Researchers are interested in determining if men and womens

Researchers are interested in determining if men and women\'s hearts tend to be different sizes. In a sample of 12 males, the mean diameter of the heart was 13.21 cm with a standard deviation of 1.05. Among 9 females, the mean diameter of the heart was found to be 11 cm with a standard deviation of 1.01. Construct a 95% confidence interval for the mean difference in heart size.

Please show very detailed work! Need help with 95% confidence interval questions.

Thanks so much!

Solution

First, we get the standard error of the difference,

sD = sqrt [s1^2/n1 + s2^2/n2]

Thus,
              
Lower Bound = (X1 - X2) - t(alpha/2) * sD              
Upper Bound = (X1 - X2) + t(alpha/2) * sD      
              
where              

df = n1 + n2 - 2 =    19          
t(alpha/2) = critical t for the confidence interval =    2.093024054          
              
Thus,              
              
Lower bound =    1.261835975          
Upper bound =    3.158164025          
              
Thus, the confidence interval is              
              
(   1.261835975   ,   3.158164025   ) [ANSWER]