Question

Farmers know that driving heavy equipment on wet soil compresses the soil and injures future crops. Here are data on the "penetrability" of the same type of soil at two levels of compression. Penetrability is a measure of how much resistance plant roots will meet when they try to grow through the soil.

Compressed Soil

2.84	2.63	2.91	2.82	2.76	2.81	2.78	3.08	2.94	2.86
3.08	2.82	2.78	2.98	3.00	2.78	2.96	2.90	3.18	3.16

Intermediate Soil

3.19	3.31	3.1	3.40	3.38	3.14	3.18	3.26	2.96	3.02
3.54	3.36	3.18	3.12	3.86	2.92	3.46	3.44	3.62	4.26

Use the data, omitting the high outlier, to give a 96% confidence interval for the decrease in penetrability of compressed soil relative to intermediate soil. Compute degrees of freedom using the conservative method.

Answer 1

from boxplot we can observe that intermediate soil has an outlier, 4.26

omitting outlier 4.26.

-----------------

Level of Significance ,    α =    0.04          
                  
Sample #1   ---->   Compressed Soil          
mean of sample 1,    x̅1=   2.90          
standard deviation of sample 1,   s1 =    0.14401
size of sample 1,    n1=   20          
                  
Sample #2   ---->   Intermediate Soil          
mean of sample 2,    x̅2=   3.286          
standard deviation of sample 2,   s2 =    0.24          
size of sample 2,    n2=   19          
                  
DF = min(n1-1 , n2-1 )=   18              
t-critical value , t* =    2.2137   (excel formula =t.inv(α/2,df)          
                  
                  
                  
std error , SE =    √(s1²/n1+s2²/n2) =    0.063          
margin of error, E = t*SE =    2.2137   *   0.063   =   0.1401
                  
difference of means = x̅1-x̅2 =    2.9035   -   3.286   =   -0.3828
confidence interval is                   
Interval Lower Limit = (x̅1-x̅2) - E =    -0.3828   -   0.1401   =   -0.5229
Interval Upper Limit = (x̅1-x̅2) + E =    -0.3828   -   0.1401   =   -0.2428