Problem 3 (15 Points): Two fertilizers, A and B, are being compared for their ef

Question

Problem 3 (15 Points): Two fertilizers, A and B, are being compared for their effectiveness on the yields of a The experiment is done on 16 different (and small) grape plant. and is blocks of land;, cach of the block has the same size, has a morh sub-block and divided into two square e the locations of the 16 blocks are scattered around in a valley, exactly in each of the 32 square sub-blocks, and one of the two plants is fertilized with Fertilizer A while the other plant is fertilized with one plants planted in a Fertilizer randomized with applied on 8 of the 16 the plant, and in the following the two tables problem. The yield of with Fertilizer the same block are assumed to have a Normal distribution. is planted ication of the two Fertilizers on the two plants of a block is also respect to the north-south position in a block. Also, Fertilizer A is B. (Appli north sub-blocks.) The yield, in lbs, has been measured for each of g two tables. Note, however, not all of the descriptive statistics provided in are relevant to this problem; choose and use the relevant data to solve this ptive statistics about the yields have been obtained and summarized a plant fertilized with Fertilizer A, the yield of a plant fertilized B as well as the difference between the yields of the two plants planted in Summaryabout the DataCollected for the Two Fertilizers (Unit-lb) Sample Mcan of the 16 Yields Sample Standard Deviation of the Fertilizer for the Corresponding Fertilizer 16 yields for corresponding Fertilizer 1.491 5.042 1.281 4.402 Summary about the Difference: Fertilizer B Yield-Fertilizer A Yield (Unit-lb) Mean of the 16 differences Sample Standard Deviation of the 16 Differences 1.052 0.641 Part (a) (3 Points): Is this problem a randomized two-sample problem or a paired- comparison problem? Explain why in one or up to two sentences. Part (b) (12 Points): Is there sufficient evidence to support the alternative hypothesis that Fertilizer B produces a higher yield than Fertilizer A. (The null hypothesis is that Fertilizer B's yield is the same as Fertilizer A's.) Show work.

Explanation / Answer

(a)

Two data sets are "paired" when the following one-to-one relationship exists between values in the two data sets.

So, this is a paired comparison problem.

b)

Given, difference between the yields of two plants planted follow normal distribution, so we will perform z-test to test the hypothesis.

Mean of 16 differences = 0.641

Standard deviation of 16 differences = 1.052

Standard error of mean of 16 differences , SE = 1.052 / sqrt(16) = 0.263

Z = (Observed difference - Hypothesized difference) / SE

Z = (0.641 - 0) / 0.263 = 2.437

P-value for Z = 2.437 is P(Z > 2.437) = 0.0074

As, p-value (0.0074) is less than the significance level (0.05), we reject the null hypothesis in favour of alternative hypothesis and conclude that there is significant evidence that Fertilizer B produces a higher yield than Fertilizer A.

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