Investigate the fluid mechanics of swimming

Question

To investigate the fluid mechanics of swimming, twenty swimmers each swam a specified distance in a water-filled pool and in a pool where the water was thickened with food grade guar gum to create a syrup-like consistency. Velocity, in meters per second, was recorded and the results are given in a table below. The researchers concluded that swimming in guar syrup does not change swimming speed. (Use a statistical computer package to calculate P.)

Swimmer	Velocity (m/s)
	Water	Guar Syrup
1	1.48	1.83
2	1.90	1.20
3	1.60	1.81
4	1.05	1.41
5	0.94	1.97
6	1.01	0.92
7	1.93	1.92
8	1.47	1.72
9	1.94	1.91
10	1.67	1.76
11	1.86	1.11
12	1.34	0.93
13	1.41	1.71
14	1.98	1.16
15	1.47	1.67
16	1.44	0.99
17	1.15	1.92
18	1.72	1.79
19	0.90	1.46
20	1.66	1.82

t	=		(Round the answer to two decimal places.)
df	=
P	=		(Round the answer to three decimal places.)

Is there sufficient evidence to suggest that there is any difference in swimming time between swimming in guar syrup and swimming in water? Carry out a hypothesis test using ? = .01 significance level.