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Statistics and Probability
College Statistics
Sampling distributions

ka1leE

Answered question

2021-01-31

Critical Thinking Let x be a random variable representing the amount of sleep each adult in New York City got last night. Consider a sampling distribution of sample means

\overset{―}{x}

.
What value will the standard deviation

σ_{\overset{―}{x}}

of the sampling distribution approach?

Answer & Explanation

Aamina Herring

Skilled2021-02-01Added 85 answers

The standard deviation of distribution is measured using the standard error of the distribution,
$σ_{\overset{―}{x}} = \frac{σ}{\sqrt{n}}$
In the formula, $σ$ denotes the population standard deviation and n denotes the sample size.
Even when the sample size is increased the standard deviation $σ_{\overset{―}{x}}$ , of $\overset{―}{x}$ distribution approaches to $\frac{σ}{\sqrt{n}}$ .

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