A hypothetical experiment is conducted on the effect of alco

A (hypothetical) experiment is conducted on the effect of alcohol on perceptual motor ability. The subjects are each tested twice, once after having two drinks and once after having two glasses of water. The two tests were on two different days to give the alcohol a chance to wear off. Half of the subjects were given alcohol first and half were given water first. The scores of the 10 subjects are show below. The first number of each subject is the performance in the \"water\" condition. Higher scores reflect better performance. Test to see if alcohol had a significant effect. Find the t and Z of the data below.

Solution

Set Up Hypothesis
Null, no significance b/w them performance Ho: u1 = u2
Alternate, Higher scores reflect better performance - H1: u1 > u2
Test Statistic
X(Mean)=15.3
Standard Deviation(s.d1)=2.6688 ; Number(n1)=10
Y(Mean)=13.4
Standard Deviation(s.d2)=2.9515; Number(n2)=10
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =15.3-13.4/Sqrt((7.12249/10)+(8.71135/10))
to =1.51
| to | =1.51
Critical Value
The Value of |t | with Min (n1-1, n2-1) i.e 9 d.f is 1.833
We got |to| = 1.50994 & | t | = 1.833
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value:Right Tail -Ha : ( P > 1.5099 ) = 0.08267
Hence Value of P0.05 < 0.08267,Here We Do not Reject Ho

no significance b/w them performance