Consider the plot of power as a function of the allocation ratio, $r$, for the two-sample z-test shown in Figure 4.4 and the $\mathrm{R}$ code for generating plot.

a. Recall that $\mathrm{n}$ is the total sample size for the function pow_ztest(). What does $\mathrm{n} 2$ represent, and why is it $\mathrm{n} /(\mathrm{r}+1)$ ?

b. Does sample size imbalance between the two groups lead to an increase or decrease in power? Explain.

c. Modify the function pow_ztest() to return the value of $\mathrm{n} 2$ and plot $\mathrm{n} 2$ versus r. Describe the relationship between the two variables.

Data from Figure 4.4

Transcribed Image Text:

Power 0.4- 0 0.6- 0.8- N- Allocation ratio ---- N=25 N = 50