Question 1050926
t=(y1-y2)/spsqrt{[((1/n1)+(1/n2)]}
y1=75;y2=86
sp1^2=120;sp2^2=100
n1=n2=12

s2p=(N1−1)s1^2+(N2−1)s2^2/(N1+N2−2) (using pooled variance)
y1-y2=-11
sp^2=11(120)+11(100)/(22)=1320+1100/22=110
sp=10.49
10.49*sqrt(2/12)=10.49*sqrt(1/6)=4.28
t=-11/4.28-2.57
Critical value for t df=22 for 0.975 is +/-2.074
This exceeds the critical value; therefore, we can consider the two groups as having different means at the 5% significance level.
At 6 participants, sp^2=5(120)+5(100)/10=110; sp=10.49;sp*sqrt(1/3)-6.06
t=-11/6.06=1.82.  This would no longer be significant at the 0.05 level, for the critical value would be larger as well, +/-2.23.