. A new diet is claimed to increase the speed of weight loss. A study with a large number
of volunteers showed a mean weight loss of 3.5 pounds in a week. A random sample of 8
volunteers followed the diet and recorded their weight loss at the end of the week. The
results recorded showed a mean of 3.4 pounds and a standard deviation of 0.2.
Using a valid distribution, test at the 5 % level whether the new diet is overstating the
mean weight loss.
Z = (mean1 - mean2)/standard error (SE) of difference between means
SEdiff = √(SEmean1^2 + SEmean2^2)
SEm = SD/√n
If only one SD is provided, you can use just that to determine SEdiff.
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to the Z score.