An agricultural company is trying to decide which type of fe

An agricultural company is trying to decide which type of fertilizer to use on its crops. The company concerned with the average yield on its crops as well as the variance of their yields. In a sample of 41 different fields with using fertilizer A, the average crop yield per acre is 186 tons with a standard deviation of 33 tons. In a separate sample of 41 different fields using fertilizer B, the average crop yield is 174 tons with a standard deviation of 29 tons. When testing the hypothesis (at the 1% level of significance) that there is no difference between the average yields using the different fertilizers, what is the test statistic? (please round your answer to 2 decimal places)

Solution

      
Calculating the means of each group,              
              
X1 =    186          
X2 =    174          
              
Calculating the standard deviations of each group,              
              
s1 =    33          
s2 =    29          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    41          
n2 = sample size of group 2 =    41          
Thus, df = n1 + n2 - 2 =    80          

Also, sD =    6.860989049          
              
Thus, the t statistic will be              
              
t = [X1 - X2 - uD]/sD =    1.74901897 = 1.75 [ANSWER]