Chapter 12.6, Problem 26E

In Exercises 19-26, (a) draw a scatter diagram; (b) determine the value of r, rounded to the nearest thousandth; (c) determine whether a correlation exists at α = 0.05; and (d) determine whether a correlation exists at α = 0.01.

26.

x	y
90	90
70	70
65	65
60	60
50	50
40	40
15	15

Table 12.9 Critical Values* for the Correlation Coefficient, r

n	α = 0.05	α = 0.01
4	0.950	0.990
5	0.878	0.959
6	0.811	0.917
7	0.754	0.875
8	0.707	0.834
9	0.666	0.798
10	0.632	0.765
11	0.602	0.735
12	0.576	0.708
13	0.553	0.684
14	0.532	0.661
15	0.514	0.641
16	0.497	0.623
17	0.482	0.606
18	0.468	0.590
19	0.456	0.575
20	0.444	0.561
22	0.423	0.537
27	0.381	0.487
32	0.349	0.449
37	0.325	0.418
42	0.304	0.393
47	0.288	0.372
52	0.273	0.354
62	0.250	0.325
72	0.232	0.302
82	0.217	0.283
92	0.205	0.267
102	0.195	0.254
The derivation of this table is beyond the scope of this text. It shows the critical values of the Pearson correlation coefficient.