udge and Cable (2010) report the results of a study demonstrating a negative relationship between weight and income for a group of men. Following are data similar to those obtained in the study. To simplify the weight variable, the men are classified into five categories that measure actual weight relative to height, from 1 = thinnest to 5 = heaviest. Income figures are annual income (in thousands), rounded to the nearest $1,000. Weight Income 4 151 5 88 3 52 2 73 1 49 3 92 1 56 5 143 These data show a positive relationship between weight and income for a sample of men. However, weight was coded in five categories, which could be viewed as an ordinal scale rather than an interval or ratio scale. If so, a Spearman correlation is more appropriate than a Pearson correlation. Convert the weights and the incomes into ranks and complete the table that follows. Ranks X Y XY 8 7 6 5 4 3 2 1 Compute ∑X, ∑Y, ∑XY, SSXX, SSYY, SP, and the Spearman correlation for these ranks. ∑X ∑Y ∑XY SSXX SSYY SP rSS Is this correlation statistically significant? Use a two-tailed test with α = .05. Critical Values df = n - 2 Level of Significance for One-Tailed Test .05 .025 .01 .005 Level of Significance for Two-Tailed Test .10 .05 .02 .01 1 .988 .997 .9995 .9999 2 .900 .950 .980 .990 3 .805 .878 .934 .959 4 .729 .811 .882 .917 5 .669 .754 .833 .874 6 .622 .707 .789 .834 7 .582 .666 .750 .798 8 .549 .632 .716 .765 9 .521 .602 .685 .735 10 .497 .576 .658 .708 11 .476 .553 .634 .684 12 .458 .532 .612 .661 13 .441 .514 .592 .641 14 .426 .497 .574 .623 15 .412 .482 .558 .606 16 .400 .468 .542 .590 17 .389 .456 .528 .575 18 .378 .444 .516 .561 19 .369 .433 .503 .549 20 .360 .423 .492 .537 21 .352 .413 .482 .526 22 .344 .404 .472 .515 23 .337 .396 .462 .505 24 .330 .388 .453 .496 25 .323 .381 .445 .487 26 .317 .374 .437 .479 27 .311 .367 .430 .471 28 .306 .361 .423 .463 29 .301 .355 .416 .456 30 .296 .349 .409 .449 35 .275 .325 .381 .418 40 .257 .304 .358 .393 45 .243 .288 .338 .372 50 .231 .273 .322 .354 60 .211 .250 .295 .325 70 .195 .232 .274 .302 80 .183 .217 .256 .283 90 .173 .205 .242 .267 100 .164 .195 .230 .254 Critical value of rSS = . This relationship significant.

udge and Cable (2010) report the results of a study demonstrating a negative relationship between weight and income for a group of men. Following are data similar to those obtained in the study. To simplify the weight variable, the men are classified into five categories that measure actual weight relative to height, from 1 = thinnest to 5 = heaviest. Income figures are annual income (in thousands), rounded to the nearest $1,000. Weight Income 4 151 5 88 3 52 2 73 1 49 3 92 1 56 5 143 These data show a positive relationship between weight and income for a sample of men. However, weight was coded in five categories, which could be viewed as an ordinal scale rather than an interval or ratio scale. If so, a Spearman correlation is more appropriate than a Pearson correlation. Convert the weights and the incomes into ranks and complete the table that follows. Ranks X Y XY 8 7 6 5 4 3 2 1 Compute ∑X, ∑Y, ∑XY, SSXX, SSYY, SP, and the Spearman correlation for these ranks. ∑X ∑Y ∑XY SSXX SSYY SP rSS Is this correlation statistically significant? Use a two-tailed test with α = .05. Critical Values df = n - 2 Level of Significance for One-Tailed Test .05 .025 .01 .005 Level of Significance for Two-Tailed Test .10 .05 .02 .01 1 .988 .997 .9995 .9999 2 .900 .950 .980 .990 3 .805 .878 .934 .959 4 .729 .811 .882 .917 5 .669 .754 .833 .874 6 .622 .707 .789 .834 7 .582 .666 .750 .798 8 .549 .632 .716 .765 9 .521 .602 .685 .735 10 .497 .576 .658 .708 11 .476 .553 .634 .684 12 .458 .532 .612 .661 13 .441 .514 .592 .641 14 .426 .497 .574 .623 15 .412 .482 .558 .606 16 .400 .468 .542 .590 17 .389 .456 .528 .575 18 .378 .444 .516 .561 19 .369 .433 .503 .549 20 .360 .423 .492 .537 21 .352 .413 .482 .526 22 .344 .404 .472 .515 23 .337 .396 .462 .505 24 .330 .388 .453 .496 25 .323 .381 .445 .487 26 .317 .374 .437 .479 27 .311 .367 .430 .471 28 .306 .361 .423 .463 29 .301 .355 .416 .456 30 .296 .349 .409 .449 35 .275 .325 .381 .418 40 .257 .304 .358 .393 45 .243 .288 .338 .372 50 .231 .273 .322 .354 60 .211 .250 .295 .325 70 .195 .232 .274 .302 80 .183 .217 .256 .283 90 .173 .205 .242 .267 100 .164 .195 .230 .254 Critical value of rSS = . This relationship significant.

