HW 87 Independent random samples of size n1 n2 100 were se

HW 8-7 Independent random samples of size n1 = n2 = 100 were selected from each of two populations. The mean and standard deviations for the two samples were x1 = 125.2, x2 = 123.1, s1 = 5.8, and s2 = 6.9.

(a) Construct a 99% confidence interval for estimating the difference in the two population means (1 2). (Round your answers to two decimal places.)

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Solution

  
Calculating the means of each group,              
              
X1 =    125.2          
X2 =    123.1          
              
Calculating the standard deviations of each group,              
              
s1 =    5.8          
s2 =    6.9          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    100          
n2 = sample size of group 2 =    100          

Also, sD =    0.901387819          
              

For the   0.99   confidence level, then      
              
alpha/2 = (1 - confidence level)/2 =    0.005          
z(alpha/2) =    2.575829304          
              
lower bound = [X1 - X2] - z(alpha/2) * sD =    -0.221821158          
upper bound = [X1 - X2] + z(alpha/2) * sD =    4.421821158          
              
Thus, the confidence interval is              
              
(   -0.221821158   ,   4.421821158   ) [ANSWER]