Answer to Question #115878 in Statistics and Probability for Shane Jessica Ballera

Question

Hypothesis Testing

A medical doctor suspects that the patient is suffering from Cushing‟s Syndrome which is indicated by a cortisol level higher than 100 micrograms per 24 hours (mcg/24h) Thus, he ordered urine cortisol test in six different days which resulted to a mean of 120mcg/24h and a sd of 15mcg/24h. Does the result support the doctor‟s hypothesis at α0.01? Use traditional and p-value method.

Answer 1

H0: μ =100

H1: μ >100

α=0.01

t=(x -μ)/(s/√n)→(120-100)/(15/√6)=3.26

From t table, a t of 3.26 correspond to a p -value to the right of 0.0112

Therefore, since p > .0112, there is no evidence to suggest that the mean is higher. As such, the test does not support the doctor’s claim.