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	-7.3	2.7	38	7.5	1.9
2	-6.5	2.7	39	7.5	2.4
3	-6.3	1.8	40	7.5	1.5
4	-4.9	2.0	41	7.7	2.6
5	-3.9	2.7	42	7.8	2.1
6	-2.0	2.4	43	7.8	1.3
7	-1.7	1.6	44	8.1	1.3
8	-0.6	1.7	45	8.4	2.5
9	-0.5	1.7	46	8.6	2.0
10	-0.5	1.9	47	8.7	0.5
11	0.4	1.4	48	8.9	2.3
12	0.6	2.3	49	8.9	2.4
13	0.6	2.5	50	9.2	2.5
14	0.7	2.5	51	9.4	1.6
15	0.8	2.3	52	10.6	2.5
16	1.5	2.3	53	10.6	1.3
17	1.7	2.2	54	10.7	2.5
18	2.0	2.0	55	10.9	1.7
19	4.1	0.8	56	11.0	2.2
20	4.5	1.4	57	11.0	1.3
21	5.0	2.5	58	11.4	0.6
22	5.0	2.5	59	11.9	1.8
23	5.5	2.7	60	12.0	2.1
24	5.6	1.9	61	13.2	2.5
25	6.0	1.9	62	13.5	2.5
26	6.0	2.3	63	14.1	1.7
27	6.1	1.7	64	14.6	2.0
28	6.3	1.9	65	14.8	1.7
29	6.4	2.0	66	15.1	1.6
30	6.4	1.3	67	15.6	0.8
31	6.8	2.1	68	17.7	2.1
32	7.1	1.6	69	18.2	2.1
33	7.1	2.0	70	19.0	1.9
34	7.1	1.7	71	19.3	1.5
35	7.1	1.2	72	24.2	1.2
36	7.2	1.5	73	25.0	0.7
37	7.2	2.3	74	26.3	1.6

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 = 0.025, 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