Algebra
Confidence Interval Explanation
Here is one sample from the before data. Hit to get a new sample.
Samples from the after data of size 100 are taken and the mean is found. This is repeated 1000 times to get a sampling distribution. The normal distribution which has mean equal to the mean of the after data and standard deviation equal to the standard deviation of the after data divided by the square root of the number of samples, this is the SE, is shown in the background. The 95% confidence interval is indicated by the red coloring on the normal distribution, this is (mean – 1.96*SE, mean + 1.96*SE). The meaning should be clear, about 95% of the sampling distribution should occur in this interval.
Here is one sample from the after data. Hit to get a new sample.
Mean of sampling distribution: 69.11
Standard Deviation of Sampling Dist: 2.1977273816
Here is another perspective. 100 samples were drawn from the After Data. A 95% CI was created for each. We should expect 95% of these CI’s to contain the true population mean. Hit to regenerate.
%CI’s that contain the mean: 93% Each CI is formed by finding the mean (M) of the sample and then the standard deviation of the sample (SD). SE is computed as SD/sqrt(# of samples). The CI is computed as (M – 1.96*SE, M + 1.96*SE)
A good intuition for the CI: The mean is a point estimate. You take a sample of the population, take the sample mean and use this as an estimate for the population mean. Why should this estimate be any good, after all, you just have one random sample. The CI is an interval estimate, a 95% CI is an interval obtained from a sample and you interpret this as: “I am 95% certain that the actual population mean is in the interval.” You are not predicting a specific mean for the population, instead you are finding an interval of possible values for the population mean and you are able to quantify how certain you are that the true population mean is inside that interval.
Before 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 > 100 5 0 0 0 0 0 0 0 0 0 0 1 2 13 13 21 16 11 2 3 0

After 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 > 100 5 0 0 0 8 0 0 6 0 3 2 13 7 8 7 1 6 10 1 3 6

1000 mean counts for samples of size 100

Normal [57…58) [58…59) [59…60) [60…61) [61…62) [62…63) [63…64) [64…65) [65…66) [66…67) [67…68) [68…69) [69…70) [70…71) [71…72) [72…73) [73…74) [74…75) [75…76) 1.9921125708130685E-4 8.8282100460376225E-4 3.2511886833645805E-3 9.9506075746811154E-3 2.5311569538967453E-2 5.3514487353852808E-2 9.404236616752075E-2 0.13736899363605978 0.16679222763955848 0.16834082053343802 0.14123093325897007 9.8490150107868546E-2 5.7091288445204835E-2 2.7507319198796232E-2 1.101568 1848986936E-2 3.66639108202782E-3 1.0141604168724117E-3 2.3312459891799975E-4 4.4530088049832273E-5 Mean Counts [57…58) [58…59) [59…60) [60…61) [61…62) [62…63) [63…64) [64…65) [65…66) [66…67) [67…68) [68…69) [69…70) [70…71) [71…72) [72…73) [73…74) [74…75) [75…76) 1E-3 2E-3 3.0000000000000001E-3 1.7999999999999999E-2 2.4E-2 7.0999 999999999994E-2 0.107 0.156 0.189 0.16400000000000001 0.129 7.8E-2 3.6999999999999998E-2 1.6E-2 4.0000000000000001E-3 1E-3 0 0 0 CI 0 0 0 0 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0 0 0 0 0 0 0

100 CI’s computed from Samples of size 100 from the After Data

