**Problem Statement:**A population has a mean $ \mu = 84 $ and a standard deviation $ \sigma = 9 $. Find the mean and standard deviation of a sampling distribution of sample means with sample size $ n = 81 $.**Solution:**The mean of the sampling distribution of sample means ($ \mu_{\bar{x}} $) is the same as the population mean:\[ \mu_{\bar{x}} = \mu = 84 \](Simplify your answer.)Additionally, the standard deviation of the sampling distribution of sample means, also known as the standard error, is calculated using the formula:\[ \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} \]where $ \sigma = 9 $ and $ n = 81 $.

Determine the sampling distribution of the sample mean for sample of size 81. The sampling…

Answered: A population has a mean p = 84 and a…

A population has a mean p = 84 and a standard deviation o = 9. Find the mean and standard deviation of a sampling distribution of sample means with sample size n = 81. (Simplify your answer.)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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**Problem Statement:**

A population has a mean $ \mu = 84 $ and a standard deviation $ \sigma = 9 $. Find the mean and standard deviation of a sampling distribution of sample means with sample size $ n = 81 $.

**Solution:**

The mean of the sampling distribution of sample means ($ \mu_{\bar{x}} $) is the same as the population mean:

\[ \mu_{\bar{x}} = \mu = 84 \]

(Simplify your answer.)

Additionally, the standard deviation of the sampling distribution of sample means, also known as the standard error, is calculated using the formula:

\[ \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} \]

where $ \sigma = 9 $ and $ n = 81 $.

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