The company SlimDown makes weight loss products. It has recently come out with a
ID: 3153660 • Letter: T
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 46 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 1%. Assume that the population standard deviation is 9% and that the significance level is =0.05.
Explanation / Answer
Note that for the critical region in the test,
Upper Bound = X + z(alpha/2) * s / sqrt(n)
where
alpha/2 = (1 - confidence level)/2 = 0.05
X = sample mean = 1
z(alpha/2) = critical z for the confidence interval = 1.644853627
s = sample standard deviation = 9
n = sample size = 46
Thus,
Upper bound = 3.182683927
Hence, we need to have a sample with percent loss mean equal to 3.182683927%.
We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as
x = critical value = 3.182683927
u = mean = 1
n = sample size = 46
s = standard deviation = 9
Thus,
z = (x - u) * sqrt(n) / s = 1.644853627
Thus, using a table/technology, the right tailed area of this is
P(z > 1.644853627 ) = Power = 0.05 [ANSWER]