Question

The number of pig farms is increasing, a study was conducted to test if composted pig manure might be a better fertilizer than composted cow manure. Eight corn fields of equal size were chosen for the experiment. One half of each corn field was fertilized with composted cow manure and the other half was fertilized with composed pig manure. The yields are given in the following table.

Field	1	2	3	4	5	6	7	8	Mean	Std Dev
Cow	85	80	110	115	105	110	85	110	100	13.2288
Pig	95	100	120	110	125	120	120	130	115	11.4564
Differences	-10	-20	-10	5	-20	-10	-35	-20	-15	10.8972

Test at a = 0.01 the claim that the average yield is higher for composted pig manure than it is for composted cow manure.

Answer 1

µd =µcow - µpig

Ho :   µd=   0
Ha :   µd <   0

mean of difference ,    D̅ =    -15.000                  
                          
std dev of difference , Sd =        10.8972                  
                          
std error , SE = Sd / √n =    10.8972   / √   8   =   3.8527      
                          
t-statistic = (D̅ - µd)/SE = (   -15   -   0   ) /    3.8527   =   -3.8933
                          
Degree of freedom, DF=   n - 1 =    7                  
  
p-value =        0.0030   [excel function: =t.dist(t-stat,df) ]              
Decision:   p-value <α , Reject null hypothesis                      
there is enough evidence to support the claim that the average yield is higher for composted pig manure than it is for composted cow manure