The General Social Survey collects data on demographics educ

The General Social Survey collects data on demographics, education, and work, among many other characteristics of US residents. The histograms below display the distributions of hours worked per week for two education groups: those with and without a college degree. Suppose we want to estimate the average difference between the number of hours worked per week by all Americans with a college degree and those without a college degree. Summary information for each group is shown in the tables to the right of the histograms.

Create a 95% confidence interval for the difference in number of hours worked between the two groups. For degrees of freedom please use Min(N1-1,N2-1), and to find t*, you can either use Table D with degrees of freedom closest to the appropriate number or you can use Excel with the exact degrees of freedom. Give your answer to 3 decimal places.

Lower Bound:

Upper Bound:

Solution

Calculating the means of each group,              
              
X1 =    41.8          
X2 =    39.4          
              
Calculating the standard deviations of each group,              
              
s1 =    15.1          
s2 =    15.1          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    505          
n2 = sample size of group 2 =    667          

Thus,

sD =    0.890701425          
              
          
For the   0.95   confidence level, then      
              
alpha/2 = (1 - confidence level)/2 =    0.025      
df = 504
  
t(alpha/2) =    1.964682003          
              
lower bound = [X1 - X2] - t(alpha/2) * sD =    0.65005494          
upper bound = [X1 - X2] + t(alpha/2) * sD =    4.14994506          
              
Thus, the confidence interval is              
              
(   0.65005494   ,   4.14994506   ) [ANSWER]