Question

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A company that stamps gaskets out of cork sheets and wants to compare the mean number of gaskets produced per hour for three different types of stamping machines. The company wants to use the data to determine whether one machine is more productive than the other. To answer these questions, the manufacturer decides to conduct an experiment with each of the machines operating for six 1-hour time periods assigned in a random order to eliminate the possibility of bias. The data for the experiment, the number of gaskets (in thousands) produced per hour is shown below. (a) State the hypotheses and conduct an analysis of variance at α = 0.05 to test the hypotheses. Create a boxplots of the data as part of the oneway ANOVA. (b) Plot and analyze the residuals from the experiment and comment on model adequacy. (c) Is there sufficient evidence to indicate that any machine is more productive than the others? Machine 1 Machine 2 Machine 3 431 427 440 436 442 448 401 394 389 404 441 418 421 409 418 425 393 422

Answer 1

ANSWER:

M1	M2	M3
431	436	401
427	442	394
440	448	389
404	441	418
421	418	393
409	425	422
SUBTRACT EACH FROM 448,WE GET NEW TABLE
	M1	M2	M3	M12	M22	M32
	17	12	47	289	144	2209
	21	6	54	441	36	2916
	8	0	59	64	0	3481
	44	7	30	1936	49	900
	27	30	55	729	900	3025
	39	23	26	1521	529	676
SUM =	156	78	271	4980	1658	13207
N=	18	G =	505	SS=	19845
	CORRECTION FACTOR =		G2/N =	(505)2/N
	(CF)		G2/N =	14168.0556
	TSS =	SS- CF
		19845-14168.06
	TSS =	5676.944444
	SSC =	(156)2/6   +	(78)2/6 +	(271)2/6	(- CF)
	SUM OF SQUARE DUE TO MACHINES
	. =	4056	1014	12240.1667	(-14168.06)
	SUM OF SQUARE DUE TO MACHINES			3142.11111
	SSE =	2534.833333