The difference of the means of two normal distributions

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QUESTION:

The difference of the means of two normal distributions with equal variance is to be estimated by sampling an equal number of observations from each distribution. If it were possible, would it be better to halve the standard deviations of the populations or double the sample sizes?

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QUESTION:

The difference of the means of two normal distributions with equal variance is to be estimated by sampling an equal number of observations from each distribution. If it were possible, would it be better to halve the standard deviations of the populations or double the sample sizes?

ANSWER:

Step 1 of 2

We know that the sample values will be near to the mean than the sample which is selected from the raw population if the standard deviation is decreased to the halving of the population standard deviation.

Therefore, a biased result will be observed because of not selecting the sample values which are away from the mean.

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