A clinic advertises that overweight patients can lose 40 pounds on average in a month if they follow the clinic’s diet and exercise program. Assume that the standard deviation for the amount patients...

A clinic advertises that overweight patients can lose 40 pounds on average in a month if they follow
the clinic’s diet and exercise program. Assume that the standard deviation for the amount patients
lose is 5 pounds. Officials from health ministry suspect that the clinic is using false advertisement
and want to investigate the clinic’s claim. They randomly sample 70 patients and find the sample
mean is 35 pounds. What can you infer from this finding?
(Hint: Use the sampling distribution of the sample mean under the clinic’s claim and see if it is
realistic to obtain the sample with mean 35 pounds in that case.)