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Cooling Down. Cooling down with a cold drink before exercise in the heat is believed to help an athlete perform. Researcher 1. Dugas explored the difference between cooling down with an ice slurry (slushy) and with cold water in the article "lce Slurry Ingestion Increases Running Time in the Heat" (Clinical Journal of Sports Medicine, Vol. 21, No, 6, pp. 541-542). Ten male participants drank a flavored ice slurry and ran on a treadmill in a controlled hot and humid environment. Days later, the same participants drank cold water and ran on a treadmill in the same bot and humid environment. The following table shows the times, in minutes, it took to fatigue on the treadmill for both the ice slurry and the cold water.

At the $1\%$significance level, do the data provide sufficient evidence to conclude that, on average, cold water is less effective than ice slurry For optimizing athletic performance in the heat? (Note; The mean and standard deviation of the paired differences are $-5.9$minutes and $1.60$minutes, respectively.)

Step by step solution

01

Given Information

Given table is:

we have to explain Whether the data provide sufficient evidence to conclude that on average cold water is less effective than ice slurry for optimizing athletic performance in heat.

02

Explanation

The null and alternative hypothesis are :

$H_0:{\mathrm{μ}}_d=0$

$H_a:{\mathrm{μ}}_d<0$

the MINITAB output is shown below:

$-11.70,0$are the test statistics and $p$-values.

Because the $p$-value is smaller than the significance level,

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