Answer to Question #204785 in Statistics and Probability for piewalt

Question

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?

Answer 1

$H0:\mu=40$

$Ha:\mu\ne40$

$z=\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n}}}$

$z=\frac{35-40}{\frac{5}{\sqrt{70}}}=-8.366600265$

Assume 95% level of confidence

$CV=Z_(0.025)=\pm1.96$

since -8.3667 is less than -1.96, we reject the null hypothesis and conclude that there is not enough evidence to support the claim that overweigh patients lose 40 pounds