A population has a mean of 37 and a standard deviation of 13. A sample of size 5 is taken at random from this population. The standard error of the sample mean equals (up to three decimal places):

Question

BlackTom AI · Accepted Answer

Consider what the standard error of the sample mean represents: it is the standard deviation of the sampling distribution of the sample mean, and for a population with known standard deviation sigma, the standard error is sigma divided by the square root of the sample size n.

Here, sigma = 13 and n = 5. Compute the square root of 5: sqrt(5) ≈ 2.236.

Then SE = sigma / sqrt(n) = 13 / 2.236 ≈ 5.813...

Rounding to three decimal places yields SE ≈ 5.814.

This aligns with the general formula SE(mean) = sigma / sqrt(n), illustrating that increasing n reduces the standard error, while increasing sigma increases it.

Note about the provided data: the answer options list is empty in this item, so there is no alternative choice to compare against. Nevertheless, the calculation above shows the correct numeric value for the standard error given the provided mean, standard deviation, and sample size.

COMM111_S2 Quiz 5: Sampling Distributions

A population has a mean of 37 and a standard deviation of 13. A sample of size 5 is taken at random from this population. The standard error of the sample mean equals (up to three decimal places):

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