Consider the data to the right from two independent samples

Consider the data to the right from two independent samples. Construct a 90% confidence interval to estimate the difference in population means.

a) The confidence interval is _____ (round to two decimal places)

Solution

a)

  
Calculating the means of each group,              
              
X1 =    27          
X2 =    20          
              
Calculating the standard deviations of each group,              
              
s1 =    4          
s2 =    2          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    36          
n2 = sample size of group 2 =    31          

Also, sD =    0.757282446          
              
              
For the   0.9   confidence level, then      
              
alpha/2 = (1 - confidence level)/2 =    0.05          
z(alpha/2) =    1.644853627          
              
lower bound = [X1 - X2] - z(alpha/2) * sD =    5.754381223          
upper bound = [X1 - X2] + z(alpha/2) * sD =    8.245618777          
              
Thus, the confidence interval is              
              
(   5.754381223   ,   8.245618777   ) [ANSWER]