c:ms:2025:lecture_note_week_02
This is an old revision of the document!
rnorm2 <- function(n,mean,sd) { mean+sd*scale(rnorm(n)) }
set.seed(1001)
df <- rnorm2(600000, 100, 10)
head(df)
n <- 1600
iter <- 10000
means <- rep (NA, iter)
for(i in 1:iter){
means[i] = mean(sample(df, n))
}
# means
hist(means)
mean(means)
sd(means)
m.the <- 100
se.the <- 10/sqrt(n)
m.the
se.the
s.s <-107.5
p.val <- (m.the-s.s)/se.the
p.val <- pnorm(p.val)
p.val
# proportions
#
p <- 0.55 # 민경욱 지지율 가정정
q <- 1-p
set.seed(1001)
el <- sample.int(2, 400000, replace=TRUE, prob=c(p, q))
table(el)
prop.table(table(el))
n <- 10000
iter <- 1000
els <- rep (NA, iter)
prop <- rep (NA, iter)
for(i in 1:iter){
els <- sample(el, n, replace=FALSE)
prop[i] <- table(els)[1]/(table(els)[1]+table(els)[2])
}
els
prop
hist(prop)
pre.vote <- 0.430
m.emp <- mean(prop)
m.theo <- p
m.emp
m.theo
se.emp <- sd(prop)
se.theo <- sqrt((p*q)/n)
se.emp
se.theo
m.theo
pre.vote
m.theo-pre.vote
se.theo
# install.packages("Rmpfr")
library(Rmpfr)
.N <- function(.) mpfr(., precBits = 100)
zval <- (m.theo-pre.vote)/se.theo
zval
p.val <- pnorm(zval, lower.tail = F)
p.val # limit in 1e-217
p.lot <- 1/1000000 # lotto를 맞을 확률을 100만분의 1이라고 하면
p.lot^21*7 # lotto를 연거퍼서 21일동안 맞을 확률의 일곱배배; not 지구나이 . . . .
> # proportions
> #
> p <- 0.55 # 민경욱 지지율 가정정
> q <- 1-p
>
> set.seed(1001)
> el <- sample.int(2, 400000, replace=TRUE, prob=c(p, q))
> table(el)
el
1 2
219618 180382
> prop.table(table(el))
el
1 2
0.549045 0.450955
>
> n <- 10000
> iter <- 1000
> els <- rep (NA, iter)
> prop <- rep (NA, iter)
> for(i in 1:iter){
+ els <- sample(el, n, replace=FALSE)
+ prop[i] <- table(els)[1]/(table(els)[1]+table(els)[2])
+ }
> els
[1] 1 1 2 1 2 2 2 2 1 1 2 1 2 1 1 2 1 2 1 2 1 1 2 1 2 2 1 1 2 2 2 1 1 2
[35] 1 1 1 1 2 1 1 1 1 2 1 2 1 2 1 2 2 2 2 1 1 1 1 2 1 1 2 1 2 2 1 1 1 2
[69] 2 1 2 1 2 1 2 1 1 1 2 1 1 1 1 2 1 1 2 1 1 1 2 2 1 2 1 2 2 1 1 1 2 2
[103] 1 2 2 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 2 1 1 1 2 2 1 2 2 1 1 1 2
[137] 2 1 2 1 2 2 2 1 1 2 1 2 2 1 2 2 1 1 2 2 2 1 1 2 1 2 1 2 2 1 1 2 1 2
[171] 1 2 2 2 2 1 2 1 2 1 1 2 1 2 2 1 1 1 2 1 1 2 1 2 2 1 2 2 1 2 2 2 2 1
[205] 1 2 1 1 2 1 2 1 1 2 1 1 2 2 1 2 1 1 1 2 1 1 1 1 1 1 1 1 1 2 2 2 1 1
[239] 1 2 1 2 1 1 1 1 1 1 1 2 1 2 1 2 1 2 1 2 2 2 2 2 1 1 2 2 1 1 1 1 1 2
[273] 1 2 1 2 2 2 1 2 1 1 1 1 1 2 1 2 2 2 2 2 2 2 1 1 2 2 1 2 1 1 1 1 2 1
[307] 1 2 1 1 1 2 2 1 1 1 1 1 1 2 1 2 1 2 1 2 1 1 2 1 2 1 1 1 2 1 2 2 1 2
[341] 1 2 2 2 2 1 2 1 2 1 2 1 2 2 1 2 2 1 1 1 2 2 1 2 1 2 2 2 1 2 2 2 1 1
