Question

Yield of wheat can be affected by Fusarium, a fungus. Antifungal agents can be researched by...

Yield of wheat can be affected by Fusarium, a fungus. Antifungal agents can be researched by measuring their impact on wheat yield in bushels per acre. A trial of five different antifungal agents could be conducted on four blocks of land, with each divided into five plots, and one randomly assigned for each agent. Do a complete hypothesis test to compare the effectiveness of antifungal agents.

Antifungal A B C D E
1 41.1 37.7 34.2 32.2 39.9
2 40.2 35.4 38.2 32.7   40.1
3 39.9 41.1 39.4 38.9 41.2
4 37.2 40.5 37.7 36.8 42.1

Homework Answers

Answer #1

Using two-way ANOVA we can test to compare the effectiveness of antifungal agents.

Here the hypothesis is,

H0: Mean effects are equal vs H1: Mean effects are not equal

Here the ANOVA table is,

ANOVA
Source of Variation SS df MS F P-value F crit
Antifungal agents 75.925 4 18.98125 4.725328 0.016016 3.259167
Blocks 30.7495 3 10.24983 2.551667 0.104558 3.490295
Error 48.203 12 4.016917
Total 154.8775 19

Here the p-value for the above hypothesis is 0.016016 < 0.05 but >0.01. So, at 1% level of significance, we don't have enough evidence to conclude that the effects are significant but at 5% level of significance, we can conclude that there is a significant difference in the effects of antifungal agents.

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