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Engineering Probability and Inference Homework 4 1

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Engineering Probability and Inference Homework 4

1. A plant biologist conducted an experiment to compare the yields of 4 varieties of peanuts (A, B, C, D). A plot of land was divided into 16 subplots (4 rows and 4 columns). The following Latin Square design was run. Use a significance level of 0.05 and conduct an analysis of variance to compare the mean peanut yield for the 4 varieties.

		Column
Row	East	East Center	West Center	West
North	26.7  (C)	19.7  (A)	29.0  (B)	29.8  (D)
North Center	23.1  (A)	21.7  (B)	24.9  (D)	29.0  (C)
South Center	29.3  (B)	20.1  (D)	29.0  (C)	27.3  (A)
South	25.1  (D)	17.4  (C)	28.7  (A)	35.1  (B)

 

 

2. The following are scores on a 70 point test for students who had three models of instruction with four different instructors. Since instructors can vary, instructors will serve as a block here. 

 

	Model of Instruction
Instructor	Lecture	Online Video	Hybrid
1	58	60	65
2	55	53	61
3	57	56	62
4	52	47	59

 

Use a 0.01 significance level to test whether there are differences in either the instructors and/or models of instruction. Construct an ANOVA table and conduct all possible hypothesis tests. Also state the design.

 

 

 

3. A researcher is investigating the appropriate planting density for three varieties of tomatoes: celebrity, sunbeam, and trust. The researcher wants to use four different planting densities: 5, 20, 35, and 50 thousand plants per hectare. There are three fields that would be appropriate for the study (and thus blocks for the study). The yield, in tons, is given below.

Use a 0.01 significance level to conduct the appropriate tests. Construct the full ANOVA table and state the design.

 

	Celebrity				Sunbeam				Trust
	Density				Density				Density
Field	5k	20k	35k	50k	5k	20k	35k	50k	5k	20k	35k	50k
1	32.2	43.2	47.6	43.5	32.5	39.9	42.5	38.2	49.9	59.0	66.3	58.3
2	33.4	51.3	52.2	44.1	33.4	47.2	44.5	43.5	60.8	66.1	70.7	60.6
3	41.8	51.2	55.9	55.9	41.1	48.7	53.5	48.4	60.8	67.6	73.2	67.8