Question

< Question 2 of 20 > Suppose that a group of researchers is planning to test a new weight loss supplement. They have selected a random sample of 50 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, o, is 1.5 lb To show that the supplement is effective, they plan to use a one-sample z test of Ho: x = 0 lb against H: x > 0 lb, where 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 0.8348 if the mean amount of weight lost is actually 0.7 lb. What is the probability that the researchers will reject their null hypothesis if the mean amount of weight lost is 0.7 lb or more? Give your answer as a percentage, precise to two decimal places,

Answer 1

Power of the test is the probability of rejecting the false null hypothesis.

Here we need to find the probability of rejecting the null hypothesis when actually mean weight loss is 0.7 or more. That is we need to find the probability of rejecting the null hypothesis when actually it is false which is equal to power of the test.

Therefore the required probability is 0.8348.

Answer: 0.8348