Data were collected on annual personal time in hours taken b

Data were collected on annual personal time (in hours) taken by a random sample of 16 women (gorup 1) and 7 men (group) employed by a medium sized company. The women took an average of 24.75 hours of personal time per year with a standard deviation of 2.84 hours. The men took an average 20.5 hours of personal time per year with a standard deviation of 2.75 hours.What is the pool estimate of the variance

Solution

              
Calculating the standard deviations of each group,              
              
s1 =    2.84          
s2 =    2.75          
              
Thus, the pooled standard deviation is given by              
              
S = sqrt[((n1 - 1)s1^2 + (n2 - 1)(s2^2))/(n1 + n2 - 2)]               
              
As n1 =    16   , n2 =    7  
              
Then              
              
S =    2.81457939   [ANSWER]