[375] 1 1 1 1 2 1 2 2 1 1 2 2 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 1 1 2 1 1 1
[409] 1 1 2 2 2 2 2 2 1 2 2 1 1 1 1 2 2 1 1 2 1 2 2 1 1 1 1 2 2 2 1 1 2 1
[443] 1 2 1 2 1 1 1 2 2 1 1 1 1 1 2 1 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 2 2
[477] 2 1 1 1 2 1 2 1 2 1 1 2 2 1 2 2 1 1 1 1 2 2 1 1 2 1 1 2 2 1 2 2 2 2
[511] 1 2 1 1 2 1 2 2 1 2 2 1 2 2 2 2 1 1 1 2 2 2 2 2 1 1 1 2 1 2 1 1 2 1
[545] 2 1 1 2 2 1 1 2 1 1 1 2 1 1 2 2 2 1 1 2 1 2 2 2 2 2 1 1 2 1 1 2 2 2
[579] 1 1 1 1 1 1 2 2 2 2 1 1 1 1 1 1 2 2 1 2 1 2 2 1 1 1 1 2 1 1 2 2 2 1
[613] 2 1 2 2 2 2 2 2 2 2 1 1 2 1 2 1 1 2 1 2 2 1 2 2 1 1 2 1 2 1 2 2 2 2
[647] 1 2 1 2 2 1 1 2 2 2 1 1 1 2 2 1 2 2 1 2 2 1 2 1 1 1 2 1 1 1 1 1 1 1
[681] 2 2 1 1 2 1 1 1 1 2 1 1 1 1 1 2 1 1 2 2 2 2 1 1 1 1 2 2 1 1 1 2 2 1
[715] 1 1 1 2 2 1 2 1 1 2 1 1 2 1 2 1 2 1 2 1 1 2 2 1 1 1 2 2 1 2 1 2 1 2
[749] 1 1 1 1 2 1 2 2 2 1 1 1 1 1 2 1 2 2 1 2 1 1 1 2 1 2 2 1 1 2 1 1 2 1
[783] 1 2 1 1 1 2 1 2 1 1 1 1 2 2 1 1 1 1 1 1 2 1 1 2 1 1 1 2 1 2 1 1 1 1
[817] 1 2 1 2 2 1 1 2 2 2 1 2 1 2 1 2 2 1 2 2 1 2 1 1 2 2 1 2 1 1 2 2 1 2
[851] 1 1 2 2 2 1 2 1 1 1 1 1 1 1 2 1 1 2 1 2 1 2 1 1 1 2 1 1 1 1 2 1 1 1
[885] 2 1 2 2 1 1 2 1 2 1 2 1 2 1 1 1 1 2 1 2 1 1 1 1 2 1 1 1 1 1 1 1 2 2
[919] 2 1 1 2 1 2 1 1 1 2 1 1 1 2 2 1 2 1 2 2 1 1 1 2 1 2 2 2 2 2 2 1 1 2
[953] 1 2 1 1 2 1 1 1 2 1 2 2 2 1 2 2 1 1 2 2 1 2 1 2 1 1 2 1 1 2 2 2 2 1
[987] 2 1 2 1 1 1 1 1 1 2 2 1 2 2
[ reached getOption("max.print") -- omitted 9000 entries ]
> prop
[1] 0.5528 0.5496 0.5470 0.5475 0.5522 0.5519 0.5442 0.5497 0.5461
[10] 0.5456 0.5419 0.5423 0.5439 0.5588 0.5459 0.5497 0.5402 0.5444
[19] 0.5637 0.5526 0.5459 0.5456 0.5567 0.5503 0.5450 0.5533 0.5501
[28] 0.5476 0.5556 0.5511 0.5548 0.5590 0.5463 0.5475 0.5551 0.5499
[37] 0.5419 0.5507 0.5485 0.5414 0.5508 0.5500 0.5445 0.5523 0.5548
[46] 0.5437 0.5517 0.5414 0.5535 0.5477 0.5613 0.5500 0.5507 0.5493
[55] 0.5543 0.5498 0.5501 0.5429 0.5490 0.5484 0.5446 0.5612 0.5464
[64] 0.5546 0.5470 0.5476 0.5491 0.5484 0.5509 0.5461 0.5412 0.5418
[73] 0.5511 0.5484 0.5481 0.5446 0.5490 0.5507 0.5432 0.5482 0.5532
[82] 0.5491 0.5573 0.5502 0.5488 0.5424 0.5520 0.5598 0.5480 0.5514
[91] 0.5550 0.5460 0.5516 0.5521 0.5567 0.5487 0.5524 0.5471 0.5537
[100] 0.5524 0.5500 0.5503 0.5523 0.5528 0.5511 0.5505 0.5547 0.5447
[109] 0.5539 0.5470 0.5531 0.5561 0.5588 0.5534 0.5474 0.5467 0.5455
[118] 0.5452 0.5541 0.5429 0.5460 0.5483 0.5447 0.5506 0.5453 0.5551
