Question

To test the effects of a new fertilizer on corn plants, we grew 20 plants with fertilizer and 20 plants without fertilizer. a. What can you conclude about the effects of this fertilize. Our results are as follows

	mean height (cm)	sample standard deviation
fertilized plants	70	6
non fertilized plants	74	10

Write an appropriate conclusion with a statistic and probability.

Answer 1

Ho :   µ1 - µ2 =   0          
Ha :   µ1-µ2 ╪   0          
                  
Level of Significance ,    α =    0.05          
                  
Sample #1   ---->   1          
mean of sample 1,    x̅1=   70.00          
standard deviation of sample 1,   s1 =    6          
size of sample 1,    n1=   20          
                  
Sample #2   ---->   2          
mean of sample 2,    x̅2=   74.000          
standard deviation of sample 2,   s2 =    10.00          
size of sample 2,    n2=   20          
                  
difference in sample means = x̅1-x̅2 =    70.000   -   74.0000   =   -4.0000
                  
std error , SE =    √(s1²/n1+s2²/n2) =    2.6077          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   -4.0000   /   2.6077   ) =   -1.5339
                  

                  
  
p-value =        0.13519   (excel function: =T.DIST.2T(t stat,df) )      
Conclusion:     p-value>α , Do not reject null hypothesis              
                  
There is not enough evidence of significant difference...*