What is the estimated standard error for a sample of n = 9 scores with s2 = 36?

Answer 1

Firstly, we must recognize what is standard error (SE), and it is the following formula, provided the information given in the problem posted here:

SE = s / √n

where "s" is the sample standard deviation and "n" the sample.

Also, recall that there's a relationship between standard deviation (s) and variance (s²) of a sample (or population, which are represented typically by a different symbol, like the Greek lowercase letter sigma, σ)--that is, they are reciprocal of each other by way of squaring and square root. When given (or after calculated) the variance, we simply square root it to find the standard deviation; on the contrary, if standard deviation is given or calculated, we would square it to find the variance.

Given the information, n = 9 and s² = 36, we do the following:

1. Find s (because we do not use variance to find the standard error, SE)

√ s² = √36

s = 6

1. Then, calculate the standard error with n = 9 and s = 6

SE = 6 / √9 = 6 / 3 = 2

So, we find the standard error is 2.