Asimple random sample of 100 observations was taken from a large population. the sample mean and the standard deviation were determined to be 80 and 12 respectively. the standard error of the mean is?

Se=1.2

Step-by-step explanation:

The standard error is the standard deviation of a sample population. "It measures the accuracy with which a sample represents a population".

The central limit theorem (CLT) states "that the distribution of sample means approximates a normal distribution, as the sample size becomes larger, assuming that all samples are identical in size, and regardless of the population distribution shape"

The sample mean is defined as:

And the distribution for the sample mean is given by:

Let X denotes the random variable that measures the particular characteristic of interest. Let, X1, X2, …, Xn be the values of the random variable for the n units of the sample.

As the sample size is large,(>30) it can be assumed that the distribution is normal. The standard error of the sample mean X bar is given by:

If we replace the values given we have:

So then the distribution for the sample mean is:

s

step-by-step explanation: