A researcher is interested in determining whether a relationship exists between sleep and quality of life. The researcher randomly invites students at Drexel University to participate in a study, which asks students to selfreport the number of hours per night they slept (on average) over the past 30 days. The students are then complete the Short-Form (36) Health Survey, a 36item survey assessing both physical and mental composite scores for quality of life. Using the Excel and JASP datasets provided, please answer the following questions when performing the bivariate correlation

1. Calculate the cross-products for each participant in the dataset and then sum and average (covariance) the cross products
2. Calculate the Pearson's Product Moment Correlation Coefficient (r) for the data.
3. Using the r distribution table, determine the r critical value and compare it to the obtained r value. Does the r-obtained value exceed the r critical value? If so, what does this mean? If not, what does this mean.
4. Write the statistical finding and conclusion statements

participant_id	hrs_sleep	sf_36
1	5	74
2	10	57
3	3	43
4	1	49
5	3	85
6	5	26
7	7	41
8	2	80
9	1	30
10	9	72
11	9	37
12	10	82
13	1	39
14	4	92
15	6	56
16	7	54
17	1	94
18	8	87
19	2	69
20	6	87
21	4	63
22	4	78
23	6	99
24	1	78
25	5	47
26	10	39
27	10	54
28	3	90
29	10	68
30	6	33
31	2	55
32	9	56
33	1	34
34	10	83
35	5	89
36	5	96
37	8	43
38	7	48
39	5	27
40	3	29
41	1	68
42	1	67
43	5	50
44	9	50
45	8	51
46	2	93
47	5	38
48	8	65
49	1	85
50	1	42
51	3	43
52	5	93
53	9	62
54	9	26
55	2	28
56	8	49
57	1	67
58	6	96
59	5	65
60	9	92
61	3	38
62	5	67
63	3	60
64	4	86
65	6	39
66	2	66
67	9	31
68	3	84
69	5	85
70	2	73
71	5	41
72	10	75
73	2	80
74	4	57
75	4	56
76	9	67
77	10	29
78	4	86
79	5	93
80	9	63
81	1	34
82	9	25
83	2	56
84	8	55