Sampling

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

1. Load the R package we will use.

library(tidyverse)
library(moderndive)

2. Quiz questions

• Replace all the instances of ‘SEE QUIZ’. These are inputs 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 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 different sample sizes from the virtual bowl

Segment 1: Sample Size = 30

1.a) Take 1200 samples of size of 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.b) 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 the red balls
• create variable prop_red equal to 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.c) Plot distribution of virtual_prop_red_30 via a histogram

Use labs to

• label x axis = “Proportion of 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

2.a) Take 1200 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 = 1200)

2.b) 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 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 = 120

3.a) Take 1200 samples of size of 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)

3.b) Compute resulting 1200 replicates of proportion red

• start with virtual_samples_120 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 / 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)

3.c) Plot distribution of virtual_prop_red_120 via a histogram

use labs to

• label 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 120 balls that were red", title = "120") 

---

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 x 1
      sd
   <dbl>
1 0.0885

n = 55

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

# A tibble: 1 x 1
      sd
   <dbl>
1 0.0611

n = 120

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

# A tibble: 1 x 1
      sd
   <dbl>
1 0.0426

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