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The standard deviation of a sample is proportional to 1/√N where N is the sample size. In this case we are decreasing N by half, so we can write:

1/√(N/2) = √2 / √N

If we say that our standard deviation is proportional to 1/√N, the difference that occurred from decreasing the sample size by half resulted in an increase in the standard deviation by a factor of √2.

Therefore, the standard deviation is multiplied by √2.

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

Read more at; https://brainly.com/question/14172956

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