Question

(Bonus question) Are coffee drinkers more likely to suffer from high blood pressure? For a random sample of 50 coffee drinkers, 30 had high blood pressure. In a random sample of 50 non-coffee drinkers, 25 had high blood pressure. Let p1, p2 denote the population proportion of high blood pressure among coffee drinkers and non-coffee drinkers respectively.

1. (a) Construct a 95% CI for the difference between these two proportions p1 − p2. (3pts).

2. (b) Someone proposes that coffee drinkers have higher proportion of high blood pressure than non-coffee drinkers. Test the claim at 0.05 significance level. Give the H0,Ha, test statistics, p-value and conclusion. (3pts)

Table A: Standard Normal Distribution. Table entry is P[Z < z]

z 0.00 -3.4 0.0003 -3.3 0.0005 -3.2 0.0007 -3.1 0.0010 -3.0 0.0013 -2.9 0.0019 -2.8 0.0026 -2.7 0.0035 -2.6 0.0047 -2.5 0.0062 -2.4 0.0082 -2.3 0.0107 -2.2 0.0139 -2.1 0.0179 -2.0 0.0228 -1.9 0.0287 -1.8 0.0359 -1.7 0.0446 -1.6 0.0548 -1.5 0.0668 -1.4 0.0808 -1.3 0.0968 -1.2 0.1151 -1.1 0.1357 -1.0 0.1587 -0.9 0.1841 -0.8 0.2119 -0.7 0.2420 -0.6 0.2743 -0.5 0.3085 -0.4 0.3446 -0.3 0.3821 -0.2 0.4207 -0.1 0.4602 -0.0 0.5000

