What are other sampling distributions for mean?

Question

Ayesha Gomez · Accepted Answer

Step 1
Sampling distributions : The probability distribution of a given statistic based on a random sample.
The sampling distribution depends on: the underlying distribution of the population, the statistic being consider.
Let

x_{1}, x_{2}, . . . . x_{n}

are random sample from population with mean µ and standard deviation σ then sampling distribution of sample follows approximately normal distribution as,

\overset{―}{x} \sim N (μ_{\overset{―}{x}}, σ_{\overset{―}{x}}) w h e r e σ_{\overset{―}{x}} = \frac{σ}{\sqrt{n}}

And if population standard deviation \sigma is unknown then,

\overset{―}{x} \sim N (μ_{\overset{―}{x}}, S_{\overset{―}{x}}) w h e r e S_{\overset{―}{x}} = \frac{S}{\sqrt{n}}

Step 2
This distribution is normal since the underlying population is normal, although sampling distributions may also often be close to normal even when the population distribution is not.

What are other sampling distributions for mean?

Answered question

Answer & Explanation

New Questions in College Statistics