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

Divide the standard deviation of the sample measures by 8

Explanation:

Given

measurements in data set=500

measurements in sample=64

Standard error of sample=?

As per the formula of standard error

Standard error= standard deviation/ square root of the number of measurements

= σ/√n

Here as we need to find standard error of the sample hence n=64

therefore √64= 8

The above equation will become:

standard error of the sample= σ/8 i.e. Divide the standard deviation of the sample measures by 8!