Consider the derivation of Equation (4.5) for the sample size of a two-sample z-test with known variance

Question:

Consider the derivation of Equation (4.5) for the sample size of a two-sample z-test with known variance and equal allocation.

a. Identify terms in Equation (4.2) that are smaller than $\alpha / 2$ and derive line (4.3) based on the information.

b. Show how Equation (4.4) is derived from Equation (4.3).

Data from Equation 4.2

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Data from Equation 4.3

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Data from Equation 4.4

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Data from Equation 4.5

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