Question

In: Statistics and Probability

1a A farmer uses a lot of fertilizer to grow his crops. The farmer’s manager thinks...

1a

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 30 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 seven pounds per batch and eight 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?

Multiple Choice

t₆ = –.9407
z = 0.9407
t₆ = 0.9407
z = –.9407

Expert Solution

Given: 2 independent samples of 4 batches are drawn from distributors A and B;where each batch in A & B contains 30 & 25 pounds of nitrogen respectively.Also, nitrogen is normally distributed with average amount per batch being µ1 and µ2 ,

hence µ₁ =30 pounds & µ2 =25 pounds and n1=n2=4

Further, standard deviations of A and B is 7 and 8 pounds respectively i.e., s1=7 pounds and s2=8 pounds

Aim: To test if fertilizer from distributor A contain more of the nitrogen that his plants need than distributor B’s fertilizer

i.e., Ho: There is no difference of the nitrogen between the products from A & B => µ1 = µ2

H1: Fertilizer from distributor A contain more of the nitrogen than that of B => µ1 > µ2

This hypothesis can be tested by using two sample t-test with unequal variances, given that nitrogen is normally distributed.

t = (30-25) / sqrt( (7² + 8²) / 4)

= 5 / sqrt(113/4)

= 5 / 5.315

= 0.9407 which is greater than tabulated value of 0.72 at 6 d.f at 5% level of significance.

Hence, we can accept the H1 concluding that fertilizer from distributor A contain more of the nitrogen than that of B

Answer to this question is 3rd option , t ₆ = 0.9407

orchestra answered 1 year ago

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