In an effort to determine whether a new type of fertilizer is more effective than the type currently in use, researchers took 12 two-acre plots of land scattered throughout the county. Each plot was divided into two equal-size subplots, one of which was treated with the current fertilizer and the other of which was treated with the new fertilizer. Wheat was planted, and the crop yields were measured. Plot 1 2 3 4 5 6 7 8 9 10 11 12
Current fertilizer 56 45 68 72 61 69 57 55 60 72 75 66
New fertilizer 60 46 66 73 59 67 61 60 58 75 72 68
a. Can we conclude at the 5% significance level that the new fertilizer is more effective than the current one?
b. Estimate with 95% confidence the difference in mean crop yields between the two fertilizers.
c. What is the required condition(s) for the validity of the results obtained in parts (a) and (b)?
d. Is the required condition(s) satisfied?
e. Are these data experimental or observational? Explain.
f. How should the experiment be conducted if the researchers believed that the land throughout the county was essentially the same?