Probability Statistics

Question

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:

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.

Answer 1

Shawna,

 

For part (a) an independent sample test you would get mean_new and mean_old  and s_new and s_old and then calculated s_pooled.

 

H₀: μ_{new =}  μ_old

H_A:  μ_{new ≠} μ_old

 

pick an α = .05 as your cutoff level

 

and do the t-test.

 

 

For part (2) you need to do a "paired sample t-test."

 

1. Calculate d = new-old (i.e. new subtract old) for each plot; this gives a sample with 15 numbers.

 

2. Calculate mean (m) and standard deviation (s) of this sample.

 

3. Since you want to know if the new is better you do a one-tailed test:

 

H₀: d ≤ 0

H_a: d > 0

 

 

Any question? comment back.

 

Answer 2

What is your question?