Question

(1 point) An agricultural field trial compares the yield of two varieties of corn. The researchers divide in half each of 10 fields of land in different locations and plant each corn variety in one half of each plot. After harvest, the yields are compared in bushels per acre at each location. The 10 differences (Variety A - Variety B) give x¯=3.35 and s=6.99. Does this sample provide evidence that Variety A had a higher yield than Variety B?

(a) State the null and alternative hypotheses: (Type "mu" for the symbol μμ , e.g. mu >> 1 for the mean is greater than 1, mu << 1 for the mean is less than 1, mu not = 1 for the mean is not equal to 1)( Hint: Use the only equal sign in the null hypothesis)
H0 :
HA:

(b) Find the value of the test statistic. (Use at least two decimal places):

(c) Does this sample provide evidence that Variety A had a higher yield than Variety B? (Use a 5% level of significance)
(Type: Yes or No)

Answer 1

a)

Ho :   µd=   0
Ha :   µd >   0

b)

mean of difference ,    D̅ =    3.350                  
                          
std dev of difference , Sd =        6.99   
                          
std error , SE = Sd / √n =    6.99/√10   =   2.2104      
                          
t-statistic = (D̅ - µd)/SE = (   3.35   -   0   ) /    2.2104   =   1.516

c)

Degree of freedom, DF=   n - 1 =    9          
  
p-value =        0.081970   [excel function: =t.dist.rt(t-stat,df) ]       
Conclusion:     p-value>α , Do not reject null hypothesis              

so, answer is NO