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Certain types of diseases tend to occur in clusters. In particular, persons affected with AIDS, syphilis, and tuberculosis may have some common characteristics and associations which increase their chances of contracting these diseases. The following table lists the number of reported cases by state in 2001.

State AIDS Syphills Tuber State AIDS
AL 438 720 265 MT 15
AK 18 9 54 NE 74
AZ 540 1147 289 NV 252
AR 199 239 162 NH 40
CA 4315 3050 3332 NJ 1756
CO 288 149 138 NM 143
CT 584 165 121 NY 7476
DE 248 79 33 NC 942
DC 870 459 74 ND 3
FL 5138 2914 1145 OH 581
GA 1745 1985 575 OK 243
HI 124 41 151 OR 259
ID 19 11 9 PA 1840
IL 1323 1541 707 HI 103
IN 378 529 115 SC 729
IA 90 44 43 SD 25
KS 98 88 63 TN 602
KY 333 191 152 TX 2892
LA 861 793 294 UT 124
ME 48 16 20 VT 25
MD 1860 937 262 VA 951
MA 765 446 270 WA 532
MI 548 1147 330 WV 100
MN 157 132 239 WI 193
MS 418 653 154 WY 5
MO 445 174 157 All States 41,868

a. Construct a scatterplot of the number of AIDS cases versus the number of syphilis cases.

b. Compute the correlation between the number of AIDS cases and the number of syphilis cases.

c. Does the value of the correlation coefficient reflect the degree of association shown in the scatterplot?

d. Why do you think there may be a correlation between these two diseases?

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