Question

1. (8pt) The director of a manufacturing company producing three brands of paper towels wants to reduce production to only two. The director argues that the ability to absorb water is the same for all three brands. The director hires you as a statistician to conduct a statistical test. A sample of 4 towels per brand was collected. Absorbency data are shown in the table below, where the absorbency values vary from 0 to 100 with 100 indicating highest absorbency. The ANOVA table is also below.                                                                             

	ANOVA	df	MS	F
SSTR	134	2	67	4.9
SSE	164	12	13.67
SST	298	14

Paper Towel Absorbency

  

	A	B	C
1	91	99	83
2	100	96	88
3	88	94	89
4	89	89	86

1. Conduct a fisher’s LSD test allowing for 10% error.
2. Do you agree with the director statement? Why?

Answer 1

(OR) TRY THIS ANSWER IN TYPING

From the ANOVA table, we infer that the Critical value of F is 3.8853 and since the calculated value of F is 4.9>the critical value, there is at least a pair of treatments whose difference is significant. Therefore, we use the LSD to find out the pair.

a).

Fisher's LSD is given by the formula where t is the tabulated value of t at 10% level with df as the error df, is the means sum of squares for error, are the replications for treatment 1 and 2. In our case, the number of replications for all the three treatments are the same.

For our case, the , , . Substituting teh values, we have,

We now calculate the means of each treatment.

	A	B	C
1	91	99	83
2	100	96	88
3	88	94	89
4	89	89	86
Mean	92	94.5	86.5

Whenever the absolute value  difference between any pair of tretments is more tahn the LSD, we then conclude that the pair is statistically significant.

We then calculate the absolute difference for comparisions as follows:

Treatments	Mean	Comparision	Difference	ABS(Diff)	LSD	Significant?
A	92	A Vs. B	-2.5	2.5	4.6596	No
B	94.5	A Vs. C	5.5	5.5	4.6596	Yes
C	86.5	B Vs. C	8	8	4.6596	Yes

b).

We see that the Differences A and B are not significant but A and C and B and C are significant. Hence we conclude that the among the three, C is the least. Hence, I don't agree with the Director's arguet that the ability to absorb water is the same for all the three brands since A and B are statistically difference from C.

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