Question 1 Since previous studies have reported that elite athletes are often de
ID: 3135023 • Letter: Q
Question
Question 1 Since previous studies have reported that elite athletes are often deficient in their nutritional intake, 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 kcal/day. The recommended amount is 2811.5 kcal/day. Is there evidence that female Canadian high performance athletes are deficient in caloric intake? (a) State the appropriate Ho and HA to test this. (b) Assuming a standard deviation of 880 kcal/day, carry out the test at the a 0.05 level. Give the P-value and then interpret the result in plain language. Now suppose a nutritionist is brought in to implement a new health program for the female athletes. This program should increase mean caloric intake but not change the standard deviation. Given the standard deviation, and how calorically deficient these athletes are, a change in the mean of 50 kcal/day to 2453.7 is of little practical importance. However, with a large enough sample, this change can be statistically significant. To see this calculate the P-value for the test of Ho Au 2403.7 versus H Au 2403.7. in each of the following situations A (c) In a sample of 500 athletes, the average caloric intake is 2453.7. (d) In a sample of 2500 athletes, the average caloric intake is 2453.7.Explanation / Answer
a)
Formulating the null and alternative hypotheses,
Ho: u >= 2811.5
Ha: u < 2811.5 [ANSWER]
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b)
As we can see, this is a left tailed test.
Getting the test statistic, as
X = sample mean = 2403.7
uo = hypothesized mean = 2811.5
n = sample size = 201
s = standard deviation = 880
Thus, z = (X - uo) * sqrt(n) / s = -6.569957769
Also, the p value is
p = 2.51648E-11 [ANSWER, p value]
As P < 0.05, we reject Ho.
There is significant evidence that the female Canadian high performance athletes are deficient in caloric intake. [CONCLUSION]
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C)
Formulating the null and alternative hypotheses,
Ho: u <= 2403.7
Ha: u > 2403.7
As we can see, this is a right tailed test.
Getting the test statistic, as
X = sample mean = 2453.7
uo = hypothesized mean = 2403.7
n = sample size = 500
s = standard deviation = 880
Thus, z = (X - uo) * sqrt(n) / s = 1.270493169
Also, the p value is
p = 0.101954507 [ANSWER]
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d)
Formulating the null and alternative hypotheses,
Ho: u <= 2403.7
Ha: u > 2403.7
As we can see, this is a right tailed test.
Getting the test statistic, as
X = sample mean = 2453.7
uo = hypothesized mean = 2403.7
n = sample size = 2500
s = standard deviation = 880
Thus, z = (X - uo) * sqrt(n) / s = 2.840909091
Also, the p value is
p = 0.002249257 [ANSWER]
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