0. 0.0 0.5000

1. 0.1 0.5398

2. 0.2 0.5793

3. 0.3 0.6179

4. 0.4 0.6554

5. 0.5 0.6915

6. 0.6 0.7257

7. 0.7 0.7580

8. 0.8 0.7881

9. 0.9 0.8159

0. 1.0 0.8413

1. 1.1 0.8643

2. 1.2 0.8849

3. 1.3 0.9032

4. 1.4 0.9192

5. 1.5 0.9332

6. 1.6 0.9452

7. 1.7 0.9554

8. 1.8 0.9641

9. 1.9 0.9713

0. 2.0 0.9772

1. 2.1 0.9821

2. 2.2 0.9861

3. 2.3 0.9893

4. 2.4 0.9918

5. 2.5 0.9938

6. 2.6 0.9953

7. 2.7 0.9965

8. 2.8 0.9974

9. 2.9 0.9981

0. 3.0 0.9987

1. 3.1 0.9990

2. 3.2 0.9993

3. 3.3 0.9995

4. 3.4 0.9997

0.01 0.02 0.03 0.0003 0.0003 0.0003 0.0005 0.0005 0.0004 0.0007 0.0006 0.0006 0.0009 0.0009 0.0009 0.0013 0.0013 0.0012 0.0018 0.0018 0.0017 0.0025 0.0024 0.0023 0.0034 0.0033 0.0032 0.0045 0.0044 0.0043 0.0060 0.0059 0.0057 0.0080 0.0078 0.0075 0.0104 0.0102 0.0099 0.0136 0.0132 0.0129 0.0174 0.0170 0.0166 0.0222 0.0217 0.0212 0.0281 0.0274 0.0268 0.0351 0.0344 0.0336 0.0436 0.0427 0.0418 0.0537 0.0526 0.0516 0.0655 0.0643 0.0630 0.0793 0.0778 0.0764 0.0951 0.0934 0.0918 0.1131 0.1112 0.1093 0.1335 0.1314 0.1292 0.1562 0.1539 0.1515 0.1814 0.1788 0.1762 0.2090 0.2061 0.2033 0.2389 0.2358 0.2327 0.2709 0.2676 0.2643 0.3050 0.3015 0.2981 0.3409 0.3372 0.3336 0.3783 0.3745 0.3707 0.4168 0.4129 0.4090 0.4562 0.4522 0.4483 0.4960 0.4920 0.4880 0.5040 0.5080 0.5120 0.5438 0.5478 0.5517 0.5832 0.5871 0.5910 0.6217 0.6255 0.6293 0.6591 0.6628 0.6664 0.6950 0.6985 0.7019 0.7291 0.7324 0.7357 0.7611 0.7642 0.7673 0.7910 0.7939 0.7967 0.8186 0.8212 0.8238 0.8438 0.8461 0.8485 0.8665 0.8686 0.8708 0.8869 0.8888 0.8907 0.9049 0.9066 0.9082 0.9207 0.9222 0.9236 0.9345 0.9357 0.9370 0.9463 0.9474 0.9484 0.9564 0.9573 0.9582 0.9649 0.9656 0.9664 0.9719 0.9726 0.9732 0.9778 0.9783 0.9788 0.9826 0.9830 0.9834 0.9864 0.9868 0.9871 0.9896 0.9898 0.9901 0.9920 0.9922 0.9925 0.9940 0.9941 0.9943 0.9955 0.9956 0.9957 0.9966 0.9967 0.9968 0.9975 0.9976 0.9977 0.9982 0.9982 0.9983 0.9987 0.9987 0.9988 0.9991 0.9991 0.9991 0.9993 0.9994 0.9994 0.9995 0.9995 0.9996 0.9997 0.9997 0.9997

0.04 0.05 0.0003 0.0003 0.0004 0.0004 0.0006 0.0006 0.0008 0.0008 0.0012 0.0011 0.0016 0.0016 0.0023 0.0022 0.0031 0.0030 0.0041 0.0040 0.0055 0.0054 0.0073 0.0071 0.0096 0.0094 0.0125 0.0122 0.0162 0.0158 0.0207 0.0202 0.0262 0.0256 0.0329 0.0322 0.0409 0.0401 0.0505 0.0495 0.0618 0.0606 0.0749 0.0735 0.0901 0.0885 0.1075 0.1056 0.1271 0.1251 0.1492 0.1469 0.1736 0.1711 0.2005 0.1977 0.2296 0.2266 0.2611 0.2578 0.2946 0.2912 0.3300 0.3264 0.3669 0.3632 0.4052 0.4013 0.4443 0.4404 0.4840 0.4801 0.5160 0.5199 0.5557 0.5596 0.5948 0.5987 0.6331 0.6368 0.6700 0.6736 0.7054 0.7088 0.7389 0.7422 0.7704 0.7734 0.7995 0.8023 0.8264 0.8289 0.8508 0.8531 0.8729 0.8749 0.8925 0.8944 0.9099 0.9115 0.9251 0.9265 0.9382 0.9394 0.9495 0.9505 0.9591 0.9599 0.9671 0.9678 0.9738 0.9744 0.9793 0.9798 0.9838 0.9842 0.9875 0.9878 0.9904 0.9906 0.9927 0.9929 0.9945 0.9946 0.9959 0.9960 0.9969 0.9970 0.9977 0.9978 0.9984 0.9984 0.9988 0.9989 0.9992 0.9992 0.9994 0.9994 0.9996 0.9996 0.9997 0.9997

