D Without Water With Water Difference 1 29.01 29.31 -.3 2 29.02 28.02 1 3 29.35 29.01 .34 4 30.02 27.98 2.04 5 28.92 28.97 -.05 6 39.12 29.04 .08 7 29.87 30.27 -.4 8 31.17 28.73 2.44 A person wonders if drinking water decreases their running time. The person records 8 times after drinking water and 8 times without drinking water. Examine if drinking water before work does in fact lower their running times. That is, test the null hypothesis.  H0: u with water = u without water vs Ha: u without water > u with water. Find the P-value

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ID Without Water With Water Difference
1 29.01 29.31 -.3
2 29.02 28.02 1
3 29.35 29.01 .34
4 30.02 27.98 2.04
5 28.92 28.97 -.05
6 39.12 29.04 .08
7 29.87 30.27 -.4
8 31.17 28.73 2.44

A person wonders if drinking water decreases their running time. The person records 8 times after drinking water and 8 times without drinking water. Examine if drinking water before work does in fact lower their running times. That is, test the null hypothesis. 

H0: u with water = u without water vs Ha: u without water > u with water. Find the P-value

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