To investigate the fluid mechanics of swimming twenty swimme

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. Round your test statistic to two decimal places and the P-value to three decimal places.)

Solution

Set Up Hypothesis
Null Hypothesis , There Is No-Significance between them Ho: u1 = u2
Alternate Hypothesis, There Is Significance between them - H1: u1 != u2
Test Statistic
X(Mean)=1.477
Standard Deviation(s.d1)=0.339 ; Number(n1)=20
Y(Mean)=1.434
Standard Deviation(s.d2)=0.333; Number(n2)=20
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =1.477-1.434/Sqrt((0.11492/20)+(0.11089/20))
to =0.4
| to | =0.4
Critical Value
The Value of |t | with Min (n1-1, n2-1) i.e 19 d.f is 2.861
We got |to| = 0.40468 & | t | = 2.861
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value: Two Tailed ( double the one tail ) - Ha : ( P != 0.4047 ) = 0.69
Hence Value of P0.01 < 0.69,Here We Do not Reject Ho

ANS:

t = 0.4

df = 19

P = 0.69

No