Since previous studies have reported that elite athletes are often deficient in
ID: 3071498 • 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 = 201 women
was 2403.7 kilocalories per day (kcal/d). The recommended amount is 2811.5 kcal/d.
For one part of the study,
n = 114 male
athletes from eight Canadian sports centers were surveyed. Their average caloric intake was 3076.0 kilocalories per day (kcal/d) with a standard deviation of 987.0. The recommended amount is 3422.1. Is there evidence that Canadian high-performance male athletes are deficient in their caloric intake?
(a) State the appropriate
H0.
H0: 3422.1
H0: = 3422.1
H0: 3422.1
H0: > 3422.1
H0: 3422.1
State the appropriate
Ha.
Ha: = 3422.1
Ha: > 3422.1
Ha: 3422.1
Ha: 3422.1
Ha: < 3422.1
(b) Carry out the test. (Round your answer for t to three decimal places.)
t =
Give the degrees of freedom.
Give the P-value. (Round your answer to four decimal places.)
State your conclusion.
We do not have sufficient evidence to conclude that Canadian high-performance male athletes are deficient in their calorie intake. We have sufficient evidence to conclude that Canadian high-performance male athletes are deficient in their calorie intake.
(c) Construct a 95% confidence interval for the daily average deficiency in caloric intake. (Round your answers to one decimal place.)
,
kcal/day
Explanation / Answer
a)
H0: mu >= 3422.1
Ha: mu < 3422.1
Test statistic, t = (3076 - 3422.1)/(987/sqrt(114))
t = -3.7440
p-value = 0.0001
df = 114 - 1 = 113
We have sufficient evidence to conclude that Canadian high-performance male athletes are deficient in their calorie intake.
c)
CI for 95%
n = 114
mean = 3076
t-value of 95% CI = 1.9812
std. dev. = 987.0000
SE = std.dev./sqrt(n) = 92.44102
ME = t*SE = 183.14233
Lower Limit = Mean - ME = 2892.85767
Upper Limit = Mean + ME = 3259.14233
95% CI (2892.8577 , 3259.1423 )