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:
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| Parcel | New Fertilizer | Old Fertilizer |
| 1 | 14.2 | 14.0 |
| 2 | 14.1 | 13.9 |
| 3 | 14.5 | 14.4 |
| 4 | 15.0 | 14.8 |
| 5 | 13.9 | 13.6 |
| 6 | 14.5 | 14.1 |
| 7 | 14.7 | 14.0 |
| 8 | 13.7 | 13.7 |
| 9 | 14.0 | 13.3 |
| 10 | 13.8 | 13.7 |
| 11 | 14.2 | 14.1 |
| 12 | 15.4 | 14.9 |
| 13 | 13.2 | 12.8 |
| 14 | 13.8 | 13.8 |
| 15 | 14.3 | 14.0 |
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.
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