Section Exercise 4-29 Noodles and Company tested consumer reaction to two spaghetti sauces. Each of 70...

Section Exercise 4-29 Noodles and Company tested consumer reaction to two spaghetti sauces. Each of 70 judges rated both sauces on a scale of 1 (worst) to 10 (best) using several taste criteria. To correct for possible bias in tasting order, half the judges tasted Sauce A first, while the other half tasted Sauce B first. Actual results are shown below for “overall liking.”

Sauce A: 5, 5, 3, 6, 7, 5, 7, 6, 2, 6, 5, 7, 7, 6, 7, 9, 8, 8, 6, 5, 7, 8, 5, 5, 8, 3, 6, 7, 8, 5, 6, 1, 6, 5, 8, 5, 5, 4, 8, 7, 6, 7, 6, 6, 7, 7, 8, 8, 7, 8, 5, 7, 5, 5, 1, 7, 9, 5, 6, 5, 6, 8, 6, 6, 5, 6, 1, 8, 7, 8

Sauce B: 8, 8, 2, 7, 9, 8, 3, 8, 7, 8, 7, 7, 1, 8, 7, 5, 1, 5, 7, 8, 7, 7, 7, 8, 7, 7, 2, 9, 5, 8, 7, 6, 6, 7, 6, 2, 8, 6, 6, 7, 7, 8, 7, 7, 5, 5, 6, 1, 5, 6, 5, 5, 2, 6, 5, 5, 5, 2, 6, 5, 6, 5, 7, 5, 4, 7, 8, 6, 8, 6 Click here for the Excel Data File (a) Calculate the mean and standard deviation for each sample. (Round your answers to 3 decimal places.) x⎯⎯ S Sauce A Sauce B (b) Calculate the coefficient of variation for each sample. (Enter your answer as a percentage rounded to 1 decimal place.) CVA % CVB % (c) What is your conclusion about consumer preferences for the two sauces? On average, consumers seem to prefer Sauce A over Sauce B. On average, consumers seem to prefer Sauce B over Sauce A.

Expert Solution

Sauce A
x	f	fx	x- mean	(x- mean)2	f*(x- mean)2
1	3	3	-5.042857143	25.43040816	76.29122449
2	1	2	-4.042857143	16.34469388	16.34469388
3	2	6	-3.042857143	9.258979593	18.51795919
4	1	4	-2.042857143	4.173265307	4.173265307
5	17	85	-1.042857143	1.087551021	18.48836735
6	16	96	-0.042857143	0.001836735	0.029387755
7	15	105	0.957142857	0.916122449	13.74183673
8	13	104	1.957142857	3.830408163	49.79530612
9	2	18	2.957142857	8.744693877	17.48938775
sum=	70	423	-9.385714287	69.78795919	214.8714286
MeanA= sum fx / sum f
Mean A =	6.042857143
SD= sqrt( sum of f*(x- mean)2 )	SD (A) =	14.65849339

CVA=( SDA/ Mean A )*100
CVA=	41.22427169

Sauce B
x	f	fx	x- mean	(x- mean)2	f*(x- mean)2
1	3	3	-5.042857143	25.43040816	76.29122449
2	5	10	-4.042857143	16.34469388	81.72346939
3	1	3	-3.042857143	9.258979593	9.258979593
4	1	4	-2.042857143	4.173265307	4.173265307
5	14	70	-1.042857143	1.087551021	15.22571429
6	12	72	-0.042857143	0.001836735	0.022040816
7	19	133	0.957142857	0.916122449	17.40632653
8	13	104	1.957142857	3.830408163	49.79530612
9	2	18	2.957142857	8.744693877	17.48938775
sum=	70	417	-9.385714287	69.78795919	271.3857143
MeanB= sum fx / sum f
MeanB=	5.957142857
SD= sqrt( sum of f*(x- mean)2 )	SD (B) =	16.4737887

CVB=( SDA/ Mean B)*100
CVB=	36.16134068

The coefficient of variation (CV) is the ratio of the standard deviation to the mean. The higher the coefficient of variation, the greater the level of dispersion around the mean. The lower the value of the coefficient of variation, the more precise the estimate.

Since CV of sauce B is lees,so we say.

On average, consumers seem to prefer Sauce B over Sauce A.

orchestra answered 1 year ago

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