Since previous studies have reported that elite athletes are often deficient in
ID: 3154934 • Letter: S
Question
Since previous studies have reported that elite athletes are often deficient in their nutritional intake (e.g., total calories, carbohydrates, protein), a group of researchers decided to evaluate Canadian high performance athletes (Lun et al., 2009). A total of n = 114 male athletes from eight Canadian sports centers participated in the study. The recommended caloric intake is 3421.7 kcal/day for such athletes. The researchers are interested in whether there is evidence that Canadian high performance male athletes are deficient in their caloric intake. Assume that caloric intake follows a normal distribution. As a reminder, from these n = 114 male athletes, the average caloric intake was 3077.0 kcal/day with a standard deviation of 987.0. Last week, you derived (and carried out) the likelihood ratio test. Now, calculate the p-value for this test.Explanation / Answer
THE N = 114
THEREFORE WE CAN USE THE Z TABLE AS THE N IS LARGE ENOUGH
THE NULL HYPOTHESIS = H0=U = 3421.7
THE ALTERNATE HYPOTHESIS = Ha= u<3421.7
AS THE ALPHA = 0.05
THE CRITICAL REGION = Z<-1.96
TEST STATIC = (3077 - 3421.7)/(987/SQRT(114)
= -3.72
AS THE Z = -3.72< -1.96 THEREFORE WE WILL REJECT THE NULL HYPOTHESIS
THE P VALUE FOR -3.72 = 0.0001