[127] 0.5465 0.5379 0.5520 0.5476 0.5476 0.5500 0.5542 0.5484 0.5613
[136] 0.5519 0.5513 0.5417 0.5401 0.5501 0.5530 0.5429 0.5421 0.5479
[145] 0.5421 0.5482 0.5479 0.5560 0.5522 0.5555 0.5580 0.5530 0.5444
[154] 0.5541 0.5492 0.5464 0.5446 0.5485 0.5515 0.5437 0.5436 0.5508
[163] 0.5460 0.5597 0.5462 0.5434 0.5463 0.5530 0.5479 0.5544 0.5529
[172] 0.5449 0.5460 0.5517 0.5509 0.5499 0.5517 0.5496 0.5494 0.5521
[181] 0.5493 0.5448 0.5442 0.5529 0.5506 0.5446 0.5496 0.5540 0.5467
[190] 0.5584 0.5593 0.5471 0.5495 0.5536 0.5514 0.5459 0.5562 0.5485
[199] 0.5425 0.5494 0.5466 0.5514 0.5417 0.5436 0.5482 0.5542 0.5450
[208] 0.5505 0.5491 0.5479 0.5450 0.5566 0.5458 0.5542 0.5516 0.5406
[217] 0.5491 0.5528 0.5510 0.5507 0.5578 0.5453 0.5481 0.5503 0.5523
[226] 0.5484 0.5482 0.5432 0.5493 0.5551 0.5560 0.5484 0.5411 0.5515
[235] 0.5504 0.5449 0.5463 0.5533 0.5507 0.5471 0.5419 0.5426 0.5471
[244] 0.5505 0.5501 0.5553 0.5603 0.5529 0.5419 0.5412 0.5333 0.5470
[253] 0.5575 0.5562 0.5504 0.5542 0.5585 0.5466 0.5463 0.5427 0.5517
[262] 0.5565 0.5490 0.5481 0.5559 0.5556 0.5507 0.5358 0.5619 0.5431
[271] 0.5480 0.5486 0.5483 0.5451 0.5467 0.5475 0.5459 0.5475 0.5428
[280] 0.5411 0.5496 0.5476 0.5545 0.5472 0.5529 0.5544 0.5472 0.5540
[289] 0.5465 0.5497 0.5475 0.5540 0.5486 0.5494 0.5496 0.5455 0.5572
[298] 0.5478 0.5383 0.5432 0.5439 0.5465 0.5401 0.5508 0.5464 0.5507
[307] 0.5459 0.5468 0.5457 0.5476 0.5494 0.5465 0.5517 0.5551 0.5491
[316] 0.5462 0.5476 0.5466 0.5454 0.5518 0.5440 0.5486 0.5518 0.5372
[325] 0.5508 0.5410 0.5443 0.5511 0.5466 0.5386 0.5429 0.5609 0.5477
[334] 0.5484 0.5546 0.5478 0.5402 0.5484 0.5455 0.5470 0.5470 0.5484
[343] 0.5573 0.5482 0.5438 0.5474 0.5447 0.5476 0.5608 0.5563 0.5460
[352] 0.5485 0.5549 0.5512 0.5513 0.5586 0.5520 0.5469 0.5475 0.5529
[361] 0.5470 0.5552 0.5564 0.5525 0.5481 0.5415 0.5458 0.5481 0.5536
[370] 0.5432 0.5374 0.5572 0.5496 0.5492 0.5512 0.5429 0.5526 0.5465
[379] 0.5536 0.5517 0.5470 0.5539 0.5461 0.5502 0.5552 0.5458 0.5480
[388] 0.5569 0.5485 0.5438 0.5472 0.5470 0.5457 0.5462 0.5527 0.5447
[397] 0.5458 0.5528 0.5503 0.5430 0.5394 0.5509 0.5519 0.5438 0.5510
[406] 0.5447 0.5500 0.5430 0.5476 0.5417 0.5437 0.5470 0.5495 0.5444
[415] 0.5464 0.5524 0.5491 0.5437 0.5534 0.5524 0.5481 0.5460 0.5439
[424] 0.5560 0.5409 0.5486 0.5509 0.5520 0.5496 0.5531 0.5440 0.5563
[433] 0.5455 0.5421 0.5427 0.5441 0.5508 0.5467 0.5468 0.5502 0.5584
[442] 0.5511 0.5495 0.5468 0.5444 0.5359 0.5475 0.5475 0.5496 0.5470
