Minitab Laboratory - Analysis of Variance In this assessment, we will use the ANOVA model to analyse some

Minitab Laboratory - Analysis of Variance

In this assessment, we will use the ANOVA model to analyse some experimental data. The data are given below. The means are included so that you can check your data input. In each case you should input the data into Minitab and carry out your analysis. Your report should consist of a Word document containing appropriate plots, analyses, and summary of your main findings and conclusions.

In detail for each question you should.

Submit appropriate plots of the data. (5 marks)
Submit an ANOVA table for each question. (5 marks)
Submit appropriate residual plots to check the assumptions underlying the ANOVA model. (5 marks)
Test for main effects (and interactions) where appropriate. (5 marks)
Produce appropriate plots of means. (5 marks)
Use appropriate reference distributions to compare means. (This can be done by hand)
(5 marks)
Produce a summary of your findings with particular reference to any practical relevance. (8 marks)
Sections(1 - 6) above should include an appropriate comment. The idea of the comment is to demonstrate understanding. (12 marks)

Question No. 1

Forty-eight devices selected from a warehouse were randomly assigned to three treatment groups, A, B and C. Nothing was done to the A devices as these acted as a control group. The B devices were immersed in water and the C devices were dropped from a height. All the devices were then tested in random order and the performance data are reported below.

Treatment	A	B	C
	0.38	0.53	0.51
	0.26	0.35	0.63
	0.41	0.38	0.46
	0.33	0.45	0.47
	0.33	1.09	0.42
	0.37	0.46	0.45
	0.54	0.57	0.41
	0.76	0.47	0.39
	0.51	0.39	0.35
	0.55	0.74	0.41
	0.53	0.32	0.49
	0.41	0.74	0.40
	0.47	0.48	0.58
	0.49	0.37	0.46
	0.42	0.52	0.38
	0.34	0.44	0.48

Means	0.444	0.519	0.456

Question No. 2

An experiment was conducted to investigate the effect of four different fertilizers (A to D) on the growth of tomato seedlings. Four plots of seedlings were randomly assigned to each of the fertilisers and the growth of the plants was recorded. The data and means are provided in the following table.

Process	A	B	C	D
	10.8	11.1	5.4	5.8
	9.1	11.1	4.6	5.3
	13.5	8.2	7.4	3.2
	9.2	11.3	5.0	7.5
Mean	10.65	10.43	5.60	5.45
Grand Mean	8.03

Question No. 3

An experiment was carried out to investigate if there were differences in the strength of four different materials (A, B, C and D below). The design used was randomised blocks with different days acting as the blocks.

Material -> Day	A	B	C	D	Mean
1	20.7	23.8	21.5	25.2	22.80
2	19.1	21.5	22.9	25.5	22.25
3	21.4	23.2	22.4	24.8	22.95
4	22.5	22.5	22.2	24.6	22.95
5	19.2	23.1	23.2	23.1	22.15
Mean	20.58	22.82	22.44	24.64
Grand Mean	22.62

Question No. 4

An experiment was carried out to investigate the effect of Temperature (Low, Medium or High) and the rate of adding a reagent (Slow, Medium or Fast) on the viscosity of paint. The current operating conditions are a fast rate of adding the reagent and 44 degrees. You are provided with the data and means below. (High numbers are desirable).

Viscosity of Paint
Temperature-> Rate	40	42	44	Mean
Slow	90 96	106 101	107 95	99.17
Medium	93 90	106 111	84 86	95.00
Fast	104 104	96 92	105 115	102.67
Mean	96.17	102.00	98.67
Grand Mean	98.94

Question No. 5

An experiment was carried out to investigate the effect of four different moulds and three different melt compositions on the carbon content of steel. Three different test pieces were selected at random from the ingots cast in each mould. The data are presented below.

		Melt
Mould	A	B	C
1	22.0	17.6	26.2
1	23.7	17.0	24.2
1	21.2	17.8	25.5
2	21.6	17.2	28.3
2	22.6	18.5	28.4
2	21.9	17.3	30.6
3	20.7	12.3	24.2
3	20.5	11.7	22.8
3	20.2	11.6	26.3
4	23.8	22.3	30.2
4	24.7	22.7	30.4
4	23.0	21.2	30.6

Means	22.16	17.27	27.31