Hi 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 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 64.833330765782577 60.321266051896259 64.118412218047538 59.237115398324228 61.527914629970354 61.201604343188862 59.098507865055559 61.338904103402498 59.51353884661799 63.795823649013123 58.943863248858968 62.427353557889177 65.123495115779292 59.82093358029617 65.141138779380626 63.856854035661812 59.140597573732116 61.522646737246149 60.338570324319129 60.700731319609226 59.406935750715363 63.305485622776757 58.169152788602084 52.671647812695625 62.526645585406655 60.112794594008115 57.549812144657743 63.00159230545669 61.002854026197276 63.406882439043706 61.984365 548001122 61.439029249184358 61.738166402883174 62.34436609404716 62.139290277478452 61.428324946290509 62.946438484231926 59.620347683876965 58.94189739851879 65.091487488311401 65.181851733414589 60.729750502579613 59.701370519707361 61.968403007792837 66.900648310543488 59.521912641830859 66.595413101639778 62.914045720627058 60.296767195493572 62.377269975699427 64.844432548712732 58.086525244727667 61.156446651238269 60.36259029574655 61.81617409375626 57.109285234610105 57.993425965289447 59.643634329641408 55.881045055892741 59.968527691343638 63.020776388175065 61.384698397573537 65.322733192849881 59.836645793878979 58.634010947345267 58.451090733750007 64.844494045581285 59.873885092046386 58.967694273536473 62.348263054418936 61.189660732109878 56.942762726432754 62.99726292841892 62.03021087922999 62.739978440059289 62.354039752714179 55.808929063808598 62.731241857582916 58.458940146621345 55.567009356003418 65.164108162941574 62.638370232113516 57.45916292674152 66.952001155555735 61.146439762840643 59.956634398330522 57.83785585918848 64.251496797243348 62.026039364882351 58.909276382683196 61.588364805211278 62.915846816777268 62.255358552938347 61.600570478629336 55.74445880529818 59.794699330453447 60.04240264309869 61.679729025758569 55.913222149966835 LOW 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 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 72.366669234217412 67.958733948103742 73.621587781952471 67.282884601675761 69.352085370029641 70.078395656811139 67.501492134944442 69.86109589659749 68.366461153382005 72.004176350986882 68.496136751141023 71.312646442110832 73.116504884220717 69.17906641970383 72.858861220619374 72.463145964338182 69.239402426267887 71.097353262753856 69.781429675680869 69.839268680390759 68.113064249284633 72.534514377223246 67.350847211397905 62.56835218730437 71.133354414593342 69.42720540599187 66.930187855342254 71.618407694543308 69.237145973802726 71.793117560956276 70.275634451998869 70.320970750815633 71.341833597116846 70.335633905952847 71.140709722521549 70.811675053709507 71.553561515768081 69.339652316123036 68.578102601481206 71.70851251168861 73.178148266585424 69.510249497420389 68.158629480292632 69.771596992207165 73.719351689456516 69.458087358169138 75.164586898360213 71.605954279372952 68.863232804506424 71.72273002430056 72.535567451287264 68.653474755272327 70.763553348761718 68.437409704253469 71.18382590624374 66.370714765389891 67.446574034710551 68.1363656703586 64.998954944107254 68.971472308656359 71.579223611824929 69.395301602426457 73.157266807150108 68.943354206121029 68.005989052654741 68.288909266249988 72.655505954418715 