# A population distribution has a normal shape, with mean μ = 100 and standard deviation σ = 4. Consider two sampling distributions from this population distribution. Sampling distribution #1 is created from the sample means from all possible random samples of size N = 16; sampling distribution #2 is created from the sample means from all possible random samples of size 256. How do the standard deviations compare? The standard deviation of sampling distribution #1 is _____ the standard deviation of sampling distribution #2.

Question

### A population distribution has a normal shape, with mean μ = 100 and standard deviation σ = 4. Consider two sampling distributions from this population distribution. Sampling distribution #1 is created from the sample means from all possible random samples of size N = 16; sampling distribution #2 is created from the sample means from all possible random samples of size 256. How do the standard deviations compare? The standard deviation of sampling distribution #1 is _____ the standard deviation of sampling distribution #2.

Step 1

Sampling distribution of sample mean:

If a random sample of size n is taken from a population with mean µ and standard deviation σ, then mean of all sample means is the population mean µ and standard deviation of all sample means is σ/sqrt (n).

Step 2

Comparing the standard deviations:

The population distribution has a normal shape with mean 100 (µ ) and standard deviation 4(σ). First sampling distribution considers all sample means from all possible sample of size 16(...

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