Consider the data to the right from two independent samples

Consider the data to the right from two independent samples. Construct a 95% confidence interval to estimate the difference in population means. Click here to view page 1 of the standard normal table. Click here to view page 2 of the standard normal table.

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u1 - u2   =   0  
Ha:   u1 - u2   =/   0  
At level of significance =    0.05          
As we can see, this is a    two   tailed test.      
Calculating the means of each group,              
              
X1 =    43          
X2 =    48          
              
Calculating the standard deviations of each group,              
              
s1 =    10          
s2 =    14          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    35          
n2 = sample size of group 2 =    39          
Thus, df = n1 + n2 - 2 =    72          
Also, sD =    2.807629584          
              
For the   0.95   confidence level, then      
              
alpha/2 = (1 - confidence level)/2 =    0.025          
Z(alpha/2) =    1.959963985          
              
lower bound = [X1 - X2] - z(alpha/2) * sD =    -10.50285287          
upper bound = [X1 - X2] + z(alpha/2) * sD =    0.502852867          
              
Thus, the confidence interval is              
              
(   -10.50285287   ,   0.502852867   ) [ANSWER]