a simple random sample of 64 observations was taken from a population of size 500. the population standard deviation is 16. what is the standard deviation of sample mean?

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09-12-2022
Mathematics

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a simple random sample of 64 observations was taken from a population of size 500. the population standard deviation is 16. what is the standard deviation of sample mean?

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abhinavjh321 abhinavjh321 · Answer 1 · 2022-12-17T04:39:25-05:00

64 observations were randomly selected at random from a population of 500. the population standard deviation is 16.The standard deviation of the sample mean is 4 (16/√64).

The standard deviation of the sample mean is calculated by dividing the population standard deviation (16) by the square root of the sample size (64).

Consequently, the sample mean's standard deviation is

16/√64 = 4.

This means that the expected spread of the sample means is 4, which is less than the population standard deviation of 16. This is because the sample is smaller than the population, so the sample standard deviation will be smaller than the population standard deviation.

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