A farmer uses a lot of fertilizer to grow his crops. The farmer’s manager thinks

Question

A farmer uses a lot of fertilizer to grow his crops. The farmer’s manager thinks fertilizer products from distributor A contain more of the nitrogen that his plants need than distributor B’s fertilizer does. He takes two independent samples of four batches of fertilizer from each distributor and measures the amount of nitrogen in each batch. Fertilizer from distributor A contained 23 pounds per batch and fertilizer from distributor B contained 18 pounds per batch. Suppose the population standard deviation for distributor A and distributor B is four pounds per batch and five pounds per batch, respectively. Assume the distribution of nitrogen in fertilizer is normally distributed. Let µA and µB represent the average amount of nitrogen per batch for fertilizer’s A and B, respectively. Specify the competing hypotheses to determine if fertilizer A contains more nitrogen per batch than fertilizer B.

Explanation / Answer

Solution:

From the given information we have
x1 = 23, s1 = 4, n1 = 4
x2 = 18, s2 = 5, n2 = 4

Test statistics = x1 - x2/ sqrt(s12/n1+ s22/n2)
= (23 - 18) / sqrt(42/4 + 52/4)
= 1.5617

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