i AM STUDYING FOR THE GMAT CAN YOU HELP ME WITH THIS ONE

A consumer preference study involving three different bottle designs
(A,B,C) for the jumbo size of  ketchup was carried out using a block
experimental design, with fast food restaurants as blocks.
Specifically, four food chains were supplied with all three designs
which were priced the same.  Each design sold in a 24 hour period at
each location. If we use SST, SSB, and SSE can be calculated to be
586.1667, 421.6667 and 1.8333.

1.	Test the null hypothesis Ho that no differences exist between  the
effects of the bottle designs on mean daily sales. Set a = .05 Can we
conclude that the different bottle designs have different effects on
mean sales?
2.	 Test the null hypothesis Ho that no differences exist between  the
effects of the food chains on mean daily sales. Set a = .05 Can we
conclude that the different food chains have different effects on mean
sales?
3.	Use Tukey simultaneous 95 per cent confidence intervals to make
pairwise comparisons of the bottle design effects on mean da ily
sales.  Which bottle design(s) maximize mean sales?

BOTTLE DESIGN        FOOD CHAIN
				1	2	3	4
A				16	14	1	6
B				33	30	19	23
C				23	21	8	12

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Clarification of Question by wrench234-ga on 21 Mar 2005 06:47 PST

ja
thank you that  do help however unless my formual is incorrect I can
not come out with the same results mine is extremely high. Can  you
assist on the formulas

Hi wrench234-ga ,


--------------------------------------DATA GIVEN ------------------
BOTTLE DESIGN        FOOD CHAIN
				1	2	3	4
A				16	14	1	6
B				33	30	19	23
C				23	21	8	12
---------------------------------------------------------------------
If this is your data then SST, SSB and SSE calculation is wrong.

Correct one is SST = 1009.666667  with d.o.f ( Degree of freedom ) = 11
SSB = 586.1666667 with d.o.f = 2
SSE = 423.5 with d.o.f = 9


1.	Test the null hypothesis Ho that no differences exist between  the
effects of the bottle designs on mean daily sales. Set a = .05 Can we
conclude that the different bottle designs have different effects on
mean sales?
If we use SST, SSB, and SSE can be calculated to be
586.1667, 421.6667 and 1.8333.

Say if we take your info also we need to have d.o.f for SSE to do the calculation.

So I will proceed with my figures of SST and SSB for a given data.

ANOVA table for given data is given by

Source of Variation	SS	   df	MS	       F	P-value
Between Groups	     586.1666667   2	293.0833333  6.2284   0.02004	
Within Groups	      423.5	   9	47.05555556			
						
Total	            1009.666667	  11				

 
As you can see p-value is 0.02 and our alpha is a = .05.  Hence we can
conclude that the different bottle designs have different effects on
mean sales.


2.	 Test the null hypothesis Ho that no differences exist between  the
effects of the food chains on mean daily sales. Set a = .05 Can we
conclude that the different food chains have different effects on mean
sales?

ANOVA is given by

Source of Variation	SS	df	MS	F	P-value
Between Groups	     421.666	3    140.555	1.9123	0.206109304
Within Groups	       588	8	73.5		
					
Total	         1009.666667	11			

This time  SST = 1009.666667 SSB = 421.666 and SSE = 588
And p-val = 0.206109304 Hence we can conclude that the different food
chains have no effects on mean sales. Ho is true in this case.

Tukey test is not difficult but given the resource I have right now it
cant be done hopefully this help you in your prepration.