To determine if chocolate milk was as effective as other carbohydrate replacemen

Question

To determine if chocolate milk was as effective as other carbohydrate replacement drieks, cyclists performed an intense workout foilowed by a drünk and a rest periad. At the end of the rest each cyclist perfarmed an endurance trial where he exarcised until exhausted and time to exhauso measured. Each cyclist completed the entire regimen on two deerent days was chacolate milk and on the other day the drink provided was a carbonydr ne day the drink prowidea nt with summary y quantities appear in the table below. (Use a statistical computer package to ent drink. Data calculate the P-val he carbohydrate replacement your test statistic to two decimal places, your df down to the nearest whole number, and the P-vaiue to three decimal places.) times from the chocolate Time to Exhaustion (minutes) Cyclist Chocolate Milk 58.24 28.12 55.54 43.07 48.86 22.04 59.13 22.57 36.38 Carbohydrate Replacement 33.60 22.84 53.48 37.68 28.02 12.39 23.41 18.27 33.99 Is there sufficient evidence to suggest that the mean time to exhaustion is greater after chocalate milk than after carbohydrate replacement drink? Use a significance level of 0.05 No

Explanation / Answer

Given that,
null, H0: Ud = 0
alternate, H1: Ud > 0
level of significance, = 0.05
from standard normal table,right tailed t /2 =1.86
since our test is right-tailed
reject Ho, if to > 1.86
we use Test Statistic  
to= d/ (S/n)
where
value of S^2 = [ di^2 – ( di )^2 / n ] / ( n-1 ) )
d = ( Xi-Yi)/n) = 12.25
We have d = 12.25
pooled variance = calculate value of Sd= S^2 = sqrt [ 2495.85-(110.27^2/9 ] / 8 = 11.96
to = d/ (S/n) = 3.07
critical Value
the value of |t | with n-1 = 8 d.f is 1.86
we got |t o| = 3.07 & |t | =1.86
make Decision
hence Value of | to | > | t | and here we reject Ho
p-value :right tail - Ha : ( p > 3.0721 ) = 0.00765
hence value of p0.05 > 0.00765,here we reject Ho
ANSWERS
---------------
null, H0: Ud =0
alternate, H1: Ud > 0
test statistic: 3.07
critical value: reject Ho, if to > 1.86
decision: Reject Ho
p-value: 0.00765

Yes, it is sufficient evidence to suggest that the mean time to exhaustion is greater after chocolate milk than after carbhohydrate replacement drink.

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