12. For each of the following scenarios: (1) State the appropriate critical Z-value you would use to compute the critical sample proportion value P * in Step 1 of the power calculation, (2) State the appropriate Pa value for the "minimum important difference" you would use to compute the probability P [P P * if P = Pa] in Step 2 of the power calculations. a. The investigator wants to determine if a new treatment for cancer reduces the proportion of patients who die within 5 years of diagnosis from the current level of P = 0.7. She would consider a 20% relative decrease in 5-yr mortality rate to be the minimum effect size required for her to implement the new treatment. She is willing to accept a Type I error rate of a = 0.05, using a one-tailed test of significance because she is only interested in whether or not the treatment reduces 5-yr mortality rate. Critical Z-value = Pa = b. Consider the same scenario as in part (a), but now the investigator would consider a 10% relative decrease in 5-yr mortality rate to be the minimum important effect size. Critical Z-value = Pa = c. Consider the same scenario as in part (a), but now the investigator decides she should use a two-tailed test of significance. Critical Z-value = Pa = d. Consider the same scenario as in part (a), but now the investigator is willing to accept a Type I error rate of only a = 0.01. Critical Z-value = Pa e. Consider the same scenario as in part (a), but now the researcher frames the question in terms of survival rate rather than mortality rate. That is, she wants to determine if the new treatment results in a 20% increase (above the current level of P - 0.3) in the proportion of patients who survive for at least 5 years after diagnosis of their cancer. Critical Z-value =