To investigate the fluid mechanics of swimming, twenty swimmers each swam a spec

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

t=

df=

p=

Swimmer Velocity (m/s) Water Guar Syrup 1 1.51 1.83 2 1.22 1.71 3 1.40 1.64 4 0.90 0.95 5 1.62 1.98 6 1.03 1.25 7 1.19 1.92 8 1.31 1.24 9 1.33 1.15 10 1.68 1.00 11 1.98 1.64 12 1.30 1.39 13 1.90 1.25 14 1.81 1.31 15 1.87 1.84 16 1.56 1.73 17 1.88 0.96 18 1.58 1.26 19 1.33 0.98 20 1.08 1.03

Explanation / Answer

The statistical software output for this problem is:

Two sample T hypothesis test:
?1 : Mean of Water
?2 : Mean of Gaur Syrup
?1 - ?2 : Difference between two means
H0 : ?1 - ?2 = 0
HA : ?1 - ?2 ? 0
(with pooled variances)

Hypothesis test results:

Hence,

t = 0.67

Df = 38

P - value = 0.505

Difference Sample Diff. Std. Err. DF T-Stat P-value ?1 - ?2 0.071 0.10541272 38 0.67354299 0.5047

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