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_d = μ_water − μ_{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	1.05	1.00
2	1.86	1.01
3	1.20	1.00
4	1.98	1.66
5	1.38	1.72
6	1.83	1.19
7	1.08	1.64
8	1.28	1.82
9	1.11	1.10
10	1.04	0.90
11	1.47	1.61
12	1.50	1.98
13	0.94	1.52
14	1.50	1.35
15	1.25	1.80
16	1.47	1.48
17	1.07	1.85
18	1.47	1.07
19	1.76	1.32
20	1.72	0.95

t	=
df	=
P	=

Is there sufficient evidence to suggest that there is any difference in swimming time between swimming in guar syrup and swimming in water? Carry out a hypothesis test using α = 0.01 significance level.

YesNo    

Answer 1

(a)

From the given data, the following Table is calculated:

Swimmer	Velocity (m/s)
	Water	Guar Syrup           d = Water - Guar Syrup
1	1.05	1.00                            0.05
2	1.86	1.01                            0.85
3	1.20	1.00                            0.20
4	1.98	1.66                            0.32
5	1.38	1.72                         - 0.34
6	1.83	1.19                           0.64
7	1.08	1.64                          - 0.56
8	1.28	1.82                          - 0.54
9	1.11	1.10                           0.01
10	1.04	0.90                           0.14
11	1.47	1.61                          - 0.14
12	1.50	1.98                          - 0.48
13	0.94	1.52                          - 0.58
14	1.50	1.35                           0.15
15	1.25	1.80                           - 0.55
16	1.47	1.48                           - 0.01
17	1.07	1.85                          - 0.78
18	1.47	1.07                            0.40
19	1.76	1.32                            0.44
20	1.72	0.95                            0.77

	From the d values, the following statistics are calculated:

n = 20

= - 0.0005

s_d = 0.4858

SE = s_d/

= 0.4858/

= 0.1086

Test Statistic is given by:

t = - 0.0005/0.1086

= - 0.0046

df = 20 - 1 = 19

By Technology, p value = 0.9964

So,

Answer is:

t	=	0.0046
df	=	19
p	=	0.9964

(b)

Correct option:

No

Explanation:
Since p - value = 0.9964 is greater than = 0.01, the difference is not significant. Fail to reject null hypothesis.

Conclusion:

There is no sufficient evidence to suggest that there is any difference in swimming time between swimming in guar syrup and swimming in water.