1. Derive (showing all steps) a sample size formula for detecting a difference of at least A between two independent population proportions ("1-2A) with power (1B) at level of significance of . 2. A pharmaceutical company will be running a parallel arm study comparing Ne w intervention against Standard Care. The response variable is a continuous measurement. On the Standard Care the standard deviation for the response v ariable is c. a. Assuming that the standard deviation is the same for the New Drug, derive a s ample size formula for the total number of patients needed to obtain (1 - )1 00% power to detect a difference of A when testing a one-sided alternative hyp othesis at level . b. Use your answer to part (a) to calculate the total sample size needed for 90% p ower to detect an increase of 6 units in the average of the new drug compared to the standard drug using =5% level of significance. Assume = 18. c. Develop a power curve graph using SAS or R for detecting an increase of 6, wit h sample size on the horizontal axis and power on the vertical axis, starting at = 0.05. Assume = 18 for both treatments. d. Repeat parts a-c, but increase the standard deviation for the new drug to be 1 5% above the standard deviation for the standard drug.