Question

fill in the blanks below using the central limit theorem to explain why it is desirable to take as large a sample as possible when trying to estimate a population value. the central limit theorem says that the standard - deviation of the frequency curve for the samples will be the select divided by the select. so the larger the sample size the select the standard deviation of this frequency curve, and hence the better the estimates.

Explanation:

Step1: Recall Central Limit Theorem

The Central Limit Theorem states that the standard - deviation of the sampling distribution of the sample mean ($\sigma_{\bar{x}}$) is given by the formula $\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}$, where $\sigma$ is the population standard - deviation and $n$ is the sample size.

Step2: Analyze the relationship with sample size

From the formula $\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}$, we can see that as the sample size $n$ increases, the value of $\sigma_{\bar{x}}$ decreases.

Answer:

The Central Limit Theorem says that the standard deviation of the frequency curve for the samples will be the population standard - deviation divided by the square root of the sample size. So the larger the sample size, the smaller the standard deviation of this frequency curve, and hence the better the estimates.