Increasing the sample size increases the power of your test. You want enough observations in your sample to achieve adequate power, but not so many that you waste time and money on unnecessary sampling.

If you provide the power that you want the test to have and the difference you want it to be able to detect, Minitab will calculate how large your sample must be. (Since sample sizes are given in integer values, the actual power may be slightly greater than your target value.)

For the energy data, the researcher wants to determine if the true energy expenditure of upper-income households is $100 greater than or less than the published value of $1080. How many households does he need to sample in order to achieve a power of 0.80, 0.85, 0.90, or 0.95 for this test?

The results indicate that:

·      in order to achieve a power of at least 0.80, he needs to sample 29 households, which gives him a power of 0.810708.

·      with 33 observations the power is 0.860742.

·      with 38 observations the power is 0.906570.

·      with 46 observations the power is 0.952146.

If the researcher can afford to sample 46 households, there is a very good chance (95.2146%) that the test will be able to detect the effect of interest.