To determine if chocolate milk was as effective as other carbohydrate replacemen
ID: 3327197 • Letter: T
Question
To determine if chocolate milk was as effective as other carbohydrate replacement drinks, nine male cyclists performed an intense workout followed by a drink and a rest period. At the end of the rest period, each cyclist performed an endurance trial where he exercised until exhausted and time to exhaustion was measured. Each cyclist completed the entire regimen on two different days. On one day the drink provided was chocolate milk and on the other day the drink provided was a carbohydrate replacement drink. Data consistent with summary quantities appear in the table below. (Use a statistical computer package to calculate the P-value. Subtract the carbohydrate replacement times from the chocolate milk times. Round your test statistic to two decimal places, your df down to the nearest whole number, and your P-value to three decimal places.)
Cyclist Time to Exhaustion (minutes) 1 2 3 4 5 6 7 8 9 ChocolateMilk 33.30 54.81 58.81 29.64 46.98 43.93 48.66 29.34 48.70 Carbohydrate
Replacement 5.32 14.90 34.01 39.75 9.40 43.47 27.72 11.66 47.88
Explanation / Answer
t=3.07 df=8 p=0.007
Detailed Solution:
n=9
df = n-1
s² = (x-x )² /(n-1)
Because it is a paired test, so we should take the differences.
Cyclist
Time to Exhaustion (minutes)
1
2
3
4
5
6
7
8
9
Chocolate
Milk
33.30
54.81
58.81
29.64
46.98
43.93
48.66
29.34
48.70
Carbohydrate
Replacement
5.32
14.90
34.01
39.75
9.40
43.47
27.72
11.66
47.88
Difference
27.98
39.91
24.8
-10.11
37.58
0.46
20.94
17.68
0.82
The mean of Differences x :
(27.98+39.91+24.8+…..+0.82)/9 = 17.78
The sample variance is s²
= [ (27.98-17.78)^2 + (39.91-17.78)^2 +………+ (0.82-17.78)^2 ]
= 301.32 and hence s is 17.35
t = (mean - 0)/(s/sqrt(n)) = 17.78/(17.35/3)= 3.07
df = n-1 = 8
P- value (using t with df = 8) is = 0.007
Cyclist
Time to Exhaustion (minutes)
1
2
3
4
5
6
7
8
9
Chocolate
Milk
33.30
54.81
58.81
29.64
46.98
43.93
48.66
29.34
48.70
Carbohydrate
Replacement
5.32
14.90
34.01
39.75
9.40
43.47
27.72
11.66
47.88
Difference
27.98
39.91
24.8
-10.11
37.58
0.46
20.94
17.68
0.82
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