A scientist for a company that manufactures processed food wants to assess the percentage of fat in the company's bottled sauce. The advertised percentage is 15%. The scientist measures the percentage of fat in 20 random samples. Previous measurements found that the population standard deviation is 2.6%.

Before collecting the data for a 1-sample Z-test, the scientist uses a power and sample size calculation to determine the sample size required to obtain a power of 0.9 and to detect a difference of 1.5% or greater.

- Choose .
- In Differences, enter
`1.5`. - In Power
values, enter
`0.9`. - In Standard
deviation, enter
`2.6`. - Click OK.

To detect a difference of 1.5% with a power of 0.9, the scientist needs to collect a sample size of 32. The scientist determines that a sample size of 32 is reasonable, and proceeds with data collection.

1-Sample Z Test

Testing mean = null (versus ≠ null)

Calculating power for mean = null + difference

α = 0.05 Assumed standard deviation = 2.6

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

1.5 | 32 | 0.9 | 0.903816 |