H0: σ = σ0, where σ0 is the hypothesized standard deviation. The true standard deviation is σ0 plus the difference to detect.
In this example the hypothesized standard deviation, σ0, is 10 (the square root of 100) and σ is 12.4499 (the square root of 100 + 55 = 155). The difference to detect is 12.4499 – 10 = 2.4499.
1.

Select DOE > Design Diagnostics > Sample Size and Power.

2.

Click the One Sample Standard Deviation button in the Sample Size and Power Window.

3.

Leave Alpha as 0.05.

4.

Enter 10 for Hypothesized Standard Deviation.

5.

Select Larger for Alternate Standard Deviation.

6.

Enter 2.4499 as Difference to Detect.

7.

Enter 0.99 for Power.

8.

Leave Sample Size blank. (See the left of Window To Compare SingleDirection OneSample Standard Deviation.)

9.

Click Continue.

The Sample Size is calculated as 171. (See the right of Window To Compare SingleDirection OneSample Standard Deviation.) This result is the sample size rounded up to the next whole number.
Note: Sometimes you want to detect a change to a smaller standard deviation. If you select Smaller from the Alternative Standard Deviation menu, enter a negative amount in the Difference to Detect field.