Question

The company SlimDown makes weight loss products. It has recently come out with a new skin cream that, when rubbed behind the ears, is thought to cause the user to lose weight. To test the cream, a random sample of 51 people was chosen, and the percentage weight loss over an eight week period recorded. Find the power of the test to determine if the the new cream is effective, when the mean percent weight reduction is actually 0.7%. Assume that the population standard deviation is 11% and that the significance level is =0.02.

Power =

Answer 1

We first find the bound for mean when we reject the null hypothesis here. For 0.02 level of significance, we get from the standard normal tables that:

P( Z > 2.054) = 0.02

Therefore the bound here is computed as:

The power is not computed here as:

Probability that the null hypothesis is rejected given that the true mean percent weight reduction is 0.7%

Getting it from the standard normal tables, we get here:

Therefore 5.48% is the required power of the test here.