Load the R packages we will use.

library(tidyverse)
library(moderndive)

Quiz questions

Replace all the instances of ‘SEE QUIZ’. These are inpute from your moodle quiz.
Replace all the instances of ‘???’. These are answers on your moodle quiz.
Run all the individual code chunks to make sure the answers in this file correspond with your quiz answers.
After you check all your code chunks run then you can knit it. It won’t knit until the ??? are replaced.
The quiz assumes that you have watched the videos and worked through the examples in Chapter 7 of ModernDive.

Question: 7.2.4 in Modern Dive with different sample sizes and repetitions

Make sure you have installed and loaded the tidyverse and 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 different sample sizes from the virtual bowl

Segment 1: sample size = 30

1. Take 1200 samples of sixe 30 instead of 1000 replicates of size 25 from the bowl dataset. Assign the output to virtual_samples_30.

virtual_samples_30  <- bowl  %>% 
rep_sample_n(size = 30, reps = 1200)

1. Compute resulting 1200 replicates of proportion red.

Start with virtual_samples_30 THEN
group_by replicate THEN
Create variable red equal to the sum of all red balls.
create variable prop_red to equal variable red/30.
Assign the output to virtual_prop_red_30.

virtual_prop_red_30 <- virtual_samples_30 %>% 
  group_by(replicate) %>% 
  summarize(red = sum(color == "red")) %>% 
  mutate(prop_red = red / 30)

1. Plot distribution of virtual_prop_red_30 via a histogram, use labs to:

Label the x axis = “Proportion fo 30 balls that were red”
Create title = “30”

ggplot(virtual_prop_red_30, aes(x = prop_red)) +
  geom_histogram(binwidth = 0.05, boundary = 0.4, color = "white") +
  labs(x = "Proportion of 30 balls that were red", title = "30")

Segment 2: sample size = 55

1. Take 1200 samples 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 = 1200)

1. Compute resulting 1200 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 the 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)

1. Plot the distribution of virtual_prop_red_55 via a histogram, use labs to:

Label the 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 = 120”

1. Take 1200 samples of size 120 instead of 1000 replicates of size 50. Assign the output to virtual_samples_120.

virtual_samples_120  <- bowl  %>% 
rep_sample_n(size = 120, reps = 1200)

1. Compute resulting 1200 replicates of proportion red.

Start with virtual_samples_120 THEN
group_by replicate THEN
Create variable red equal to the sym of all the red balls.
Create variable prop_red equal to variable red/120.
Assign the output to virtual_prop_red_120.

virtual_prop_red_120 <- virtual_samples_120 %>% 
  group_by(replicate) %>% 
  summarize(red = sum(color == "red")) %>% 
  mutate(prop_red = red / 120)

1. Plot the dsitribution of virtual_prop_red_120 via a histogram, use labs to:

Label the x axis = “Proportion of 120 balls that were red”
Create title = “120”

ggplot(virtual_prop_red_120, aes(x = prop_red)) +
  geom_histogram(binwidth = 0.05, boundary = 0.4, color = "white") +
  labs(x = "Proportion of 114 balls that were red", title = "120")

ggsave(filename = "preview.png", 
       path = here::here("_posts", "2022-04-19-sampling"))

Calculate the standard deviations for your three sets of 1200 values of prop_red using the standard deviation.

n = 30

virtual_prop_red_30 %>% 
  summarize(sd = sd(prop_red))

# A tibble: 1 × 1
      sd
   <dbl>
1 0.0856

n = 55

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

# A tibble: 1 × 1
      sd
   <dbl>
1 0.0668

n = 120

virtual_prop_red_120 %>% 
  summarize(sd = sd(prop_red))

# A tibble: 1 × 1
      sd
   <dbl>
1 0.0421

The distribution with sample size n = 120, has the smallest standard deviation (spread) around the estimated proportion of red balls.

Sampling