Below are percentages for annual sales growth and net sales attributed to loyalty card usage at 74 Noodies & Company restaurants. Annual Sales Growth (X) and Loyalty Card Us age (X of Net Sales) Loyalty 2.1 2.5 (n = 74 restaurants) Store 38 39 40 Loyalty 1.6 1.8 Store Growth Growth -8.3 7.1 7.4 -4.0 -3.9 -3.4 -3.3 7.7 7.9 2.2 2.2 2.8 1.7 2.1 2.5 41 42 8.1 8.3 8.5 -1.9 3.0 2.3 2.3 43 2.4 3.1 -e.8 44 -e.4 45 -e.2 e.2 2.2 2.3 8.6 8.7 2.2 1.3 1.8 46 10 47 8.8 e.5 2.5 1.9 11 2.1 2.5 48 8.8 12 0.6 e.8 49 8.9 2.0 2.0 2.0 50 51 52 9.1 9.5 1e.2 2.0 2.4 13 14 15 1.9 2.0 2.2 2.2 e.3 1.9 10.7 11.e 16 2.1 2.6 53 17 2.2 54 55 2.8 2.9 4.8 4.0 2.1 1.9 2.2 e.7 18 11.3 19 20 56 57 11.4 11.5 1.9 11.7 11.8 2.2 2.6 2.2 21 4.8 4.8 4.2 58 59 22 2.0 23 1.8 60 11.9 2.1 2.0 12.5 24 25 4.6 2.1 61 62 5.1 5.1 5.5 2.5 2.6 e.9 1.1 3.4 12.8 13.8 14.1 14.2 26 63 27 2.0 64 65 5.9 5.9 28 2.0 1.2 2.1 e.9 29 1.4 2.0 2.1 66 67 14.6 14.9 30 6.0 6.1 6.1 6.1 6.3 6.6 31 32 33 2.1 2.7 68 69 70 15.4 16.2 17.2 2.2 1.7 2.4 2.8 34 2.0 2.0 71 72 18.4 35 20.8 25.5 28.8 1.1 6.9 6.9 1.6 1.9 36 73 e.6 37 74 1.8 Click here for the Excel Data File () Find the correlation coefficient. (Round your answer to 3 decimal places. A negative value should be Indicated by a minus sign.) (e-1) To test the correlation coefficient for significance at a = 0.05. fill i the following. (Use the rounded value of the correletion coefficient from part b in all calculations. For final answers, round tcale to 3 decimal places and the p-value to 4 decimal places. Negative values should be indicated by a minus sign.) tcale p-value (c-2) There is no significant correlation. O True False d) Does it appear that increased loyalty card usage is associated with decreased sales growth? Yes O No
Below are percentages for annual sales growth and net sales attributed to loyalty card usage at 74 Noodies & Company restaurants. Annual Sales Growth (X) and Loyalty Card Us age (X of Net Sales) Loyalty 2.1 2.5 (n = 74 restaurants) Store 38 39 40 Loyalty 1.6 1.8 Store Growth Growth -8.3 7.1 7.4 -4.0 -3.9 -3.4 -3.3 7.7 7.9 2.2 2.2 2.8 1.7 2.1 2.5 41 42 8.1 8.3 8.5 -1.9 3.0 2.3 2.3 43 2.4 3.1 -e.8 44 -e.4 45 -e.2 e.2 2.2 2.3 8.6 8.7 2.2 1.3 1.8 46 10 47 8.8 e.5 2.5 1.9 11 2.1 2.5 48 8.8 12 0.6 e.8 49 8.9 2.0 2.0 2.0 50 51 52 9.1 9.5 1e.2 2.0 2.4 13 14 15 1.9 2.0 2.2 2.2 e.3 1.9 10.7 11.e 16 2.1 2.6 53 17 2.2 54 55 2.8 2.9 4.8 4.0 2.1 1.9 2.2 e.7 18 11.3 19 20 56 57 11.4 11.5 1.9 11.7 11.8 2.2 2.6 2.2 21 4.8 4.8 4.2 58 59 22 2.0 23 1.8 60 11.9 2.1 2.0 12.5 24 25 4.6 2.1 61 62 5.1 5.1 5.5 2.5 2.6 e.9 1.1 3.4 12.8 13.8 14.1 14.2 26 63 27 2.0 64 65 5.9 5.9 28 2.0 1.2 2.1 e.9 29 1.4 2.0 2.1 66 67 14.6 14.9 30 6.0 6.1 6.1 6.1 6.3 6.6 31 32 33 2.1 2.7 68 69 70 