Question

Suppose that a group of researchers is planning to test a new weight loss supplement. They have selected a random sample of 30 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, σ, is 1.1 lb.

To show that the supplement is effective, they plan to use a one-sample z‑test of H0:μ=0 lb against H1:μ>0 lb, where μ 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 0.7458 if the mean amount of weight lost is actually 0.6 lb.

What is the probability that the researchers will reject their null hypothesis if the mean amount of weight lost is 0.6 lb or more? Give your answer as a percentage, precise to two decimal places.

Answer 1

Answer:

Ho : μ = 0

H1 : μ > 0

Power the test is the likelihood of dismissing the bogus invalid theory i.e., Ho.

Here we have to discover the likelihood that the specialists will dismiss the invalid theory if the mean measure of weight lost is 0.6 lb or more, that is we have to discover the likelihood of dismissing the bogus invalid speculation.

That is we have to discover the intensity of the test. It is given that intensity of the test is 0.7458.

So required likelihood is 74.58%.