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 the P-value to three decimal places.)

Explanation / Answer

Ho: No Change in the swimming speed

H1: Change in the swimming spped.

Paired T-Test and CI: Water, Guar_Syrup

Paired T for Water - Guar_Syrup

N Mean StDev SE Mean
Water 20 1.3140 0.3115 0.0696
Guar_Syrup 20 1.4640 0.2782 0.0622
Difference 20 -0.1500 0.2916 0.0652

95% CI for mean difference: (-0.2865, -0.0135)
T-Test of mean difference = 0 (vs not = 0): T-Value = -2.30 P-Value = 0.033

Conclusion: The estimated p-value is 0.033 and less than 0.05 level of significance. hence, we can accept the null hypothesis and conclude that there is change of swimming speed due to Guar Syrup at 0.05 level of significance.

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