Since previous studies have reported that elite athletes are often deficient in
ID: 3153265 • 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. What hypotheses make sense to test in this case? Explain how you know. Derive the likelihood ratio test (LRT) for testing the hypotheses you provided in (a). Find an exact critical value assuming a significance level of alpha = 0.01. From these n = 114 male athletes, the average caloric intake was 3077.0 kcal/day with a standard deviation of 987.0. Carry out the test and state your conclusion.Explanation / Answer
Answer to the question)
Answer to part a)
The claim is that the calorie intake is less
Thus the hypothesis would be:
Null hypothesis: Mean intake is 3421.7
Ho: M = 3421.7
Alternate hypothesis: Mean intake is less than 3421.7
Ha: M < 3421.7
[it is left tailed test]
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Answer to part b)
Since the sampel size is 114
The test to be used is Z test
The significance level is 0.05 , and the test is left tailed because the claim is that they get less calories hence the claim is directional.
One tailed Z critical value for significance level 0.05 is -1.645
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Answer to part c)
Given:
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The formula of test statistic is:
Z = (x bar - M ) / (s/sqrt(n))
Z = (3077 - 3421.7) / (987/sqrt(114))
Z = -3.73
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P value = 0.000
[this Z value is very low and it is not avaliable in Z table , we cna still find the exact P value , with the help of excel command =NORMSDIST(-3.73)
We get P value = 0.000096
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Inference: Since this P value is leas than the significance level 0.05 , we reject the null hypothesis
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Conclusion: Since we reject the null hypothesis we conclude that there is significant evidence that the mean intake of calroies is less than 3421.7kcal