Question

A simple random sample of 100 observations was taken from a large population. The sample mean and the standard deviation was determined to be 80 and 12, respectively. The standard error of mean is _______

Answer 1

Concept:

No of observations

\(N = {\left( {\frac{{{C_V}}}{ϵ}} \right)^2}\)

Where,

ϵ = allowable % error of mean

Cv = coefficient of variation.

\(C_v= \frac{\sigma}{\bar{x}}~\times 100\)

σ = Standard deviation, x̅ = Mean

Calculation:

Given:

x̅ = 80, σ = 12, N = 100

\(C_v= \frac{\sigma}{\bar{x}}~\times 100\)

\({C_v} = \frac{{12}}{{80}} × 100\)

Cv = 15%

\(N = {\left( {\frac{{{C_V}}}{ϵ}} \right)^2}\)

\(100 = {\left( {\frac{{{15}}}{ϵ}} \right)^2}\)

ϵ = 1.5%

The standard error of mean = mean × percentage of absolute mean error = \(80\times {{1.5} \over 100}\) = 1.2