10. n = 114 male athletes from eight Canadian sports centers were surveyed and t
ID: 2936879 • Letter: 1
Question
10. n = 114 male athletes from eight Canadian sports centers were surveyed and their average caloric intake was 3077.0 kilocalories per day (kcal/d) with a standard deviation of 987.0 kcal/d. The recommended amount is 3421.7 kcal/d. Is there evidence that Canadian high-performance male athletes are deficient in their caloric intake?
(a) State the appropriate H0 and Ha to test this.
(b) Carry out the test, give the P-value, and state your conclusion.
(c) Construct a 95% confidence interval for the average deficiency in caloric intake.
Explanation / Answer
(a) Ho: 3421.7 and Ha: < 3421.7
(b)
Data:
n = 114
= 3421.7
s = 987
x-bar = 3077
Hypotheses:
Ho: 3421.7
Ha: < 3421.7
Decision Rule:
= 0.05
Degrees of freedom = 114 - 1 = 113
Critical t- score = -1.658450217
Reject Ho if t < -1.658450217
Test Statistic:
SE = s/n = 987/114 = 92.4410196
t = (x-bar - )/SE = (3077 - 3421.7)/92.4410196031132 = -3.728864107
p- value = 0.000151164
Decision (in terms of the hypotheses):
Since -3.728864107 < -1.658450217 we reject Ho and accept Ha
Conclusion (in terms of the problem):
There is sufficient evidence that the Canadian high-performance male athletes are deficient in their caloric intake
(c)
n = 114
x-bar = 3077
s = 987
% = 95
Standard Error, SE = s/n = 987/114 = 92.4410196
Degrees of freedom = n - 1 = 114 -1 = 113
t- score = 1.981180296
Width of the confidence interval = t * SE = 1.9811802961545 * 92.4410196031132 = 183.1423266
Lower Limit of the confidence interval = x-bar - width = 3077 - 183.14232659412 = 2893.857673
Upper Limit of the confidence interval = x-bar + width = 3077 + 183.14232659412 = 3260.142327
The 95% confidence interval is [2893.86, 3260.14]
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