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 the P-value to three decimal places.)

Cyclist	Time to Exhaustion (minutes)
	1	2	3	4	5	6	7	8	9
Chocolate Milk	40.06	47.69	34.79	57.60	45.80	59.65	55.00	25.02	30.30
Carbohydrate Replacement	50.69	14.98	10.24	29.96	10.95	19.82	24.73	13.81	32.14

t	=
df	=
P	=

Answer 1

S. No	Chocolate	Carbohydrate	diff:(d)=x1-x2	d2
1	40.06	50.69	-10.63	113.00
2	47.69	14.98	32.71	1069.94
3	34.79	10.24	24.55	602.70
4	57.6	29.96	27.64	763.97
5	45.8	10.95	34.85	1214.52
6	59.65	19.82	39.83	1586.43
7	55	24.73	30.27	916.27
8	25.02	13.81	11.21	125.66
9	30.3	32.14	-1.84	3.39
	total	=	Σd=188.59	Σd2=6395.8871
	mean dbar=	d̅     =	20.9544
	degree of freedom =n-1                            =		8
	Std deviaiton SD=√(Σd2-(Σd)2/n)/(n-1) =		17.478874
	std error=Se=SD/√n=		5.8263
	test statistic            =	(d̅-μd)/Se         =	3.597
	p value	=	0.00702	from excel: tdist(3.597,8,2)

from above"

t	= 3.60
df	= 8
P	= 0.007