Suppose that a group of researchers is planning to test a new weight loss supplement.
they have selected a random sample of 40 people who are trying to lose weight and plan to measure the amount of weight lost after one month of using the supplement.

assume that the researchers know from prior experiments that the standard deviation of weight lost in one month. sigma, is 1.1 lb.

to show that the supplement is effective, they plan to use a one-sample z-test of h_0: mu = 0 lb against, h_1: mu > 0 lb, where mu is the mean amount of weight lost in one month.

they have also determined that, for a test with a significance level of 0.01, the power of the test is 0.7083 if the mean amount of weight lost is actually 0.5 lb.

what is the probability that the researchers will reject their null hypothesis if the mean amount of weight lost is 0.5 lb or more?