To study the effectiveness of a weight-loss training method, a random sample of 40 females went through the training. After a 2-month period of training, change of the weight is recorded for each participant. The researcher wants to test that the mean weight reduction is larger than 5 pounds at level a = 0.05. (a) The researcher knows that the population standard deviation is approximately 7 pounds. What is the required sample size to detect the power (1-P) of 80% when the true weight reduction is 8 pounds? Is the sample size of 40 enough? (b) The average weight loss for the 40 women in the sample was 7.2 pounds with the sample standard deviation of 4.5 pounds. Is there sufficient evidence that the training is effective? Test using a = 0.05. (c) Find the power of the test conducted in part (b) if the true mean weight reduction is 8 pounds.