Suppose you are testing two treatments for an illness, Treatment A and Treatment B. Assume that your populations for Treatments A and B are both normal, and both have variances 02. Treatment A is a new treatment, and Treatment B is the established treatment, The effects of the two treatments are measured on a numerical scale. You want to show that Treatment A is better than Treatment B. Through long experience, you know that the average result of Treatment B gives a numerical score of 70. Moreover you also know that the standard deviation is approximately 2. You make the null hypothesis that \"A = 80. (a) Suppose you have 1,000 volunteers for Treatment A and 900 for Treatment B. You take a random sample of size n = 100, and you nd that for Treatment A you have if, = 120. What, if anything, can you conclude? (b) What are the probabilities for Type I and Type II errors under the assumption H0 : \"A = 80