When testing H0 1 2 2 vs HA 1 2 2 where Picture 1 522 Pi

When testing H0: 1 - 2 = 2 vs HA: 1 - 2> 2, where Picture 1 = 522, Picture 2 = 516, 12 = 28, 22 = 24, n1= 40, n2 = 30, at = .01, what is the test statistic?

Solution

Null, Ho: u1 - u2 = 2
Alternate, H1: u1 - u2 > 2
Test Statistic
X(Mean)=522
Standard Deviation(s.d1)=5.2915
Number(n1)=40
Y(Mean)=516
Standard Deviation(s.d2)=4.899
Number(n2)=30
we use Test Statistic (Z) = (X-Y) - (U1-U2)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
Zo= (522-516) - (2) /Sqrt((27.99997/40)+(24.0002/30))
Zo = 3.2659