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 the table below. Swimmer Velocity (m/s) Water Guar Syrup 1 0.90 0.94 2 0.92 0.97 3 1.00 0.95 4 1.10 1.15 5 1.20 1.24 6 1.25 1.24 7 1.25 1.27 8 1.30 1.30 9 1.35 1.32 10 1.40 1.43 11 1.40 1.42 12 1.50 1.54 13 1.65 1.58 14 1.70 1.70 15 1.75 1.80 16 1.80 1.77 17 1.80 1.82 18 1.85 1.86 19 1.90 1.88 20 1.95 1.95   The researchers concluded that swimming in guar syrup does not change mean swimming speed. Are the given data consistent with this conclusion? Carry out a hypothesis test using a 0.01 significance level. (Use  ?d = ?water − ?guar syrup.)   Find the test statistic and P-value. (Use a table or SALT. Round your test statistic to one decimal place and your P-value to three decimal places.) t=  P-value=

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 18EQ
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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 the table below.
Swimmer Velocity (m/s)
Water Guar Syrup
1 0.90 0.94
2 0.92 0.97
3 1.00 0.95
4 1.10 1.15
5 1.20 1.24
6 1.25 1.24
7 1.25 1.27
8 1.30 1.30
9 1.35 1.32
10 1.40 1.43
11 1.40 1.42
12 1.50 1.54
13 1.65 1.58
14 1.70 1.70
15 1.75 1.80
16 1.80 1.77
17 1.80 1.82
18 1.85 1.86
19 1.90 1.88
20 1.95 1.95
 
The researchers concluded that swimming in guar syrup does not change mean swimming speed. Are the given data consistent with this conclusion? Carry out a hypothesis test using a 0.01 significance level. (Use 
?d = ?water − ?guar syrup.)
 
Find the test statistic and P-value. (Use a table or SALT. Round your test statistic to one decimal place and your P-value to three decimal places.)
tP-value= 
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