Question

Consider the following data for two independent (not matched) random samples taken from two normal populations. Sample 1 10 7 13 7 9 8 Sample 2 8 7 8 4 6 9 In the next question you will be asked to develop a confidence interval for the difference between the two population means.

Answer 1

Sample #1   ---->   1
mean of sample 1,    x̅1=   9.00
standard deviation of sample 1,   s1 =    2.28
size of sample 1,    n1=   6
      
Sample #2   ---->   2
mean of sample 2,    x̅2=   7.00
standard deviation of sample 2,   s2 =    1.79
size of sample 2,    n2=   6

α=0.05

Degree of freedom, DF=   n1+n2-2 =    10              
t-critical value =    t α/2 =    2.2281   (excel formula =t.inv(α/2,df)          
                      
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    2.0494              
                      
std error , SE =    Sp*√(1/n1+1/n2) =    1.1832              
margin of error, E = t*SE =    2.2281   *   1.18   =   2.64  
                      
difference of means =    x̅1-x̅2 =    9.0000   -   7.000   =   2.0000
95% confidence interval is                       
Interval Lower Limit=   (x̅1-x̅2) - E =    2.0000   -   2.6364   =   -0.6364
Interval Upper Limit=   (x̅1-x̅2) + E =    2.0000   +   2.6364   =   4.6364