An economist wants to determine whether the monthly energy cost for families has changed from the previous year, when the mean cost per month was $200.

Before collecting the data for a 1-sample t-test, the economist uses a power and sample size calculation to determine how large the sample must be to obtain a power of 90% (0.9). Any difference of at least $100 in either direction is considered to be meaningful and the estimated standard deviation is $150.

- Choose .
- In Differences, enter
`100`. - In Power
values, enter
`0.9`. - In Standard
deviation, enter
`150`. - Click OK.

To detect a difference of 100 with a power of 0.9, the economist needs to collect a sample of 26 observations. This is an obtainable sample size, so the economist continues with the data collection and the 1-sample t-test.

1-Sample t Test

Testing mean = null (versus ≠ null)

Calculating power for mean = null + difference

α = 0.05 Assumed standard deviation = 150

Difference | Sample Size | Target Power | Actual Power |
---|---|---|---|

100 | 26 | 0.9 | 0.904254 |