14. (15 pts) Nutritional intake in Canadian high performance athletes, Since pre

Question

14. (15 pts) Nutritional intake in Canadian high performance athletes, 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. A total of 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. Assume a standard deviation for all athletes' nutritional intake is 880 kcal/day. Is there evidence that female Canadian athletes are deficient in the caloric intake? 511.5 2311,5 0- a) State clearly your H, and Ha b) State your significance level. c) Calculate the test statistics Z. 2 C.57 d) You should sketch a standard normal curve and mark the Z-score obtained from c) on it. Then find the p-value and shade the appropriate areas under the curve to illustrate your calculation. e First, draw a statistical conclusion. Next, suppose you are explaining your results to someone N sttistics. Could you draw a non-statistical conclusion so that (o)he can understand your conclusion?

Explanation / Answer

Given that,
population mean(u)=2811.5
standard deviation, =880
sample mean, x =2403.7
number (n)=324
null, Ho: =2811.5
alternate, H1: <2811.5
level of significance, = 0.05
from standard normal table,left tailed z /2 =1.645
since our test is left-tailed
reject Ho, if zo < -1.645
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 2403.7-2811.5/(880/sqrt(324)
zo = -8.34
| zo | = 8.34
critical value
the value of |z | at los 5% is 1.645
we got |zo| =8.34 & | z | = 1.645
make decision
hence value of | zo | > | z | and here we reject Ho
p-value : left tail - ha : ( p < -8.34 ) = 0
hence value of p0.05 > 0, here we reject Ho
ANSWERS
---------------
null, Ho: =2811.5
alternate, H1: <2811.5
test statistic: -8.34
critical value: -1.645
decision: reject Ho
p-value: 0
female candian athelets are deficient in the caloric intake

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