Two Population Means

A tomato
farmer with a very large farm of approximately 2200 acres had heard about a new
type of rather expensive fertilizer which would supposedly significantly
increase his production. The frugal farmer wanted to test the new fertilizer
before committing the large investment required to fertilize a farm of his
size. He therefore selected 15 parcels of land on his property and divided them
each into two portions.  He bought just
enough of the new fertilizer to spread over one half of each parcel and then
spread the old fertilizer over the other half of each parcel. His yields in
pounds per tomato plant were as follows:

The farmer had taken statistics many years ago when in
college and consequently made a couple of mistakes when testing to find if the
new fertilizer was more effective:  (1)
He tested the data as two independent samples, and (2) He performed a
two-tailed test. He decided that he was unable to conclude that there was a
difference between the two fertilizers. 

What if you were the fertilizer sales representative and
your job was to prove the superiority of the new product to the farmer?

(1) 
You should start by running the same test he did
in which he came to the decision that he could not conclude a difference. 

(2) 
Perform the test as it should have been done and
find if you come to a different conclusion.

(3) 
Explain why the results were different and why
your test was a stronger and more reliable test.