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 33 pounds per batch and fertilizer from distributor B contained 25 pounds per batch. Suppose the population standard deviation for distributor A and distributor B is three pounds per batch and four 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?

Group of answer choices

t6 = 3.2000

z = 3.2000

z = -3.2000;

t6 = -3.2000;

Answer 1

Solution:

Distributor A:

Sample size = n_A = 4

Sample mean =

The population standard deviation =

Distributor B:

Sample size = n_B = 4

Sample mean =

The population standard deviation =

Since the distribution of nitrogen in fertilizer is normally distributed with known population standard deviations, we use z test statistic.