True or False
As sample size increases, the value of the standard error also increases.
As sample size increases, the value of the standard error also increases.
Ans false
SEm = SD/√n
From this equation, you can see why it is false.
it decreases
False.
As the sample size increases, the value of the standard error decreases. The standard error is a measure of the variability or dispersion of the sample mean. It quantifies the precision of an estimate from a sample.
To understand why the standard error decreases as sample size increases, we need to look at the formula for calculating it:
Standard Error = Standard Deviation / √(Sample Size)
The standard deviation represents the spread or variability of the population data. Dividing it by the square root of the sample size accounts for the fact that a larger sample size provides more information, which leads to more precise estimates.
Intuitively, it makes sense that as we increase the sample size, we have more observations and can better capture the true population parameters. This reduces the uncertainty and tightens the estimate, resulting in a smaller standard error.
So, in summary, as the sample size increases, the value of the standard error decreases.