0.06 0.07 0.0003 0.0003 0.0004 0.0004 0.0006 0.0005 0.0008 0.0008 0.0011 0.0011 0.0015 0.0015 0.0021 0.0021 0.0029 0.0028 0.0039 0.0038 0.0052 0.0051 0.0069 0.0068 0.0091 0.0089 0.0119 0.0116 0.0154 0.0150 0.0197 0.0192 0.0250 0.0244 0.0314 0.0307 0.0392 0.0384 0.0485 0.0475 0.0594 0.0582 0.0721 0.0708 0.0869 0.0853 0.1038 0.1020 0.1230 0.1210 0.1446 0.1423 0.1685 0.1660 0.1949 0.1922 0.2236 0.2206 0.2546 0.2514 0.2877 0.2843 0.3228 0.3192 0.3594 0.3557 0.3974 0.3936 0.4364 0.4325 0.4761 0.4721 0.5239 0.5279 0.5636 0.5675 0.6026 0.6064 0.6406 0.6443 0.6772 0.6808 0.7123 0.7157 0.7454 0.7486 0.7764 0.7794 0.8051 0.8078 0.8315 0.8340 0.8554 0.8577 0.8770 0.8790 0.8962 0.8980 0.9131 0.9147 0.9279 0.9292 0.9406 0.9418 0.9515 0.9525 0.9608 0.9616 0.9686 0.9693 0.9750 0.9756 0.9803 0.9808 0.9846 0.9850 0.9881 0.9884 0.9909 0.9911 0.9931 0.9932 0.9948 0.9949 0.9961 0.9962 0.9971 0.9972 0.9979 0.9979 0.9985 0.9985 0.9989 0.9989 0.9992 0.9992 0.9994 0.9995 0.9996 0.9996 0.9997 0.9997

0.08 0.09 0.0003 0.0002 0.0004 0.0003 0.0005 0.0005 0.0007 0.0007 0.0010 0.0010 0.0014 0.0014 0.0020 0.0019 0.0027 0.0026 0.0037 0.0036 0.0049 0.0048 0.0066 0.0064 0.0087 0.0084 0.0113 0.0110 0.0146 0.0143 0.0188 0.0183 0.0239 0.0233 0.0301 0.0294 0.0375 0.0367 0.0465 0.0455 0.0571 0.0559 0.0694 0.0681 0.0838 0.0823 0.1003 0.0985 0.1190 0.1170 0.1401 0.1379 0.1635 0.1611 0.1894 0.1867 0.2177 0.2148 0.2483 0.2451 0.2810 0.2776 0.3156 0.3121 0.3520 0.3483 0.3897 0.3859 0.4286 0.4247 0.4681 0.4641 0.5319 0.5359 0.5714 0.5753 0.6103 0.6141 0.6480 0.6517 0.6844 0.6879 0.7190 0.7224 0.7517 0.7549 0.7823 0.7852 0.8106 0.8133 0.8365 0.8389 0.8599 0.8621 0.8810 0.8830 0.8997 0.9015 0.9162 0.9177 0.9306 0.9319 0.9429 0.9441 0.9535 0.9545 0.9625 0.9633 0.9699 0.9706 0.9761 0.9767 0.9812 0.9817 0.9854 0.9857 0.9887 0.9890 0.9913 0.9916 0.9934 0.9936 0.9951 0.9952 0.9963 0.9964 0.9973 0.9974 0.9980 0.9981 0.9986 0.9986 0.9990 0.9990 0.9993 0.9993 0.9995 0.9995 0.9996 0.9997 0.9997 0.9998

6

Table C: t distribution critical values Table entries are t∗ values for confidence level C 1-sided and 2-sided P-values are also shown

Confidence Level C

7

df 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 35 40 45 50 z∗

1-sided P 2-sided P

50% 60% 80% 1.0000 1.3764 3.0777 0.8165 1.0607 1.8856 0.7649 0.9785 1.6377 0.7407 0.9410 1.5332 0.7267 0.9195 1.4759 0.7176 0.9057 1.4398 0.7111 0.8960 1.4149 0.7064 0.8889 1.3968 0.7027 0.8834 1.3830 0.6998 0.8791 1.3722 0.6974 0.8755 1.3634 0.6955 0.8726 1.3562 0.6938 0.8702 1.3502 0.6924 0.8681 1.3450 0.6912 0.8662 1.3406 0.6901 0.8647 1.3368 0.6892 0.8633 1.3334 0.6884 0.8620 1.3304 0.6876 0.8610 1.3277 0.6870 0.8600 1.3253 0.6864 0.8591 1.3232 0.6858 0.8583 1.3212 0.6853 0.8575 1.3195 0.6848 0.8569 1.3178 0.6844 0.8562 1.3163 0.6840 0.8557 1.3150 0.6837 0.8551 1.3137 0.6834 0.8546 1.3125 0.6830 0.8542 1.3114 0.6828 0.8538 1.3104 0.6816 0.8520 1.3062 0.6807 0.8507 1.3031 0.6800 0.8497 1.3006 0.6794 0.8489 1.2987

