Question

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: 8, 1, 9, 7, 6, 2, 5, 6, 6, 5, 8, 5, 7, 6, 5, 6, 8, 2, 7, 6, 5, 7, 5, 5, 8,

5, 8, 8, 3, 7, 8, 8, 8, 6, 8, 6, 5, 5, 8, 5, 3, 6, 7, 7, 7, 5, 5, 5, 6, 6,

5, 8, 8, 6, 1, 9, 7, 5, 8, 7, 7, 8, 5, 1, 7, 7, 7, 7, 5, 7

Sauce B:

5, 8, 2, 6, 6, 5, 7, 7, 4, 6, 8, 9, 8, 8, 8, 6, 5, 7, 6, 8, 8, 8, 6, 6, 8,

3, 8, 6, 9, 5, 7, 1, 7, 8, 8, 7, 8, 1, 7, 7, 7, 6, 5, 6, 8, 5, 8, 5, 8, 5,

7, 8, 8, 5, 2, 8, 7, 7, 6, 7, 8, 8, 7, 8, 7, 6, 4, 6, 5, 5

Picture 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

Answer 1

Solution:	The given data is:
			Sauce A	Sauce B
			8	5
			1	8
			9	2
			7	6
			6	6
			2	5
			5	7
			6	7
			6	4
			5	6
			8	8
			5	9
			7	8
			6	8
			5	8
			6	6
			8	5
			2	7
			7	6
			6	8
			5	8
			7	8
			5	6
			5	6
			8	8
			5	3
			8	8
			8	6
			3	9
			7	5
			8	7
			8	1
			8	7
			6	8
			8	8
			6	7
			5	8
			5	1
			8	7
			5	7
			3	7
			6	6
			7	5
			7	6
			7	8
			5	5
			5	8
			5	5
			6	8
			6	5
			5	7
			8	8
			8	8
			6	5
			1	2
			9	8
			7	7
			5	7
			8	6
			7	7
			7	8
			8	8
			5	7
			1	8
			7	7
			7	6
			7	4
			7	6
			5	5
			7	5
		Mean	6.071	6.414
		Standard deviation	1.852	1.781
		Coefficient of varation	30.5	27.8
Formula Used:
	Mean=(sum of observations)/number of observation
	standard deviation=(sum of (Xi-Mean)2)/number of observation
	Coefficient of varation= (standard deviation/mean)*100
(a).	Mean and standard deviation of each sample given below:
	Mean of sample A =		6.071
	Mean of sample B =		6.414
	Standard deviation for sample A =		1.852
	Standard deviation for sample B =		1.781
(b).	Coefficient of variation for sample A =		30.5	%
	Coefficient of variation for sample B =		27.8	%