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 the table below.

Swimmer	Velocity (m/s)
Water	Guar Syrup
1	0.90	0.93
2	0.92	0.97
3	1.00	0.95
4	1.10	1.14
5	1.20	1.23
6	1.25	1.23
7	1.25	1.27
8	1.30	1.30
9	1.35	1.34
10	1.40	1.42
11	1.40	1.44
12	1.50	1.53
13	1.65	1.58
14	1.70	1.70
15	1.75	1.80
16	1.80	1.77
17	1.80	1.84
18	1.85	1.86
19	1.90	1.88
20	1.95	1.95

(A) Find the test statistic and P-value. (Round your test statistic to one decimal place and your P-value to three decimal places.)

t=

P-value=

Answer 1

Sol:

Ho:mu1=mu2

Ha:mu not =mu2

In excel go to data >Data analysis>t test assuming unequal variance

we get

from

t-Test: Two-Sample Assuming Unequal Variances
	Water	Guar Syrup
Mean	1.4485	1.4565
Variance	0.112677	0.109298
Observations	20	20
Hypothesized Mean Difference	0
df	38
t Stat	-0.07594
P(T<=t) one-tail	0.469934
t Critical one-tail	1.685954
P(T<=t) two-tail	0.939868
t Critical two-tail	2.024394

t=--0.1

p value=0.940