Load the R packages we will use

library(tidyverse)
library(moderndive)

Question: Modify the code for comparing different sample sizes from the virtual bowl

Segment 1: Sample size = 26

1A.

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

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

1B.

Compute the resulting 1180 replicates of proportion Red.
Start with virtual_samples_26 THEN
group_by replicate THEN
Create variable red equal to the sum of all the red balls
Create variable prop_red equal to the variable red/26
Assign the output to virtual_prop_red_26

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

1C.

Plot distribution of virtual_prop_red_26 via a histogram
Use labs to:
- label x-axis = “Proportion of 26 balls that were red”
- create title = “26”

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")

Segment 2: Sample size = 55

2A.

Take 1180 sample of size 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)

2B.

Compute resulting 1180 replicates of proportion Red
Start with virtual_samples_55 THEN
group_by replicate THEN
Create variable read equal to them sum of all red balls
Create variable prop_red equal to variable red/55
Assign the output to virtual_prop_red_55

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

2C.

Plot distribution of virtual_prop_red_55 via a histogram
Use labs to:
- label x-axis = “Proportion of 55 balls that were red”
- create title = “55”

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

Segment 3: Sample size = 110

3A.

Take 1180 samples of size 110 instead of 1000 replicates of size 100
Assign the output to virtual_samples_110

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

3B.

Compute the resulting 1180 replicates of proportion Red
Start with virtual_samples_110 THEN
group_by replicate THEN
Create variable red equal to the sum of all the red balls
Create variable prop_red equal to variable red/110
Assign output to virtual_prop_red_110

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

3C.

Plot distribution of virtual_prop_red_110 via a histogram
Use labs to:
- label x-axis = “Proportion of 110 balls that were red”
- create title = “110”

ggplot(virtual_prop_red_110, aes(prop_red)) +
  geom_histogram(binwidth = 0.05, boundary = 0.4, color = "white") +
  labs(x = "Proportion of 110 balls that were red", title = "110")

Calculate the standard deviation for samples n = 26, n = 55, and n = 110 of 1180 values of prop_red using standard deviation

n = 26

virtual_prop_red_26 %>% 
  summarise(sd = sd(prop_red))

# A tibble: 1 x 1
      sd
   <dbl>
1 0.0929

n = 55

virtual_prop_red_55 %>% 
  summarise(sd = sd(prop_red))

# A tibble: 1 x 1
      sd
   <dbl>
1 0.0634

n = 110

virtual_prop_red_110 %>% 
  summarise(sd = sd(prop_red))

# A tibble: 1 x 1
      sd
   <dbl>
1 0.0438

The distribution with sample size, n = 110, has the smallest standard deviation (spread) around the estimated proportion of red balls.

ggsave(filename = "preview.png", path = here::here("_posts", "2022-04-14-sampling"))

Sampling

Segment 1: Sample size = 26

Segment 2: Sample size = 55

Segment 3: Sample size = 110