Question

Use the accompanying data table to
(b) determine the linear correlation
​(c) determine the critical value

Data Table:

Index, i	Observed Value	f_i	Expected z-score
1	35	0.08	-1.41
2	37	0.2	-0.84
3	41	0.32	-0.47
4	43	0.44	-0.15
5	55	0.56	0.15
6	57	0.68	0.47
7	60	0.8	0.84
8	65	0.92	1.41

Critical Value Table

Sample Size, n	Critical Value
5	0.88
6	0.888
7	0.898
8	0.906
9	0.912
10	0.918
11	0.923
12	0.928
13	0.923
14	0.935
15	0.939
16	0.941
17	0.944
18	0.946
19	0.949
20	0.951
21	0.952
22	0.954
23	0.956
24	0.957
25	0.959
30	0.96

Answer 1

index, i	Observed Value	f_i	Expected z-score
1	35	0.08	-1.41
2	37	0.2	-0.84
3	41	0.32	-0.47
4	43	0.44	-0.15
5	55	0.56	0.15
6	57	0.68	0.47
7	60	0.8	0.84
8	65	0.92	1.41
		r	0.9666333
		critical r	0.906

Formuila

index, i	Observed Value	f_i	Expected z-score
1	35	0.08	-1.41
2	37	0.2	-0.84
3	41	0.32	-0.47
4	43	0.44	-0.15
5	55	0.56	0.15
6	57	0.68	0.47
7	60	0.8	0.84
8	65	0.92	1.41
		r	=CORREL(B2:B9,D2:D9)
		critical r	0.906

Correlation between observed value and Expected z-score

r = 0.9666

critical r - 0.906   {see n = 8}

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