Question

DISCUSSION -

When estimating a population characteristic based on a sample statistic, why it is important to use standard error as part of your estimate?

Answer 1

Solution :-

The standard error (SE) of a statistic is the approximate standard deviation of a statistical sample population.

The standard error is a statistical term that measures the accuracy with which a sample distribution represents a population by using standard deviation. In statistics, a sample mean deviates from the actual mean of a population—this deviation is the standard error of the mean.

• The standard error is the approximate standard deviation of a statistical sample population.
• The standard error can include the variation between the calculated mean of the population and one which is considered known, or accepted as accurate.
• The more data points involved in the calculations of the mean, the smaller the standard error tends to be.

The relationship between the standard error and the standard deviation is such that, for a given sample size, the standard error equals the standard deviation divided by the square root of the sample size. The standard error is also inversely proportional to the sample size; the larger the sample size, the smaller the standard error because the statistic will approach the actual value.

Standard Error Formula for σ known is,

σx = σ / √ n

σx -- Standard Error.

σ -- Population Standard Deviation.

n -- Sample Size.

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Standard Error Formula for σ Unknown is,

Sx = s / √ n

Sx -- Standard Error.

s -- Sample Standard Deviation.

n -- Sample Size.