Question

When we test H0: μ1 £ μ2, HA: μ1 > μ2 at α = .10, where Picture = 77.4, Picture = 72.2, s1 = 3.3, s2 = 2.1, n1 = 6, and n2 = 6, what is the estimated pooled variance?

Answer 1

Sample #1   ---->
mean of sample 1,    x̅1=   77.40              
standard deviation of sample 1,   s1 =    3.300              
size of sample 1,    n1=   6              
                      
Sample #2   ---->   
mean of sample 2,    x̅2=   72.20              
standard deviation of sample 2,   s2 =    2.100              
size of sample 2,    n2=   6              
                      
difference in sample means =    x̅1-x̅2 =    77.4000   -   72.2   =   5.200
                      
pooled variance, Sp²=   ([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) = 7.65 (answer)   

the estimated pooled variance = 7.65