Decreasing the sample size from 750 to 375 would multiply the standard deviation by

Decreasing the sample size from 750 to 375 would multiply the standard deviation by;

A multiplicative factor of √2

       In statistics, when writing the formula for standard deviation with a sample size N is given as;

σ ∝ 1/√N

This means that the standard deviation is directly proportional to the inverse of the square root of the sample size.

        Now, we are told that the sample size is decreased from 750 to 375. This means N is divided by 2. Thus;

Sample size is now N/2

Thus;

σ ∝ 1/√(N/2)

⇒ σ ∝ √2/√N

We can see that the standard deviation will increase by a multiplicative factor of √2

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