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

(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.)
  

tcalc
p-value

Answer 1