Since previous studies have reported that elite athletes are often deficient in
ID: 3043201 • Letter: S
Question
Since previous studies have reported that elite athletes are often deficient in their nutritional intake (for example, total calories, carbohydrates, protein), a group of researchers decided to evaluate Canadian high-performance athletes. A total of n = 324 athletes from eight Canadian sports centers participated in the study. One reported finding was that the average caloric intake among the n = 206 women was 2,403.7 kilocalories per day (kcal/d). The recommended amount is 2,817.5 kcal/d. Is there evidence that female Canadian athletes are deficient in caloric intake? Is this result significant at the 5% level?
(a) State the appropriate H0 and Ha to test this.
H0: = 2,817.5 kcal/d; Ha: < 2,817.5 kcal/d (THIS IS CORRECT)
H0: = 2,817.5 kcal/d; Ha: 2,817.5 kcal/d
H0: = 2,817.5 kcal/d; Ha: > 2,817.5 kcal/d
H0: > 2,817.5 kcal/d; Ha: = 2,817.5 kcal/d
H0: < 2,817.5 kcal/d; Ha: = 2,817.5 kcal/d
(b) Assuming a standard deviation of 890 kcal/d, carry out the test. (Round your value for z to two decimal places and round your P-value to four decimal places.)
z =
P-value =
Explanation / Answer
The statistical software output for this problem is:
One sample Z summary hypothesis test:
: Mean of population
H0 : = 2817.5
HA : < 2817.5
Standard deviation = 890
Hypothesis test results:
Hence,
b) z = - 6.67
P - value = 0
Mean n Sample Mean Std. Err. Z-Stat P-value 206 2403.7 62.009238 -6.6731992 <0.0001