Use the Central Limit Theorem to find the mean and standard error of the mean of the sampling distribution. Then sketch a graph of the sampling distribution. each sample is determined. The mean price of photo printers on a website is $229 with a standard deviation of $63. Random samples of size 24 are drawn from this population and the mean The mean of the distribution of sample means is
Use the Central Limit Theorem to find the mean and standard error of the mean of the sampling distribution. Then sketch a graph of the sampling distribution. each sample is determined. The mean price of photo printers on a website is $229 with a standard deviation of $63. Random samples of size 24 are drawn from this population and the mean The mean of the distribution of sample means is
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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![**Central Limit Theorem and Sampling Distribution**
To apply the Central Limit Theorem to find the mean and standard error of the mean for the sampling distribution, follow these steps:
1. **Problem Description:**
- We have a mean price of photo printers on a website, which is $229.
- The standard deviation of the prices is $63.
- Random samples of size 24 are drawn from this population, and the mean of each sample is calculated.
2. **Objective:**
- Determine the mean of the distribution of sample means.
- Calculate the standard error.
- Sketch a graph of the sampling distribution.
### Mean of the Distribution of Sample Means
The mean of the distribution of sample means is the same as the mean of the population. Therefore, the mean is $229.
### Standard Error of the Mean
The standard error (SE) can be calculated using the formula:
\[
SE = \frac{\sigma}{\sqrt{n}}
\]
Where:
- \(\sigma\) is the population standard deviation ($63).
- \(n\) is the sample size (24).
### Graph Explanation
- **Sampling Distribution Graph:**
- Should be approximately normally distributed (bell-shaped) because of the Central Limit Theorem, assuming a sufficiently large sample size.
- Centered at the population mean, $229.
- The spread of the distribution is characterized by the standard error calculated above.
This setup allows you to understand the variability of sample means around the population mean.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F607f2521-e0fb-4d93-825f-3649340ede50%2Fdb2d43b2-c14d-48ab-b98c-f1c2beeffe51%2F2zjlr2k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Central Limit Theorem and Sampling Distribution**
To apply the Central Limit Theorem to find the mean and standard error of the mean for the sampling distribution, follow these steps:
1. **Problem Description:**
- We have a mean price of photo printers on a website, which is $229.
- The standard deviation of the prices is $63.
- Random samples of size 24 are drawn from this population, and the mean of each sample is calculated.
2. **Objective:**
- Determine the mean of the distribution of sample means.
- Calculate the standard error.
- Sketch a graph of the sampling distribution.
### Mean of the Distribution of Sample Means
The mean of the distribution of sample means is the same as the mean of the population. Therefore, the mean is $229.
### Standard Error of the Mean
The standard error (SE) can be calculated using the formula:
\[
SE = \frac{\sigma}{\sqrt{n}}
\]
Where:
- \(\sigma\) is the population standard deviation ($63).
- \(n\) is the sample size (24).
### Graph Explanation
- **Sampling Distribution Graph:**
- Should be approximately normally distributed (bell-shaped) because of the Central Limit Theorem, assuming a sufficiently large sample size.
- Centered at the population mean, $229.
- The spread of the distribution is characterized by the standard error calculated above.
This setup allows you to understand the variability of sample means around the population mean.
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