122,000 seemed absurdly large to me so I just looked up the paper you reference [1]. It looks like there is a calculation error in the paper.
The formula they use is n = 16 σ^2 / Δ^2. σ is the standard deviation, and Δ is the size of the difference. Thus in this problem, Δ = 0.05 and their formula gives n = 16 * (0.05 * (1-0.05)) / 0.05^2 = 304. This is much more in line with what you get from using a 2 sample proportion test (with H_a: p_1 =/= p_2), ~440 in each group [2].
The formula they use is n = 16 σ^2 / Δ^2. σ is the standard deviation, and Δ is the size of the difference. Thus in this problem, Δ = 0.05 and their formula gives n = 16 * (0.05 * (1-0.05)) / 0.05^2 = 304. This is much more in line with what you get from using a 2 sample proportion test (with H_a: p_1 =/= p_2), ~440 in each group [2].
But maybe I misunderstand their formula.
[1] http://exp-platform.com/hippo_long.aspx
[2] http://statpages.org/proppowr.html
edit: fixed Greek letters and added final comment.