15.4 16.2 17.2 2.2 1.7 2.4 2.8 34 2.0 2.0 71 72 18.4 35 20.8 25.5 28.8 1.1 6.9 6.9 1.6 1.9 36 73 e.6 37 74 1.8 Click here for the Excel Data File () Find the correlation coefficient. (Round your answer to 3 decimal places. A negative value should be Indicated by a minus sign.) (e-1) To test the correlation coefficient for significance at a = 0.05. fill i the following. (Use the rounded value of the correletion coefficient from part b in all calculations. For final answers, round tcale to 3 decimal places and the p-value to 4 decimal places. Negative values should be indicated by a minus sign.) tcale p-value (c-2) There is no significant correlation. O True False d) Does it appear that increased loyalty card usage is associated with decreased sales growth? Yes O No
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 8PPS
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Transcribed Image Text:Below are percentages for annual sales growth and net sales attributed to loyalty card usage at 74 Noodies & Company restaurants.
Annual Sales Growth (X) and Loyalty Card Usage (% of Net Sales)
(n = 74 restaurants)
Loyalty
2.1
2.5
1.7
Store
Growth
7.1
7.4
Growth
Store
Loyalty
1.6
1.8
2.2
1
-8.3
-4.0
-3.9
38
2
39
40
7.7
7.9
4
-3.4
2.1
2.5
41
2.2
2.8
-3.3
42
43
8.1
8.3
-1.9
3.0
2.4
8.5
8.6
-e.8
2.3
2.3
44
3.1
2.2
-0.4
45
-e.2
-e.2
0.5
2.2
2.3
8.7
8.8
46
1.3
1.8
2.5
1.9
2.0
10
47
11
2.1
48
8.8
12
e.6
e.8
2.5
2.e
49
5e
51
8.9
9.1
9.5
13
14
1.9
2.0
2.0
2.6
2.4
15
2.0
52
1e.2
10.7
2.2
2.2
e.3
1.9
16
2.1
53
17
2.8
2.9
2.2
54
11.e
11.3
11.4
18
2.1
55
19
4.0
1.9
56
1.9
20
4.0
2.2
e.7
57
58
11.5
2.2
11.7
11.8
11.9
21
4.e
4.0
2.6
22
2.8
59
60
2.2
2.1
23
4.2
1.8
2.1
2.5
12.5
12.8
13.8
24
4.6
61
62
2.8
25
26
5.1
e.9
5.1
2.6
63
1.1
3.4
5.5
5.9
2.0
64
14.1
14.2
28
2.0
65
1.2
1.4
5.9
6.0
2.1
e.9
66
14.6
30
2.0
67
14.9
15.4
16.2
17.2
18.4
2.2
1.7
2.4
31
6.1
6.1
2.1
68
32
33
2.1
2.7
69
70
6.1
2.8
1.1
34
6.3
2.0
71
20.8
25.5
35
2.0
72
73
6.6
36
6.9
1.6
e.6
37
6.9
1.9
74
28.8
1.8
Click here for tne Excel Data File
() Find the correlation coefficient. (Round your answer to 3 declmal places. A negative value should be Indicated by a minus sign.)
(c-1) To test the correlation coefficient for significance at a = 0.05. fill in the following. (Use the rounded value of the correlation
coefficlent from part b in all calculations. For final answers, round fcalc to 3 decimal places and the p-value to 4 decimal places.
Negative values should be indicated by a minus sign.)
tcale
p-value
(c-2) There is no significant correlation.
O True
False
d) Does it appear that increased loyalty card usage is associated with decreased sales growth?
Yes
O No
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