[451] 0.5492 0.5486 0.5638 0.5512 0.5479 0.5505 0.5484 0.5509 0.5521
[460] 0.5494 0.5504 0.5503 0.5487 0.5435 0.5485 0.5397 0.5505 0.5527
[469] 0.5447 0.5576 0.5565 0.5454 0.5431 0.5525 0.5369 0.5554 0.5511
[478] 0.5394 0.5604 0.5464 0.5475 0.5466 0.5491 0.5511 0.5488 0.5445
[487] 0.5536 0.5477 0.5485 0.5470 0.5493 0.5496 0.5550 0.5473 0.5444
[496] 0.5557 0.5446 0.5526 0.5582 0.5505 0.5483 0.5449 0.5496 0.5555
[505] 0.5505 0.5538 0.5535 0.5535 0.5441 0.5541 0.5475 0.5521 0.5484
[514] 0.5467 0.5547 0.5479 0.5511 0.5511 0.5582 0.5503 0.5446 0.5499
[523] 0.5423 0.5498 0.5507 0.5486 0.5536 0.5431 0.5454 0.5535 0.5507
[532] 0.5474 0.5466 0.5433 0.5515 0.5419 0.5485 0.5493 0.5545 0.5524
[541] 0.5456 0.5509 0.5531 0.5499 0.5404 0.5463 0.5497 0.5486 0.5459
[550] 0.5449 0.5444 0.5433 0.5501 0.5369 0.5469 0.5518 0.5489 0.5439
[559] 0.5540 0.5442 0.5544 0.5330 0.5467 0.5515 0.5488 0.5593 0.5434
[568] 0.5513 0.5498 0.5498 0.5446 0.5532 0.5499 0.5472 0.5528 0.5487
[577] 0.5535 0.5541 0.5497 0.5481 0.5498 0.5395 0.5489 0.5461 0.5442
[586] 0.5552 0.5445 0.5539 0.5437 0.5482 0.5461 0.5535 0.5527 0.5497
[595] 0.5490 0.5523 0.5556 0.5549 0.5456 0.5423 0.5588 0.5438 0.5427
[604] 0.5485 0.5501 0.5494 0.5545 0.5521 0.5475 0.5472 0.5538 0.5426
[613] 0.5446 0.5452 0.5514 0.5475 0.5401 0.5440 0.5532 0.5538 0.5492
[622] 0.5567 0.5568 0.5521 0.5483 0.5427 0.5449 0.5508 0.5384 0.5475
[631] 0.5518 0.5495 0.5515 0.5450 0.5473 0.5429 0.5516 0.5513 0.5485
[640] 0.5578 0.5499 0.5572 0.5405 0.5505 0.5539 0.5468 0.5569 0.5579
[649] 0.5463 0.5531 0.5435 0.5494 0.5512 0.5425 0.5481 0.5511 0.5519
[658] 0.5438 0.5529 0.5539 0.5413 0.5515 0.5618 0.5530 0.5451 0.5542
[667] 0.5548 0.5459 0.5486 0.5517 0.5590 0.5432 0.5465 0.5589 0.5454
[676] 0.5492 0.5512 0.5513 0.5488 0.5432 0.5477 0.5441 0.5506 0.5529
[685] 0.5518 0.5506 0.5526 0.5484 0.5410 0.5537 0.5445 0.5535 0.5513
[694] 0.5501 0.5520 0.5432 0.5540 0.5458 0.5533 0.5481 0.5533 0.5476
[703] 0.5383 0.5363 0.5444 0.5512 0.5572 0.5452 0.5388 0.5513 0.5504
[712] 0.5489 0.5524 0.5479 0.5588 0.5474 0.5408 0.5487 0.5514 0.5530
[721] 0.5572 0.5524 0.5503 0.5532 0.5424 0.5565 0.5537 0.5437 0.5455
[730] 0.5398 0.5512 0.5487 0.5419 0.5514 0.5615 0.5523 0.5489 0.5468
[739] 0.5438 0.5414 0.5495 0.5482 0.5426 0.5473 0.5511 0.5401 0.5562
[748] 0.5505 0.5499 0.5488 0.5404 0.5472 0.5488 0.5504 0.5551 0.5462
[757] 0.5578 0.5488 0.5567 0.5488 0.5524 0.5547 0.5538 0.5559 0.5440
[766] 0.5388 0.5448 0.5436 0.5408 0.5509 0.5520 0.5422 0.5433 0.5463
