The R function size2z.test () shown below implements the sample size formula for calculating the sample size for a test of $H_{0}: \theta=0$ versus $H_{1}: \theta eq 0$, where $\theta=\mu_{1}-\mu_{2}$.

a. What are the main assumptions behind this sample size formula?

b. Assuming all other parameters remain fixed, indicate whether the sample size increases or decreases in each of the following cases.i. As $\sigma$ decreases.

ii. As $\alpha$ decreases.

iii. As $\theta$ decreases.

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size2z.test