Question

Conservationists have despaired over destruction of tropical rain forest by logging, clearing, and burning." These words begin a report on a statistical study of the effects of logging in Borneo. Here are data on the number of tree species in 12 unlogged forest plots and 9 similar plots logged 8 years earlier:

Unlogged	22	18	22	20	15	21	13	13	19	13	19	15
Logged	17	4	18	14	18	15	15	10	12

Use the data to give a 90% confidence interval for the difference in mean number of species between unlogged and logged plots. Compute degrees of freedom using the conservative method.

Answer 1

Sample #1   ---->   Unlogged
mean of sample 1,    x̅1=   17.50
standard deviation of sample 1,   s1 =    3.5291
size of sample 1,    n1=   12
      
Sample #2   ---->   Logged
mean of sample 2,    x̅2=   13.667
standard deviation of sample 2,   s2 =    4.50
size of sample 2,    n2=   9

Level of Significance ,    α =    0.1
DF = min(n1-1 , n2-1 )=   8              
t-critical value , t* =    1.8595   (excel formula =t.inv(α/2,df)          
                  
                  
                  
std error , SE =    √(s1²/n1+s2²/n2) =    1.813          
margin of error, E = t*SE =    1.8595   *   1.813   =   3.3718
                  
difference of means = x̅1-x̅2 =    17.5000   -   13.667   =   3.8333
confidence interval is                   
Interval Lower Limit = (x̅1-x̅2) - E =    3.8333   -   3.3718   =   0.4615
Interval Upper Limit = (x̅1-x̅2) + E =    3.8333   -   3.3718   =   7.2052