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 ?_water ? ?_{guar syrup}.Round your test statistic to two decimal places and the P-value to three decimal places.)

Swimmer	Velocity (m/s)
	Water	Guar Syrup
1	1.75	1.33
2	1.96	0.95
3	2.00	1.55
4	1.05	0.93
5	1.69	1.14
6	0.93	1.77
7	1.80	0.90
8	1.70	1.27
9	1.07	1.74
10	1.89	1.34
11	1.72	1.68
12	1.73	1.45
13	1.01	1.34
14	1.19	1.87
15	1.34	1.39
16	1.47	1.08
17	1.75	1.78
18	1.61	1.69
19	1.55	1.98
20	1.96	1.20

t	=
df	=
P	=

Answer 1

Result:

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 ?_water ? ?_{guar syrup}.Round your test statistic to two decimal places and the P-value to three decimal places.)

t	= 1.18
df	= 19
P	= 0.254

Paired t Test
Data
Hypothesized Mean Difference	0
Level of significance	0.05
Intermediate Calculations
Sample Size	20
DBar	0.1395
Degrees of Freedom	19
SD	0.5309
Standard Error	0.1187
t Test Statistic	1.1752
Two-Tail Test
Lower Critical Value	-2.0930
Upper Critical Value	2.0930
p-Value	0.2544
Do not reject the null hypothesis