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Statistics: Experiment Design, Results, and Interpretation

A completely randomized (CRD) experiment was conducted in a glasshouse to test whether mature sugar beet roots are heavier when using a new fertilizer (A). Twenty pots of equal size were filled with the same compost and randomly placed on the bench in two parallel rows as shown below. To ten of pots the old fertilizer (B) was added, and to the other ten pots the new fertilizer (A) was added. Sugar beet seedlings of the same age and similar size were then planted into these pots.

(i) Use descriptive statistics and graphic display to present the results. Are the parametric assumptions met? With reference to the test assumptions, choose a statistical test to determine whether the new fertilizer produces heavier sugar beet roots than the old fertilizer.

(ii) State the null hypothesis and analyze the data. Interpret the results using 95% confidence limits and the test of significance. Is there evidence that the average weight of roots is increased by using the new fertilizer?

(iii) Suggest an improvement in the design of this experiment? Are there any disadvantages to the new design?

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Bench side next to the window, facing south

Old (B) Old (B) Old (B) New (A) New (A) Old (B) Old (B) New (A) Old (B) Old (B)
New (A) Old (B) New (A) New (A) Old (B) New (A) New (A) Old (B) New (A) New (A)

Unfortunately, two of the pots were damaged during the experiment and had to be discarded. The following weights (g) at maturity were recorded.

Mass of mature sugar bee roots in grams (g)
Old fertilizer (B) 48.2 54.6 58.3 47.8 51.4 52 55.2 49.1 49.9 52.6
New fertilizer (A) 52.3 57.4 55.6 53.2 61.3 58 59.8 54.8

(i) Use descriptive statistics and graphic display to present the results. Are the parametric assumptions met? With reference to the test assumptions, choose a statistical test to determine whether the new fertilizer produces heavier sugar bee roots than the old fertilizer.

I did all of this in SPSS, but you can use Excel or any other statistical program to get the same results.

First, the descriptive statistics:

The plants with the new fertilizer have a ...

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