Preliminary Survey :
N <- 100
M = 900
Mbar <- M/N
f <- c(3/6, 2/6, 1/2, 1/2, 2/2, 1/2, 1/2, 0/2, 6/8, 0/2, 0/2, 8/8, 7/8, 4/4, 4/4, 4/4, 2/4, 1/6, 1/10, 2/4, 6/10, 6/10, 4/8, 8/12)
mi <- c(6, 6, 2, 2, 2, 2, 2, 2, 8, 2, 2, 8, 8, 4, 4, 4, 4,6,10,4,10, 10,8,12)
ai <- c(3, 2, 1, 1, 2, 1, 1, 0, 6, 0, 0, 8, 7, 4,4,4,2,1,1,2,6,6,4,8)
mbar <- mean(mi)
phat_per <- ai/mi
phat <- mean(phat_per)
# est variance :
sp2 <- sum((ai - phat*mi)^2)/(length(mi)-1)
B <- .1 # off by 5 pct : bound-of-err
D <- ((B^2)*mbar^2)/4
n_est <- (N*sp2)/(N*D + sp2)
n_est <- ceiling(n_est) #round to nxt whole Drawing Sample :
set.seed(123)
samp <- sample(1:100, 30)
samp |> as.data.frame() # True Order ## samp
## 1 31
## 2 79
## 3 51
## 4 14
## 5 67
## 6 42
## 7 50
## 8 43
## 9 97
## 10 25
## 11 90
## 12 69
## 13 57
## 14 9
## 15 72
## 16 26
## 17 7
## 18 95
## 19 87
## 20 36
## 21 78
## 22 93
## 23 76
## 24 15
## 25 32
## 26 84
## 27 82
## 28 41
## 29 23
## 30 27# samp |> as.data.frame() |> dplyr::arrange(samp)
df <- samp |>
as.data.frame() |>
dplyr::arrange(samp) |>
dplyr::mutate(
day = rep(c("Mon", "Tue", "Wed", "Thu", "Fri"), each = 6)
)mi <-
c(10, 10, 10, 8, 8,8,4,8,8,4,4,2,2,2,8,12,12,12,14,14,10,10,2,10,2,2,2,10,10,2)
df <- cbind(df, mi)
c <-
c(4,4,6,4,4,4,2,1,4,2,1,1,1,0,7,6,4,8,7,6,4,6,1,4,1,1,1,4,5,1)
df <- cbind(df, c)
p <- mean(c/mi) # amt chairs used
phat <- 1-p # amt not used
library(dplyr)
df <- df |> mutate(ai=mi-c)
df <- df |> dplyr::mutate(p=ai/mi)df <- df |> select(-c) |> select(day, samp, ai, mi, p)
df## day samp ai mi p
## 1 Mon 7 6 10 0.6000000
## 2 Mon 9 6 10 0.6000000
## 3 Mon 14 4 10 0.4000000
## 4 Mon 15 4 8 0.5000000
## 5 Mon 23 4 8 0.5000000
## 6 Mon 25 4 8 0.5000000
## 7 Tue 26 2 4 0.5000000
## 8 Tue 27 7 8 0.8750000
## 9 Tue 31 4 8 0.5000000
## 10 Tue 32 2 4 0.5000000
## 11 Tue 36 3 4 0.7500000
## 12 Tue 41 1 2 0.5000000
## 13 Wed 42 1 2 0.5000000
## 14 Wed 43 2 2 1.0000000
## 15 Wed 50 1 8 0.1250000
## 16 Wed 51 6 12 0.5000000
## 17 Wed 57 8 12 0.6666667
## 18 Wed 67 4 12 0.3333333
## 19 Thu 69 7 14 0.5000000
## 20 Thu 72 8 14 0.5714286
## 21 Thu 76 6 10 0.6000000
## 22 Thu 78 4 10 0.4000000
## 23 Thu 79 1 2 0.5000000
## 24 Thu 82 6 10 0.6000000
## 25 Fri 84 1 2 0.5000000
## 26 Fri 87 1 2 0.5000000
## 27 Fri 90 1 2 0.5000000
## 28 Fri 93 6 10 0.6000000
## 29 Fri 95 5 10 0.5000000
## 30 Fri 97 1 2 0.5000000