):** 8 | Statistic | Value | |-------------|----------| | Mean of \( \bar{x} \) | | | Variance of \( \bar{x} \) | | | Standard Deviation of \( \bar{x} \) | | ### Instructions 1. **Mean of \( \bar{x} \):** The mean of the sampling distribution is equal to the population mean \( \mu \). 2. **Variance of \( \bar{x} \):** Calculate using the formula \(\sigma^2 / n\). 3. **Standard Deviation of \( \bar{x} \):** Calculate using the formula \(\sigma / \sqrt{n}\). This exercise provides practice in understanding

MATLAB: An Introduction with Applications
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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# Educational Exercise: Sampling Distribution of the Sample Mean In this exercise, we explore the sampling distribution of the sample mean \( \bar{x} \) by considering a random sample of size \( n \) taken from a population with a known mean \( \mu \) and standard deviation \( \sigma \). For each scenario provided, calculate the mean, variance, and standard deviation of the sampling distribution of \( \bar{x} \). Ensure that all answers are rounded to four decimal places. ### Scenario A - **Population Mean (\( \mu \)):** 7 - **Population Standard Deviation (\( \sigma \)):** 4 - **Sample Size (\( n \)):** 39 | Statistic | Value | |-------------|----------| | Mean of \( \bar{x} \) | | | Variance of \( \bar{x} \) | | | Standard Deviation of \( \bar{x} \) | | ### Scenario B - **Population Mean (\( \mu \)):** 559 - **Population Standard Deviation (\( \sigma \)):** 3 - **Sample Size (\( n \)):** 119 | Statistic | Value | |-------------|----------| | Mean of \( \bar{x} \) | | | Variance of \( \bar{x} \) | | | Standard Deviation of \( \bar{x} \) | | ### Scenario C - **Population Mean (\( \mu \)):** 3 - **Population Standard Deviation (\( \sigma \)):** 6 - **Sample Size (\( n \)):** 8 | Statistic | Value | |-------------|----------| | Mean of \( \bar{x} \) | | | Variance of \( \bar{x} \) | | | Standard Deviation of \( \bar{x} \) | | ### Instructions 1. **Mean of \( \bar{x} \):** The mean of the sampling distribution is equal to the population mean \( \mu \). 2. **Variance of \( \bar{x} \):** Calculate using the formula \(\sigma^2 / n\). 3. **Standard Deviation of \( \bar{x} \):** Calculate using the formula \(\sigma / \sqrt{n}\). This exercise provides practice in understanding
Transcribed Image Text:# Educational Exercise: Sampling Distribution of the Sample Mean In this exercise, we explore the sampling distribution of the sample mean \( \bar{x} \) by considering a random sample of size \( n \) taken from a population with a known mean \( \mu \) and standard deviation \( \sigma \). For each scenario provided, calculate the mean, variance, and standard deviation of the sampling distribution of \( \bar{x} \). Ensure that all answers are rounded to four decimal places. ### Scenario A - **Population Mean (\( \mu \)):** 7 - **Population Standard Deviation (\( \sigma \)):** 4 - **Sample Size (\( n \)):** 39 | Statistic | Value | |-------------|----------| | Mean of \( \bar{x} \) | | | Variance of \( \bar{x} \) | | | Standard Deviation of \( \bar{x} \) | | ### Scenario B - **Population Mean (\( \mu \)):** 559 - **Population Standard Deviation (\( \sigma \)):** 3 - **Sample Size (\( n \)):** 119 | Statistic | Value | |-------------|----------| | Mean of \( \bar{x} \) | | | Variance of \( \bar{x} \) | | | Standard Deviation of \( \bar{x} \) | | ### Scenario C - **Population Mean (\( \mu \)):** 3 - **Population Standard Deviation (\( \sigma \)):** 6 - **Sample Size (\( n \)):** 8 | Statistic | Value | |-------------|----------| | Mean of \( \bar{x} \) | | | Variance of \( \bar{x} \) | | | Standard Deviation of \( \bar{x} \) | | ### Instructions 1. **Mean of \( \bar{x} \):** The mean of the sampling distribution is equal to the population mean \( \mu \). 2. **Variance of \( \bar{x} \):** Calculate using the formula \(\sigma^2 / n\). 3. **Standard Deviation of \( \bar{x} \):** Calculate using the formula \(\sigma / \sqrt{n}\). This exercise provides practice in understanding
Expert Solution
Step 1

a)

Given :

μ = 7

σ = 4

n = 39

μx¯ = μ = 7

σX¯2 = σ2n

σX¯2 = 1639

σX¯2 = 0.4103

σX¯ = σn

σX¯ = 439

σX¯ = 0.6405

 

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