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 μ_water − μ_{guar syrup}. Round your test statistic to two decimal places and the P-value to three decimal places.)

t=

df=

p=

Swimmer	Velocity (m/s)
	Water	Guar Syrup
1	1.52	1.10
2	0.97	1.92
3	1.05	1.14
4	1.74	1.02
5	0.97	1.84
6	1.55	1.29
7	1.53	1.13
8	1.20	1.99
9	1.97	1.50
10	1.62	1.39
11	1.70	1.29
12	1.20	1.18
13	1.87	0.96
14	1.19	1.48
15	1.72	1.20
16	1.46	1.91
17	1.14	1.36
18	1.61	1.61
19	1.02	1.83
20	1.83	1.70

Answer 1

Null hypothesis ( H0 ) : The researchers concluded that swimming in guar syrup does not change swimming speed.

Alternative hypothesis ( Ha ) : The researchers concluded that swimming in guar syrup change swimming speed.

Using t-Test: Two-Sample Assuming Equal Variances in Excel we get output as :

	Water	Guar Syrup
Mean	1.443	1.442
Variance	0.1042116	0.10816421
Observations	20	20
Pooled Variance	0.1061879
Hypothesized Mean Difference	0
df	38
t Stat	0.0097043
P(T<=t) one-tail	0.496154
t Critical one-tail	1.6859545
P(T<=t) two-tail	0.992308
t Critical two-tail	2.0243941

From the above output we get

t= 0.0097 = 0.01

d.f = 38

p = 0.992