Researchers tested two different herbicides, group A and B, and their effects on crop yields along with control group C. At the end of growing season, the yields (in bushels per acre) were obtained as follows:

x = c(39,44,38,45,46,38,46,45,46,50,38,45,40,41,38,39,38,42,38,42,39,42,42,38,42,36,40,42,42,39,41,42,41,39,38,40)

grp = c('A','A','A','A','A','A','A','A','A','A','A','A','B','B','B','B','B','B','B','B','C','C','C','C','C','C','C','C','C','C','C','C','C','C','C','C')

Data set, yield.csv, can be downloaded.

1. Find the between-group variation.

   340.306 7.655 252.604 43.851 87.701

2. Find the critical value for hypothesis test with significance level 0.1

   5.729 5.312 3.285 2.471

3. Do you reject the null hypothesis or not? Complete the hypothesis test with significance level 0.1

   The null hypothesis can be rejected. The null hypothesis cannot be rejected.

4. Do group A and B yield differently?

   Group A has higher yields than Group B Group A has lower yields than Group B Group A has no different yields than Group B

5. Choose a concluding sentence of the study from the following:

   (i) The result does not show the effect of herbicides on crop yields.
   (ii) The result shows the effect of herbicides on crop yields.
   (iii) The result shows the effect of herbicides on crop yields, and Group A has a higher yields.
   (iv) The result shows the effect of herbicides on crop yields, and Group B has a higher yields.

   (i) (iii) (iv) (ii)