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 15PPS

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Judge and Cable (2010) report the results of a study demonstrating a negative relationship between weight and income for a group of men. Following are data similar to those obtained in the study. To simplify the weight variable, the men are classified into five categories that measure actual weight relative to height, from 1 = thinnest to 5 = heaviest. Income figures are annual income (in thousands), rounded to the nearest $1,000.

Weight	Income
4	151
5	88
3	52
2	73
1	49
3	92
1	56
5	143

These data show a positive relationship between weight and income for a sample of men. However, weight was coded in five categories, which could be viewed as an ordinal scale rather than an interval or ratio scale. If so, a Spearman correlation is more appropriate than a Pearson correlation. Convert the weights and the incomes into ranks and complete the table that follows.

Ranks
X	Y	XY
	8
	7
	6
	5
	4
	3
	2
	1

Compute ∑X, ∑Y, ∑XY, SSXX, SSYY, SP, and the Spearman correlation for these ranks.

∑X	∑Y	∑XY	SSXX	SSYY	SP	rSS

Is this correlation statistically significant? Use a two-tailed test with α = .05.

Critical Values

df = n - 2	Level of Significance for One-Tailed Test
.05	.025	.01	.005
Level of Significance for Two-Tailed Test
.10	.05	.02	.01
1	.988	.997	.9995	.9999
2	.900	.950	.980	.990
3	.805	.878	.934	.959
4	.729	.811	.882	.917
5	.669	.754	.833	.874
6	.622	.707	.789	.834
7	.582	.666	.750	.798
8	.549	.632	.716	.765
9	.521	.602	.685	.735
10	.497	.576	.658	.708
11	.476	.553	.634	.684
12	.458	.532	.612	.661
13	.441	.514	.592	.641
14	.426	.497	.574	.623
15	.412	.482	.558	.606
16	.400	.468	.542	.590
17	.389	.456	.528	.575
18	.378	.444	.516	.561
19	.369	.433	.503	.549
20	.360	.423	.492	.537
21	.352	.413	.482	.526
22	.344	.404	.472	.515
23	.337	.396	.462	.505
24	.330	.388	.453	.496
25	.323	.381	.445	.487
26	.317	.374	.437	.479
27	.311	.367	.430	.471
28	.306	.361	.423	.463
29	.301	.355	.416	.456
30	.296	.349	.409	.449
35	.275	.325	.381	.418
40	.257	.304	.358	.393
45	.243	.288	.338	.372
50	.231	.273	.322	.354
60	.211	.250	.295	.325
70	.195	.232	.274	.302
80	.183	.217	.256	.283
90	.173	.205	.242	.267
100	.164	.195	.230	.254