in an experimental study on response time in minutes 8 indiv

in an experimental study on response time (in minutes). 8 individuals were randomly sampled and their response times were recorded under two visibilty conditions as follows:

Good visibility: .43 1.17 .37 .47 .68 .58 .50

poor visibilty: 1.47 .80 1.58 4.33 4.23 3.25 3.22

perform a test of hypothesis to examine the clain that the poor visibilty leads to a higher response time than does the good visibilty. Give the p-value

Solution

Set Up Hypothesis
Null, Ho: u1 = u2
Alternate, H1: u1 < u2
Test Statistic
X(Mean)=0.6
Standard Deviation(s.d1)=0.2709 ; Number(n1)=7
Y(Mean)=2.6971
Standard Deviation(s.d2)=1.4111; Number(n2)=7
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =0.6-2.6971/Sqrt((0.07339/7)+(1.9912/7))
to =-3.86
| to | =3.86
Critical Value
The Value of |t | with Min (n1-1, n2-1) i.e 6 d.f is 1.943
We got |to| = 3.86146 & | t | = 1.943
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value:Left Tail - Ha : ( P < -3.8615 ) = 0.00417
Hence Value of P0.05 > 0.00417,Here we Reject Ho

the poor visibilty leads to a higher response time than does the good visibilty