Example of Power and Sample Size for 1-Sample Z

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.

  1. Choose Stat > Power and Sample Size > 1-Sample Z.
  2. In Differences, enter 1.5.
  3. In Power values, enter 0.9.
  4. In Standard deviation, enter 2.6.
  5. Click OK.

Interpret the results

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.

Power and Sample Size

1-Sample Z Test Testing mean = null (versus ≠ null) Calculating power for mean = null + difference α = 0.05 Assumed standard deviation = 2.6
Results Sample Target Difference Size Power Actual Power 1.5 32 0.9 0.903816
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