68.926114907953632 68.69230572646353 71.851736945581052 69.770339267890137 67.237237273567246 71.50273707158108 70.769789120770028 70.580021559940704 70.525960247285823 66.551070936191408 70.088758142417078 68.261059853378654 64.792990643996575 72.295891837058434 72.361629767886484 66.700837073258484 74.367998844444259 69.633560237159358 69.023365601669468 66.542144140811516 72.228503202756642 70.27396063511766 68.31072361731681 69.93163519478874 71.944153183222753 72.144641447061659 69.299429521370669 65.275541194701816 70.165300669546568 69.297597356901306 70.680270974241452 66.446777850033172 Population Mean 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 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55 65.55

Histogram
min 57.62 57 Low Hi Interval CumFreq Freq
max 72.91 73 56 57 [56…57) 0 0 0.0000440159 0.0000440159 0
delta 1 57 58 [57…58) 1 0.001 0.0002432271 0.0001992113 0
58 59 [58…59) 3 0.002 0.0011260481 0.000882821 0
59 60 [59…60) 6 0.003 0.0043772368 0.0032511887 0
60 61 [60…61) 24 0.018 0.0143278444 0.0099506076 0.01
61 62 [61…62) 48 0.024 0.0396394139 0.0253115695 0.01
62 63 [62…63) 119 0.071 0.0931539013 0.0535144874 0.01
63 64 [63…64) 226 0.107 0.1871962674 0.0940423662 0.01
64 65 [64…65) 382 0.156 0.3245652611 0.1373689936 0.01
65 66 [65…66) 571 0.189 0.4913574887 0.1667922276 0.01
69.11 66 67 [66…67) 735 0.164 0.6596983092 0.1683408205 0.01
2.1977273816 67 68 [67…68) 864 0.129 0.8009292425 0.1412309333 0.01
68 69 [68…69) 942 0.078 0.8994193926 0.0984901501 0.01
69 70 [69…70) 979 0.037 0.9565106811 0.0570912884 0
65.55 70 71 [70…71) 995 0.016 0.9840180003 0.0275073192 0
2.3078423611 71 72 [71…72) 999 0.004 0.9950336821 0.0110156818 0
72 73 [72…73) 1000 0.001 0.9987000732 0.0036663911 0
73 74 [73…74) 1000 0 0.9997142336 0.0010141604 0
74 75 [74…75) 1000 0 0.9999473582 0.0002331246 0
75 76 [75…76) 1000 0 0.9999918883 0.0000445301 0
1000 mean counts for samples of size 100

Normal [57…58) [58…59) [59…60) [60…61) [61…62) [62…63) [63…64) [64…65) [65…66) [66…67) [67…68) [68…69) [69…70) [70…71) [71…72) [72…73) [73…74) [74…75) [75…76) 1.9921125708130685E-4 8.8282100460376225E-4 3.2511886833645805E-3 9.9506075746811154E-3 2.5311569538967453E-2 5.3514487353852808E-2 9.404236616752075E-2 0.13736899363605978 0.16679222763955848 0.16834082053343802 0.14123093325897007 9.8490150107868546E-2 5.7091288445204835E-2 2.7507319198796232E-2 1.101568 1848986936E-2 3.66639108202782E-3 1.0141604168724117E-3 2.3312459891799975E-4 4.4530088049832273E-5 Mean Counts [57…58) [58…59) [59…60) [60…61) [61…62) [62…63) [63…64) [64…65) [65…66) [66…67) [67…68) [68…69) [69…70) [70…71) [71…72) [72…73) [73…74) [74…75) [75…76) 1E-3 2E-3 3.0000000000000001E-3 1.7999999999999999E-2 2.4E-2 7.0999 999999999994E-2 0.107 0.156 0.189 0.16400000000000001 0.129 7.8E-2 3.6999999999999998E-2 1.6E-2 4.0000000000000001E-3 1E-3 0 0 0 CI 0 0 0 0 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0 0 0 0 0 0 0

WaterSafetyData
Before wells were dug After wells were dug – Villager provided samples After wells were dug – Team collected samples
E. coli per milliliter in drinking water
Windows User: these need to be between 0 and 150 and the unit is millions of bacteria per mlliliter E. coli per milliliter in drinking water E. coli per milliliter in drinking water
0 Mean 0 Mean 0 Mean 0
