(Solved): A group of agricultural researchers wants to compare the yield of com plants using four different ty ...

A group of agricultural researchers wants to compare the yield of com plants using four different types of fertilizer (

, and D ). The researchers conduct an experiment where 40 com plants are grown, with 10 plants receiving each type of fertilizer. After a growing season, they measure the total yield (in kilograms) for each plant. Here are the summary statistics for the experiment: \table[[Fertilizer Type,Number of Plants,Mean Yield,Standard Deviation],[A,10,25.4,1.95],[B,10,28.2,2.02],[C,10,30.5,1.79],[D,10,22.8,2.24]] The researchers perform a one-way ANOVA to determine if there are significant differences in the average yield of corn plants between the four fertilizer types. Based on the calculations, the following ANOVA table is generated: \table[[Sources of Variation,df,SS,MS,F],[Regression,,230.6,,],[Error,,,,],[Total,,717.0,,]] (a) (7 points) Complete the Anova Table by filling in the blank cells. \table[[Sources of Variation,df,SS,MS,F],[Regression,,230.6,,],[Error,,,,],[Total,,717.0,,]] (b) (2 points) Write down the Null and Alternative Hypothesis for the testing related to the above ANOVA table. (c) (2 points) Provide the numerical value of the appropriate Test Statistic. 4 (d) (2 points) What is the distribution of the test statistic assuming the null hypothesis to be true. (e) (2 points) What is the decission of the above statistical testing procedure. (f) (2 points) How does the

Value of the test compares (larger or smaller) to the level

? (g) (2 points) Provide an estimate of the

, the commonn variability of each group of data. (h) Provide a

Confidence interval for the difference between the following pair of groups i. (3 points) A, and B ii. (3 points)

, and