Sampling

Code for Quiz 11.

Load the R package we will use.
```
library(tidyverse)
library(moderndive)
```

Quiz questions

Question

7.2.4 in Modern Dive with different sample sizes and repetitions

Make sure you have installed and loaded the tidyverse and the moderndive packages
Fill in the blanks
Put the command you use in the Rchunks in your Rmd file for this quiz.
Modify the code for comparing differnet sample sizes from the virtual bowl
Segment 1: sample size = 26

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

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 variable red / 26
Assign the output to virtual_prop_red_26

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

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

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

start with virtual_samples_55 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 / 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)

2.c) 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 balls that were red", title = "55")

Segment 3: sample size = 110

3.a) Take 1180 samples of size of 110 instead of 1000 replicates of size 50. Assign the output to virtual_samples_110

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

3.b) Compute 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 the output to virtual_prop_red_110

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_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(x = 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 deviations for your three sets of 1180 values of prop_red using the standard deviation

n = 26

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

# A tibble: 1 × 1
      sd
   <dbl>
1 0.0973

n = 55

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

# A tibble: 1 × 1
      sd
   <dbl>
1 0.0632

n = 110

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

# A tibble: 1 × 1
      sd
   <dbl>
1 0.0453

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", "2022-04-19-sampling"))