Below are percentages for annual sales growth and net sales attributed to loyalty card usage at 74 Noodles & Company restaurants. Annual Sales Growth (%) and Loyalty Card Usage (% of Net Sales)(n = 74 restaurants) Store Growth% Loyalty% Store Growth% Loyalty% 1 -8.3 2.1 38 7.1 1.6 2 -4.0 2.5 39 7.4 1.8 3 -3.9 1.7 40 7.7 2.2 4 -3.4 2.1 41 7.9 2.2 5 -3.3 2.5 42 8.1 2.8 6 -1.9 3.0 43 8.3 2.4 7 -0.8 2.3 44 8.5 3.1 8 -0.4 2.3 45 8.6 2.2 9 -0.2 2.2 46 8.7 1.3 10 -0.2 2.3 47 8.8 1.8 11 0.5 2.1 48 8.8 2.5 12 0.6 2.5 49 8.9 1.9 13 0.8 2.0 50 9.1 2.0 14 1.9 2.0 51 9.5 2.4 15 2.0 2.0 52 10.2 2.2 16 2.1 2.6 53 10.7 2.2 17 2.8 2.2 54 11.0 0.3 18 2.9 2.1 55 11.3 1.9 19 4.0 1.9 56 11.4 1.9 20 4.0 2.2 57 11.5 2.2 21 4.0 0.7 58 11.7 2.6 22 4.0 2.0 59 11.8 2.2 23 4.2 1.8 60 11.9 2.1 24 4.6 2.1 61 12.5 2.0 25 5.1 2.5 62 12.8 0.9 26 5.1 2.6 63 13.8 1.1 27 5.5 2.0 64 14.1 3.4 28 5.9 2.0 65 14.2 1.2 29 5.9 1.4 66 14.6 2.1 30 6.0 2.0 67 14.9 0.9 31 6.1 2.1 68 15.4 2.2 32 6.1 2.1 69 16.2 1.7 33 6.1 2.7 70 17.2 2.4 34 6.3 2.0 71 18.4 2.8 35 6.6 2.0 72 20.8 1.1 36 6.9 1.6 73 25.5 0.6 37 6.9 1.9 74 28.8 1.8 Click here for the Excel Data File (b) Find the correlation coefficient. (Round your answer to 3 decimal places. A negative value should be indicated by a minus sign.) r (c-1) To test the correlation coefficient for significance at α = 0.05, fill in the following. (Use the rounded value of the correlation coefficient from part b in all calculations. For final answers, round tcalc to 3 decimal places and the p-value to 4 decimal places. Negative values should be indicated by a minus sign.) tcalc p-value

Below are percentages for annual sales growth and net sales attributed to loyalty card usage at 74 Noodles & Company restaurants. Annual Sales Growth (%) and Loyalty Card Usage (% of Net Sales)(n = 74 restaurants) Store Growth% Loyalty% Store Growth% Loyalty% 1 -8.3 2.1 38 7.1 1.6 2 -4.0 2.5 39 7.4 1.8 3 -3.9 1.7 40 7.7 2.2 4 -3.4 2.1 41 7.9 2.2 5 -3.3 2.5 42 8.1 2.8 6 -1.9 3.0 43 8.3 2.4 7 -0.8 2.3 44 8.5 3.1 8 -0.4 2.3 45 8.6 2.2 9 -0.2 2.2 46 8.7 1.3 10 -0.2 2.3 47 8.8 1.8 11 0.5 2.1 48 8.8 2.5 12 0.6 2.5 49 8.9 1.9 13 0.8 2.0 50 9.1 2.0 14 1.9 2.0 51 9.5 2.4 15 2.0 2.0 52 10.2 2.2 16 2.1 2.6 53 10.7 2.2 17 2.8 2.2 54 11.0 0.3 18 2.9 2.1 55 11.3 1.9 19 4.0 1.9 56 11.4 1.9 20 4.0 2.2 57 11.5 2.2 21 4.0 0.7 58 11.7 2.6 22 4.0 2.0 59 11.8 2.2 23 4.2 1.8 60 11.9 2.1 24 4.6 2.1 61 12.5 2.0 25 5.1 2.5 62 12.8 0.9 26 5.1 2.6 63 13.8 1.1 27 5.5 2.0 64 14.1 3.4 28 5.9 2.0 65 14.2 1.2 29 5.9 1.4 66 14.6 2.1 30 6.0 2.0 67 14.9 0.9 31 6.1 2.1 68 15.4 2.2 32 6.1 2.1 69 16.2 1.7 33 6.1 2.7 70 17.2 2.4 34 6.3 2.0 71 18.4 2.8 35 6.6 2.0 72 20.8 1.1 36 6.9 1.6 73 25.5 0.6 37 6.9 1.9 74 28.8 1.8 Click here for the Excel Data File (b) Find the correlation coefficient. (Round your answer to 3 decimal places. A negative value should be indicated by a minus sign.) r (c-1) To test the correlation coefficient for significance at α = 0.05, fill in the following. (Use the rounded value of the correlation coefficient from part b in all calculations. For final answers, round tcalc to 3 decimal places and the p-value to 4 decimal places. Negative values should be indicated by a minus sign.) tcalc p-value

