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Black_prince [1.1K]
3 years ago
14

A simple random sample of 100 observations was taken from a large population. The sample mean and the standard deviation were de

termined to be 80 and 12 respectively. The standard error of the mean is?
Mathematics
1 answer:
olga2289 [7]3 years ago
5 0

Answer:

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:

\bar X =\frac{\sum_{i=1}^n x_i}{n}

And the distribution for the sample mean is given by:

\bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}})

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:

Se=\frac{\sigma}{\sqrt{n}}

If we replace the values given we have:

Se=\frac{12}{\sqrt{100}}=1.2

So then the distribution for the sample mean \bar X is:

\bar X \sim N(\mu=80,Se=1.2)

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