0.674 0.841 1.282 0.25 0.20 0.10 0.50 0.40 0.20

90% 95% 6.3138 12.706 2.9200 4.3027 2.3534 3.1824 2.1318 2.7764 2.0150 2.5706 1.9432 2.4469 1.8946 2.3646 1.8595 2.3060 1.8331 2.2622 1.8125 2.2281 1.7959 2.2010 1.7823 2.1788 1.7709 2.1604 1.7613 2.1448 1.7531 2.1314 1.7459 2.1199 1.7396 2.1098 1.7341 2.1009 1.7291 2.0930 1.7247 2.0860 1.7207 2.0796 1.7171 2.0739 1.7139 2.0687 1.7109 2.0639 1.7081 2.0595 1.7056 2.0555 1.7033 2.0518 1.7011 2.0484 1.6991 2.0452 1.6973 2.0423 1.6896 2.0301 1.6839 2.0211 1.6794 2.0141 1.6759 2.0086

1.645 1.96 0.05 0.025 0.10 0.05

96% 98% 99% 99.8% 15.895 31.821 63.657 318.31 4.8487 6.9646 9.9248 22.327 3.4819 4.5407 5.8409 10.215 2.9985 3.7469 4.6041 7.1732 2.7565 3.3649 4.0321 5.8934 2.6122 3.1427 3.7074 5.2076 2.5168 2.9980 3.4995 4.7853 2.4490 2.8965 3.3554 4.5008 2.3984 2.8214 3.2498 4.2968 2.3593 2.7638 3.1693 4.1437 2.3281 2.7181 3.1058 4.0247 2.3027 2.6810 3.0545 3.9296 2.2816 2.6503 3.0123 3.8520 2.2638 2.6245 2.9768 3.7874 2.2485 2.6025 2.9467 3.7328 2.2354 2.5835 2.9208 3.6862 2.2238 2.5669 2.8982 3.6458 2.2137 2.5524 2.8784 3.6105 2.2047 2.5395 2.8609 3.5794 2.1967 2.5280 2.8453 3.5518 2.1894 2.5176 2.8314 3.5272 2.1829 2.5083 2.8188 3.5050 2.1770 2.4999 2.8073 3.4850 2.1715 2.4922 2.7969 3.4668 2.1666 2.4851 2.7874 3.4502 2.1620 2.4786 2.7787 3.4350 2.1578 2.4727 2.7707 3.4210 2.1539 2.4671 2.7633 3.4082 2.1503 2.4620 2.7564 3.3962 2.1470 2.4573 2.7500 3.3852 2.1332 2.4377 2.7238 3.3400 2.1229 2.4233 2.7045 3.3069 2.1150 2.4121 2.6896 3.2815 2.1087 2.4033 2.6778 3.2614

2.054 2.326 2.576 3.091 0.02 0.01 0.005 0.001 0.04 0.02 0.01 0.002

99.9% 636.62 31.599 12.924 8.6103 6.8688 5.9588 5.4079 5.0413 4.7809 4.5869 4.4370 4.3178 4.2208 4.1405 4.0728 4.0150 3.9651 3.9216 3.8834 3.8495 3.8193 3.7921 3.7676 3.7454 3.7251 3.7066 3.6896 3.6739 3.6594 3.6460 3.5911 3.5510 3.5203 3.4960

3.291 0.0005 0.001

Answer 1