A Farmer Uses a Lot of Fertilizer to Grow His

Multiple Choice

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 µ₁ and µ₂ represent the average amount of nitrogen per batch for fertilizer's A and B, respectively. Which of the following is the appropriate conclusion at the 5% significance level?

A) Reject H₀; we can conclude that the mean amount of fertilizer per batch for distributor A is greater than the amount of fertilizer per batch for distributor B.
B) Reject H₀; we cannot conclude that the mean amount of fertilizer per batch for distributor A is greater than the amount of fertilizer per batch for distributor B.
C) Fail to reject H₀; we can conclude that the mean amount of fertilizer per batch for distributor A is greater than the amount of fertilizer per batch for distributor B.
D) Fail to reject H₀; we cannot conclude that the mean amount of fertilizer per batch for distributor A is greater than the amount of fertilizer per batch for distributor B.