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.5: Correlation And Causation

Problem 2CYU

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Question

Below are percentages for annual sales growth and net sales attributed to loyalty card usage at 74 Noodles & Company restaurants.

Annual Sales Growth (%) and Loyalty Card Usage (% of Net Sales) (n = 74 restaurants)
Store	Growth%	Loyalty%	Store	Growth%	Loyalty%
	1			-8.3		2.1	38	7.1	1.6
	2			-4.0		2.5	39	7.4	1.8
	3			-3.9		1.7	40	7.7	2.2
	4			-3.4		2.1	41	7.9	2.2
	5			-3.3		2.5	42	8.1	2.8
	6			-1.9		3.0	43	8.3	2.4
	7			-0.8		2.3	44	8.5	3.1
	8			-0.4		2.3	45	8.6	2.2
	9			-0.2		2.2	46	8.7	1.3
	10			-0.2		2.3	47	8.8	1.8
	11			0.5		2.1	48	8.8	2.5
	12			0.6		2.5	49	8.9	1.9
	13			0.8		2.0	50	9.1	2.0
	14			1.9		2.0	51	9.5	2.4
	15			2.0		2.0	52	10.2	2.2
	16			2.1		2.6	53	10.7	2.2
	17			2.8		2.2	54	11.0	0.3
	18			2.9		2.1	55	11.3	1.9
	19			4.0		1.9	56	11.4	1.9
	20			4.0		2.2	57	11.5	2.2
	21			4.0		0.7	58	11.7	2.6
	22			4.0		2.0	59	11.8	2.2
	23			4.2		1.8	60	11.9	2.1
	24			4.6		2.1	61	12.5	2.0
	25			5.1		2.5	62	12.8	0.9
	26			5.1		2.6	63	13.8	1.1
	27			5.5		2.0	64	14.1	3.4
	28			5.9		2.0	65	14.2	1.2
	29			5.9		1.4	66	14.6	2.1
	30			6.0		2.0	67	14.9	0.9
	31			6.1		2.1	68	15.4	2.2
	32			6.1		2.1	69	16.2	1.7
	33			6.1		2.7	70	17.2	2.4
	34			6.3		2.0	71	18.4	2.8
	35			6.6		2.0	72	20.8	1.1
	36			6.9		1.6	73	25.5	0.6
	37			6.9		1.9	74	28.8	1.8

Click here for the Excel Data File

(b) Find the correlation coefficient. (Round your answer to 3 decimal places. A negative value should be indicated by a minus sign.)

r

(c-1) To test the correlation coefficient for significance at α = 0.05, fill in the following. (Use the rounded value of the correlation coefficient from part b in all calculations. For final answers, round t_calc to 3 decimal places and the p-value to 4 decimal places. Negative values should be indicated by a minus sign.)

t_calc
p-value

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