0 74.65 0 65.55 0 0
0 Median 0 Median 0 Median 0
0 0 0 1
0 SD 54 0 0
57 19.1845766124 59 1 42
60 46 1 54
63 61 2 23
63 21 62 45
64 84 65 63
65 79 66 42
65 81 70 70
66 46 70 60
66 87 71 60
67 58 72 60
67 64 74 40
67 67 74 49
67 70 74 55
68 23 75 47
69 47 79 69
69 59 83
69 60 59
70 72 65
70 37 77
70 68 66
72 49 50
73 64 58
73 100 74
73 35 64
73 61 79
73 45 62
74 70 73
74 89 66
74 58 48
75 79 63
75 80 81
75 61 85
75 61 62
75 58 64
76 39 83
76 68 76
76 69 50
76 73 86
77 99 82
77 73 39
77 107 46
78 59 36
78 97 81
78 91 72
79 60 92
79 35 74
79 58 81
79 68 42
79 66 53
80 40 76
80 20 64
80 50 68
80 82 60
80 66 49
81 87 59
81 53 19
81 84 86
81 62 96
81 58 39
81 72 92
82 102 72
82 87 80
83 37 101
83 85 109
84 67 69
84 82 67
84 63 60
84 73 83
84 84 87
84 47 73
85 90 77
85 77 84
85 73 84
85 86 58
85 73 51
85 76 76
86 85 88
86 70 71
87 89 88
87 49 75
87 92 70
88 91 68
88 55 95
88 72 49
88 59 70
88 89 79
90 56 80
90 86 81
90 99 101
92 68 78
93 92 43
95 89 107
96 49 68
97 67 75
99 107 84
Charts
First sample of 100
Second sample of 100
Sample of 20
Hypothesis Test
t-Test: Two-Sample Assuming Unequal Variances
Samples before wells All samples after wells
Mean 74.7 36.8
Variance 368.0 1243.5
Observations 100 120
Hypothesized Mean Difference 0
df 190
t Stat 10.10
P-value for one-tail < 0.001 t Critical one-tail 1.65 P-value for two-tail < 0.001 t Critical two-tail 1.97 AfterSamples 66 49 21 64 70 102 64 79 97 100 84 58 53 50 73 67 47 0 47 86 64 85 70 85 73 61 59 50 60 107 89 69 46 66 67 85 102 68 73 67 53 91 49 90 68 92 63 87 86 70 59 47 67 21 100 59 47 40 79 59 67 56 61 0 64 49 40 72 64 97 85 58 37 69 73 81 37 35 63 70 47 73 37 70 64 64 61 58 73 70 55 45 54 72 82 70 53 89 58 87 73 77 86 91 89 107 45 59 100 46 62 40 89 64 53 69 68 54 79 0 0 91 63 58 64 47 45 50 61 87 99 79 35 55 66 99 68 56 73 84 49 72 76 84 84 46 82 63 77 72 73 61 49 59 92 70 59 35 82 64 64 100 92 47 46 72 59 67 59 63 37 56 64 58 56 61 97 61 68 46 82 70 21 107 76 68 58 64 89 0 50 85 59 59 87 70 82 66 73 58 67 40 97 73 100 49 89 70 87 89 79 89 46 77 73 37 69 90 87 58 86 66 47 85 102 58 72 72 86 67 56 73 58 70 99 21 69 92 100 92 72 87 59 55 86 92 56 20 91 58 58 67 67 58 85 49 0 79 59 89 68 72 58 73 89 73 70 107 56 73 67 99 107 49 20 69 79 54 60 73 99 99 84 61 82 69 67 82 47 47 87 86 72 61 84 85 58 60 66 45 35 84 68 80 68 92 86 84 67 70 68 61 76 84 37 47 61 58 20 58 66 100 60 66 60 86 90 73 87 99 89 59 59 81 90 64 61 59 77 87 67 50 55 91 46 73 56 0 87 66 35 84 84 67 82 73 61 99 59 91 58 20 97 66 20 46 54 68 85 76 67 79 81 81 72 99 91 39 49 0 45 79 72 39 102 60 73 47 21 58 59 70 92 62 56 79 89 73 84 23 39 68 92 68 58 92 56 87 92 50 49 20 67 63 82 56 35 92 72 23 61 59 69 59 20 84 67 47 100 89 37 39 72 61 54 68 89 58 59 39 53 67 76 73 67 99 64 54 72 60 0 87 102 59 92 87 100 70 37 82 56 50 81 72 66 67 0 99 72 92 85 58 85 89 70 107 70 66 35 91 55 72 89 64 90 79 85 76 46 60 99 73 82 67 68 40 0 39 84 47 35 79 61 60 49 58 62 89 35 59 50 72 59 80 73 59 70 91 86 0 61 64 76 35 0 55 89 70 50 68 79 61 59 61 66 20 84 89 62 37 39 102 64 68 76 66 49 85 99 63 92 58 58 37 0 37 39 50 72 23 0 64 69 80 55 68 107 73 37 77 91 70 66 89 107 61 54 61 73 53 0 87 87 87 85 58 107 76 100 56 90 58 68 72 54 58 50 73 70 35 79 73 102 84 39 0 61 66 59 55 89 0 60 59 46 76 67 53 73 49 63 87 87 67 73 91 60 58 82 60 84 97 37 81 0 70 91 67 87 73 58 72 69 23 92 59 87 