MullOverThing

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# How do you describe the sampling distribution of the sample mean?

## How do you describe the sampling distribution of the sample mean?

If the population is normal to begin with then the sample mean also has a normal distribution, regardless of the sample size. For samples of any size drawn from a normally distributed population, the sample mean is normally distributed, with mean μX=μ and standard deviation σX=σ/√n, where n is the sample size.

How is the bias of a sampling distribution measured?

note: The bias of a sampling distribution is measured by computing the distance between the center of the sampling distribution and the population parameter. The precision of an estimator does not depend on the size of the population.

Is the sampling distribution of the sample mean normal?

Now we may invoke the Central Limit Theorem: even though the distribution of household size X is skewed, the distribution of sample mean household size (x-bar) is approximately normal for a large sample size such as 100.

### Which is an example of the sample mean X-bar?

We are now moving on to explore the behavior of the statistic x-bar, the sample mean, relative to the parameter μ (mu), the population mean (when the variable of interest is quantitative). Let’s begin with an example. Birth weights are recorded for all babies in a town. The mean birth weight is 3,500 grams, µ = mu = 3,500 g.

What is the behavior of the statistic P-hat?

So far, we’ve discussed the behavior of the statistic p-hat, the sample proportion, relative to the parameter p, the population proportion (when the variable of interest is categorical).

Is the spread of sample mean related to sample size?

As for the spread of all sample means, theory dictates the behavior much more precisely than saying that there is less spread for larger samples. In fact, the standard deviation of all sample means is directly related to the sample size, n as indicated below.