How does sample size (n) affect SE (Standard Error)? As sample size increases, so does SE. As sample size decreases, so does SE. It doesn't. None of the above.
Answer (1)
To understand how sample size (n) affects the Standard Error (SE), we need to look at the formula for the Standard Error in statistics:
SE = n σ
where σ is the population standard deviation and n is the sample size.
From the formula, we can see that SE is inversely related to the square root of the sample size. Here's how different sample sizes affect the Standard Error:
As sample size increases, SE decreases. This is because the Standard Error is divided by the square root of the sample size. A larger denominator means a smaller Standard Error. This implies that with a larger sample size, the estimate of the population parameter becomes more accurate.
As sample size decreases, SE increases. Conversely, if the sample size is smaller, the Standard Error becomes larger, implying less precision in estimating the population parameter.
The answer to the multiple-choice question is: As sample size increases, SE decreases.