[775] 0.5521 0.5439 0.5434 0.5497 0.5427 0.5480 0.5506 0.5499 0.5572
[784] 0.5572 0.5497 0.5522 0.5461 0.5431 0.5494 0.5498 0.5533 0.5450
[793] 0.5512 0.5521 0.5491 0.5516 0.5468 0.5491 0.5428 0.5529 0.5487
[802] 0.5407 0.5519 0.5464 0.5463 0.5547 0.5480 0.5426 0.5489 0.5476
[811] 0.5488 0.5453 0.5509 0.5455 0.5402 0.5462 0.5425 0.5532 0.5529
[820] 0.5474 0.5513 0.5430 0.5481 0.5470 0.5449 0.5434 0.5396 0.5402
[829] 0.5575 0.5474 0.5550 0.5445 0.5527 0.5507 0.5470 0.5445 0.5519
[838] 0.5493 0.5491 0.5473 0.5551 0.5515 0.5516 0.5579 0.5608 0.5480
[847] 0.5539 0.5491 0.5523 0.5527 0.5422 0.5414 0.5492 0.5479 0.5441
[856] 0.5497 0.5521 0.5572 0.5511 0.5477 0.5386 0.5545 0.5544 0.5504
[865] 0.5490 0.5414 0.5515 0.5431 0.5479 0.5485 0.5406 0.5563 0.5492
[874] 0.5564 0.5432 0.5504 0.5412 0.5496 0.5476 0.5458 0.5477 0.5505
[883] 0.5550 0.5508 0.5471 0.5533 0.5555 0.5446 0.5519 0.5454 0.5450
[892] 0.5553 0.5515 0.5559 0.5432 0.5392 0.5556 0.5437 0.5486 0.5530
[901] 0.5537 0.5436 0.5443 0.5520 0.5509 0.5528 0.5539 0.5563 0.5439
[910] 0.5565 0.5415 0.5539 0.5474 0.5485 0.5578 0.5473 0.5524 0.5475
[919] 0.5468 0.5424 0.5539 0.5400 0.5372 0.5507 0.5374 0.5595 0.5484
[928] 0.5466 0.5457 0.5495 0.5490 0.5455 0.5411 0.5393 0.5550 0.5450
[937] 0.5614 0.5449 0.5460 0.5459 0.5546 0.5452 0.5459 0.5471 0.5488
[946] 0.5532 0.5412 0.5480 0.5522 0.5489 0.5508 0.5480 0.5521 0.5465
[955] 0.5511 0.5440 0.5533 0.5435 0.5500 0.5481 0.5488 0.5519 0.5506
[964] 0.5453 0.5458 0.5466 0.5375 0.5546 0.5509 0.5549 0.5465 0.5457
[973] 0.5533 0.5496 0.5473 0.5437 0.5461 0.5393 0.5488 0.5453 0.5464
[982] 0.5435 0.5439 0.5438 0.5472 0.5436 0.5403 0.5454 0.5434 0.5473
[991] 0.5475 0.5497 0.5484 0.5533 0.5515 0.5534 0.5519 0.5581 0.5487
[1000] 0.5558
> hist(prop)
>
>
> pre.vote <- 0.430
> m.emp <- mean(prop)
> m.theo <- p
> m.emp
[1] 0.5489203
> m.theo
[1] 0.55
>
> se.emp <- sd(prop)
> se.theo <- sqrt((p*q)/n)
> se.emp
[1] 0.0048724
> se.theo
[1] 0.004974937
>
>
> m.theo
[1] 0.55
> pre.vote
[1] 0.43
> m.theo-pre.vote
[1] 0.12
> se.theo
[1] 0.004974937
> # install.packages("Rmpfr")
>
> library(Rmpfr)
> .N <- function(.) mpfr(., precBits = 100)
>
> zval <- (m.theo-pre.vote)/se.theo
> zval
[1] 24.12091
> p.val <- pnorm(zval, lower.tail = F)
> p.val # limit in 1e-217
[1] 7.54328e-129
>
> p.lot <- 1/1000000 # lotto를 맞을 확률을 100만분의 1이라고 하면
> p.lot^21*7 # lotto를 연거퍼서 21일동안 맞을 확률의 일곱배배; not 지구나이 . . . .
[1] 7e-126
>
c/ms/2025/lecture_note_week_02.1741736766.txt.gz · Last modified: by hkimscil