Assume the population standard deviation is σ=25 . Compute the standard error of the mean, σx̅,

Name: Problem 39, Chapter 7: Essentials of Modern Business Statistics
Uploaded: 2022-09-19T23:15:42-08:00
Duration: 3 min 3 s
Channel: Sheryl Ezze
Description: Assume the population standard deviation is σ=25 . Compute the standard error of the mean, σx̅, for sample sizes of 500,000 ; 1,000,000 ; 5,000,000 ; 10,000,000 ; and 100,000,000 . What can you say about the size of the standard error of the mean as the sample size is increased?

step 1 So we're looking at what the standard air will be if we have the population standard deviations

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Assume the population standard deviation is $\sigma=25 .$ Compute the standard error of the mean, $\sigma_{\bar{x}}$, for sample sizes of 500,$000 ; 1,000,000 ; 5,000,000 ; 10,000,000 ;$ and $100,000,000 .$ What can you say about the size of the standard error of the mean as the sample size is increased?

   Assume the population standard deviation is $\sigma=25 .$ Compute the standard error of the mean, $\sigma_{\bar{x}}$, for sample sizes of 500,$000 ; 1,000,000 ; 5,000,000 ; 10,000,000 ;$ and $100,000,000 .$ What can you say about the size of the standard error of the mean as the sample size is increased?

Essentials of Modern Business Statistics

David R. Anderson,… 8th Edition

Chapter 7, Problem 39

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Solved by Expert Sheryl Ezze

09/19/2022

Step 1

Step 1: First, we need to understand the formula for the standard error of the mean, which is given by $\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}$, where $\sigma$ is the population standard deviation and $n$ is the sample size. Show more…

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Assume the population standard deviation is $\sigma=25 .$ Compute the standard error of the mean, $\sigma_{\bar{x}}$, for sample sizes of 500,$000 ; 1,000,000 ; 5,000,000 ; 10,000,000 ;$ and $100,000,000 .$ What can you say about the size of the standard error of the mean as the sample size is increased?

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Key Concepts

Relationship Between Sample Size and Standard Error

This concept explains the inverse relationship between sample size and the standard error of the mean. As the sample size increases, the standard error decreases because the variability of the sample means becomes smaller, leading to more precise estimates of the population mean.

Population Standard Deviation

This is a measure of the dispersion or variability in a population. When known, as in this case with ? = 25, it serves as a crucial parameter in statistical inference and is used to calculate other important measures such as the standard error of the mean.

Standard Error of the Mean

This is a statistic that quantifies how much the sample mean is expected to vary from the true population mean. It is calculated as the population standard deviation divided by the square root of the sample size, thereby providing insight into the precision of the sample mean as an estimate of the population mean.

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