Question

The standard deviation of the sampling distribution of Xbar, SIGMAx, is called the:

a) Population variance
b) Sample variance
c) Population standard deviation
d) Sample standard deviation

Answer 1

The standard deviation of the sampling distribution of Xbar, SIGMAx, is called the: c) Population standard deviation

Step-by-step explanation:

The standard deviation of the c)sampling distribution of the sample mean
`(\( \bar{X} \)),` denoted as
`\( \sigma_{\bar{X}} \),` is called the population standard deviation
`(\( \sigma \)).` This standard deviation represents the variability of sample means if multiple random samples were taken from the same population.

In statistical terms, when we calculate the mean of several samples taken from a population and examine the distribution of those sample means, the standard deviation of this distribution is referred to as the standard error of the mean or the standard deviation of the sampling distribution of the sample mean. It is calculated by dividing the population standard deviation
`(\( \sigma \))` by the square root of the sample size
`(\( n \)).`

`\[ \sigma_{\bar{X}} = (\sigma)/(√(n)) \]`

This standard error is crucial in inferential statistics, especially when estimating confidence intervals or conducting hypothesis tests based on sample means. A smaller standard error indicates a more precise estimate of the population mean.