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 mu_water - mu_guar syrup. Round your test statistic to two decimal places and your P-value to three decimal places.)

Explanation / Answer

In this case, the same 20 swimmers velocity has been captured in guar syrup and water so we will use paired t - test here.

The statistical software output for this problem is:

Paired T hypothesis test:
D = 1 - 2 : Mean of the difference between Water and Guar Syrup
H0 : D = 0
HA : D 0
Hypothesis test results:

So,

t = -1.21

df = 19

p - value = 0.239

Difference Mean Std. Err. DF T-Stat P-value Water - Guar Syrup -0.139 0.1144527 19 -1.2144755 0.2394

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