The travel times between an airport and center city is sampl

The travel times between an airport and center city is sampled for public buses and private taxicabs A sample of eight bus trips yields times of 44, 56, 39, 42, 48, 51, 36, 43 min Ten taxis are included in the survey with times of 37, 46, 40, 32, 35, 46,. 39, 41, 29, 36 min Given the cost difference, can we conclude that the taxis cabs get the riders to center city at a significantly faster time?

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)=44.875
Standard Deviation(s.d1)=6.512 ; Number(n1)=8
Y(Mean)=38.1
Standard Deviation(s.d2)=5.507; Number(n2)=10
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =44.875-38.1/Sqrt((42.40614/8)+(30.32705/10))
to =2.35
| to | =2.35
Critical Value
The Value of |t | with Min (n1-1, n2-1) i.e 7 d.f is 2.365
We got |to| = 2.34691 & | t | = 2.365
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value: Two Tailed ( double the one tail ) - Ha : ( P != 2.3469 ) = 0.051
Hence Value of P0.05 < 0.051,Here We Do not Reject Ho