In determining the sample size you need for a study to test the null hypothesis

Question

In determining the sample size you need for a study to test the null hypothesis that the population mean change is 0 versus the alternative hypothesis that it equals some constant, which of the following change will require increasing the sample size to achieve certain power at a fixed significance level, for rejecting the null hypothesis? (4 points)

1) The power (with which you wish to detect the difference) decreases.

2) The population variance increases.

3) The constant of the alternative hypothesis gets larger.

4) Both a & b.

5) All a & b & c.

Explanation / Answer

Standard deviations of averages are smaller than standard deviations of individual observations. [Here I will assume independent identically distributed observations with finite populationvariance; something similar can be said if you relax the first two conditions

These are correct

1) The power (with which you wish to detect the difference) decreases.

2) The population variance increases.

So,

4) Both a & b.

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