Question

A scientist has a data set consisting of the temperature at which a chemical solution begins to evaporate. There are 500 measurements in the data set. He plans to estimate the standard error for the mean temperature by drawing a random sample from the data set consisting of 64 measurements.

What formula would produce an estimate for the standard error of the sample?

Divide the sum of all the measures by 500.
Divide the standard deviation of the sample measures by 8
Divide the sum of the sample measurements by 64
Calculate the sum of the squares of the deviations of the sample

Answer 1

The standard error (SE) is the standard deviation of the sampling distribution of a statistic.

The relationship between the standard deviation of a sample drawn from a population with the standard deviation of the population is defined such that, for a given sample size, the standard error equals the standard deviation divided by the square root of the sample size.

Therefore, the formula that would produce an estimate for the standard error of the sample is "Divide the standard deviation of the sample measures by 8". [8 is the square root of 64].