86 87 58 102 67 56 39 85 76 59 0 23 64 66 59 60 64 60 91 72 58 70 45 59 84 53 87 61 91 60 58 91 45 76 68 55 81 54 85 37 84 47 61 82 82 61 79 89 90 89 89 107 87 47 21 85 91 58 49 23 77 91 72 67 92 66 37 58 91 23 0 39 37 76 70 92 82 59 50 0 67 46 85 92 68 59 39 68 59 0 40 73 79 0 67 20 63 46 58 81 87 87 20 82 70 82 49 70 90 100 91 0 99 90 40 60 73 85 59 47 84 68 92 58 37 86 87 47 80 73 58 68 70 39 80 79 46 63 35 40 49 60 73 86 68 66 23 61 58 58 0 68 54 92 92 58 45 85 86 68 53 60 62 85 86 53 86 87 58 87 72 70 70 82 99 84 37 58 61 58 91 89 90 70 45 59 63 46 60 79 68 69 107 73 91 76 89 92 86 73 59 66 61 73 86 85 0 67 47 67 85 90 60 50 35 61 107 91 99 59 92 86 73 73 64 50 67 49 59 82 73 86 79 66 89 89 68 85 60 68 61 99 84 21 84 72 58 50 80 85 68 58 0 0 100 55 0 82 37 68 80 100 76 85 80 40 84 82 99 85 0 102 68 68 86 47 99 107 84 53 92 61 85 37 72 54 99 85 0 58 60 85 37 47 55 90 85 97 102 84 47 67 40 49 37 35 20 59 73 23 87 58 69 0 67 73 84 39 20 102 0 86 99 67 100 0 61 64 70 66 0 39 70 0 86 87 21 0 59 67 64 47 79 97 85 92 45 40 59 50 20 79 58 90 87 58 79 86 86 90 46 49 73 49 49 89 82 73 69 40 46 82 87 84 58 68 59 89 58 73 70 46 100 66 0 68 61 79 89 68 49 86 85 92 47 67 55 62 59 62 61 0 89 91 53 102 87 37 58 60 20 84 49 64 20 72 67 35 49 59 60 62 70 0 23 77 85 72 85 107 60 79 73 59 64 91 61 67 67 58 84 55 99 37 84 37 56 82 64 90 73 62 62 73 81 63 66 92 66 50 67 73 58 73 91 89 73 66 102 59 67 0 58 47 58 102 49 99 97 58 35 50 85 64 102 0 102 35 84 91 107 40 21 68 67 79 55 85 91 89 58 67 68 70 62 55 70 80 59 0 66 46 0 0 53 73 86 86 47 107 58 70 73 87 81 68 67 79 80 47 67 107 91 59 61 80 69 89 49 54 66 66 107 23 89 84 64 84 59 85 60 59 107 58 89 68 89 70 20 80 39 58 60 61 70 0 47 68 69 89 55 73 59 49 39 90 21 58 59 37 72 92 66 60 99 66 87 61 107 37 87 64 68 0 100 62 59 85 45 23 68 82 64 61 107 0 61 46 73 58 58 67 72 68 73 67 87 61 35 47 55 47 81 67 70 99 84 80 67 97 99 58 59 73 92 45 72 73 69 0 84 102 47 73 86 99 20 82 46 68 0 61 54 73 40 92 37 84 0 79 53 89 89 58 89 35 77 54 67 73 50 61 89 72 89 91 89 59 37 70 99 67 35 85 66 20 89 68 61 84 77 46 92 37 87 60 68 86 84 37 46 61 63 87 39 76 69 47 46 59 68 72 79 35 46 46 66 64 79 84 84 92 37 89 107 73 61 59 84 76 56 86 82 70 0 68 50 56 45 90 47 67 62 49 0 39 73 69 59 62 68 82 107 47 61 49 54 84 0 21 72 60 67 73 58 61 0 72 68 53 99 59 37 89 59 73 60 58 61 84 59 73 79 91 54 58 92 70 100 54 58 40 67 86 68 67 68 99 0 47 61 70 89 37 91 68 68 66 81 59 63 92 59 86 79 68 73 20 73 86 49 21 87 107 70 79 49 70 72 76 61 91 67 54 68 49 89 85 73 68 73 84 61 84 87 37 99 84 49 58 49 99 56 97 63 68 39 60 99 72 49 80 63 35 66 58 99 66 70 63 102 62 0 0 21 92 79 39 99 89 100 58 67 50 60 47 73 59 70 70 0 49 99 82 55 87 82 62 67 69 21 97 73 59 49 91 73 73 91 87 82 86 35 73 99 58 84 86 79 89 0 68 62 58 68 45 49 89 80 85 68 89 67 67 59 73 82 84 0 86 49 107 20 73 69 49 79 61 53 80 35 90 67 0 59 0 76 89 67 0 66 67 Read more Applied Sciences Architecture and Design Biology Business & Finance Chemistry Computer Science Geography Geology Education Engineering English Environmental science Spanish Government History Human Resource Management Information Systems Law Literature Mathematics Nursing Physics Political Science Psychology Reading Science Social Science Home Homework Answers Blog Archive Tags Reviews Contact twitterfacebook Copyright © 2021 SweetStudy.com