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 correct value of the test statistic? A) t₆ = −1.5617 B) t₆ = 1.5617 C) z = −1.5617 D) z = 1.5617

Question

Quizplus · Accepted Answer

The correct value of the test statistic is a z-score because the population standard deviations are known. The formula for the z-score in this context is $z = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}}$, where $\bar{x}_1$ and $\bar{x}_2$ are the sample means, $\sigma_1$ and $\sigma_2$ are the population standard deviations, and $n_1$ and $n_2$ are the sample sizes. Given that $\bar{x}_1 = 23$, $\bar{x}_2 = 18$, $\sigma_1 = 4$, $\sigma_2 = 5$, and $n_1 = n_2 = 4$, the calculation will result in a positive z-score, indicating that the mean of distributor A's fertilizer is higher than that of distributor B's, consistent with option D.

A Farmer Uses a Lot of Fertilizer to Grow His