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 the P-value. Use ?d = ?water − ?guar syrup. Round your test statistic to two decimal places and your P-value to three decimal places.

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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 the P-value. Use ?d = ?water − ?guar syrup. Round your test statistic to two decimal places and your P-value to three decimal places.)

Swimmer Velocity (m/s)
Water Guar Syrup
1 1.43 1.23
2 1.02 1.96
3 1.37 1.54
4 1.23 1.76
5 1.42 1.07
6 1.09 1.63
7 1.56 1.31
8 1.33 1.58
9 1.96 1.30
10 1.89 1.23
11 1.15 1.15
12 1.11 2.00
13 1.31 1.59
14 1.79 1.23
15 1.12 1.05
16 1.84 1.12
17 1.72 1.42
18 1.99 1.79
19 1.53 1.80
20 0.92 1.69
t
df
P-value


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 ? = 0.01 significance level.

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