Explain Why Decreases as the Size of the Samples

Question

Explain Why  Decreases as the Size of the Samples

Examlex · Accepted Answer

The Answer is $decreases when the sample size increases first because the formula for is to divide \sigma by the square root of N. Thus, as N increases, we are dividing by a larger number, resulting in a smaller number. This makes sense because as sample size increases, the mean of each sample should be closer to \mu (we are including more of the population in the samples, and thus the sample means would be more similar to \mu ), and thus the standard deviation (or the standard error of the mean) would be smaller because the sample means on which it is calculated would be closer to \mu , resulting in less variability.$ decreases when the sample size increases first because the formula for $decreases when the sample size increases first because the formula for is to divide \sigma by the square root of N. Thus, as N increases, we are dividing by a larger number, resulting in a smaller number. This makes sense because as sample size increases, the mean of each sample should be closer to \mu (we are including more of the population in the samples, and thus the sample means would be more similar to \mu ), and thus the standard deviation (or the standard error of the mean) would be smaller because the sample means on which it is calculated would be closer to \mu , resulting in less variability.$ is to divide

\sigma

by the square root of N. Thus, as N increases, we are dividing by a larger number, resulting in a smaller number. This makes sense because as sample size increases, the mean of each sample should be closer to

\mu

(we are including more of the population in the samples, and thus the sample means would be more similar to

\mu

), and thus the standard deviation (or the standard error of the mean) would be smaller because the sample means on which it is calculated would be closer to

\mu

, resulting in less variability.

Explain Why Decreases as the Size of the Samples

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Explain Why Decreases as the Size of the Samples

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