Sampling

Based on Chapter 7 of ModernDive. Code for Quiz 11.

Load Libraries

library(tidyverse)
library(moderndive)
library(ggplot2)
library(here)

1.a

Take 1180 samples of size of 26 instead of 1000 replicates of size 25 from the bowl dataset. Assign the output to virtual_samples_26

virtual_samples_26 <- bowl %>% 
  rep_sample_n(size = 26, reps = 1180)

1.b

Compute resulting 1180 replicates of proportion red

virtual_prop_red_26 <- virtual_samples_26 %>% 
  group_by(replicate) %>% 
  summarize(red = sum(color == "red")) %>% 
  mutate(prop_red = red / 26)

1.c

Plot distribution of virtual_prop_red_26 via a histogram use labs to

ggplot(virtual_prop_red_26, aes(x = prop_red)) +
  geom_histogram(binwidth = 0.05, boundary = 0.4, color = "white") +
  labs(x = "Proportion of 26 balls that were red", title = "26") 

2.a

Take 1180 samples of size of 55 instead of 1000 replicates of size 50. Assign the output to virtual_samples_55

virtual_samples_55 <- bowl %>% 
  rep_sample_n(size = 55, reps = 1180)

2.b

Compute resulting 1180 replicates of proportion red

virtual_prop_red_55 <- virtual_samples_55 %>% 
  group_by(replicate) %>% 
  summarize(red = sum(color == "red")) %>% 
  mutate(prop_red = red / 55)

2.c

Plot distribution of virtual_prop_red_55 via a histogram use labs to

ggplot(virtual_prop_red_55, aes(x = prop_red)) +
  geom_histogram(binwidth = 0.05, boundary = 0.4, color = "white") +
  labs(x = "Proportion of 55 balls that were red", title = "55") 

3.a

Take 1180 samples of size of 110 instead of 1000 replicates of size 50. Assign the output to virtual_samples_55

virtual_samples_110 <- bowl %>% 
  rep_sample_n(size = 110, reps = 1180)

3.b

Compute resulting 1180 replicates of proportion red

virtual_prop_red_110 <- virtual_samples_110 %>% 
  group_by(replicate) %>% 
  summarize(red = sum(color == "red")) %>% 
  mutate(prop_red = red / 110)

3.c

Plot distribution of virtual_prop_red_55 via a histogram use labs to

ggplot(virtual_prop_red_110, aes(x = prop_red)) +
  geom_histogram(binwidth = 0.05, boundary = 0.4, color = "white") +
  labs(x = "Proportion of 110 balls that were red", title = "110") 
# save plot for post preview
ggsave("prop_of_110.png", 
       path = here("_posts", "2021-05-04-sampling"))

Standard Deviations

n = 26
virtual_prop_red_26 %>% 
  summarise(sd = sd(prop_red))
# A tibble: 1 x 1
      sd
   <dbl>
1 0.0969
n = 55
virtual_prop_red_55 %>% 
  summarise(sd = sd(prop_red))
# A tibble: 1 x 1
      sd
   <dbl>
1 0.0661
n = 110
virtual_prop_red_110 %>% 
  summarise(sd = sd(prop_red))
# A tibble: 1 x 1
      sd
   <dbl>
1 0.0448

Footnotes