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 though the examples in Chapter 7 of ModernDive.

#Question 7.2.4 in Modern Dive with different sample sizes and repetititions

-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 Sement 1: sample size = 28

1.a)Take 1150 samples of size of 28 instead of 1000 replicates of size 25 from the bowl dataset. Assign the output to virtual_samples_28

virtual_samples_28 <- bowl %>% 
  rep_sample_n(size = 28, reps = 1150)

1.b)Compute resulting 1150 replicates of proportion red

-Start with virtual_samples_28 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 / 28

-Assign the output to virtual_prop_red_28

virtual_prop_red_28 <- virtual_samples_28 %>% 
  group_by(replicate) %>% 
  summarize(red = sum(color == "red")) %>% 
  mutate(prop_red = red / 28)

1.c) Plot distribution of virtual_prop_red_28 via a histogram use labs to

-label x axis = “Proportion of 28 balls that were red”

-create title = “28”

ggplot(virtual_prop_red_28, aes(x = prop_red)) +
  geom_histogram(binwidth = 0.05, boundary = 0.4, color = "white") +
  labs(x = "Proportion of 28 balls that were red", title = "28")

#Segment 2: sample size = 53

2.a)Take 1150 samples of size of 53 instead of 1000 replicates of size 50. Assign the output to virtual_samples_53

virtual_samples_53 <- bowl %>% 
  rep_sample_n(size = 53, reps = 1150)

2.b)Compute resulting 1150 replicates of proprtion red

-start with virtual_samples_53 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 / 53

-Assign the output to virtual_prop_red_53

virtual_prop_red_53 <- virtual_samples_53 %>% 
  group_by(replicate) %>% 
  summarize(red = sum(color == "red")) %>% 
  mutate(prop_red = red / 53)

2.c)Plot distribution of virtual_prop_red_53 via a histogram use labs to

-label x axis = “Proportion of 53 balls that weree red”

-create title = “53”

ggplot(virtual_prop_red_53, aes(x = prop_red)) +
  geom_histogram(binwidth = 0.05, boundary = 0.4, color = "white") +
  labs(x = "Proportion of 53 balls that were red", title = "53")

#Segment 3: sample size = 118

3.a) Take 1150 samples of size of 118 instead of 1000 replicates of size 50. Assign the output to virtual_samples_118

virtual_samples_118 <- bowl %>% 
  rep_sample_n(size = 118, reps = 1150)

3.b)Compute resulting 1150 replicates of proportion red

-start with virtual_samples_118 THEN

-group_by replicate THEN

-create variable red equal to the sum of all the red balls

-create variable pop_red equal to variable red / 118

-Assign the output to virtual_prop_red_118

virtual_prop_red_118 <- virtual_samples_118 %>% 
  group_by(replicate) %>% 
  summarize(red = sum(color == "red")) %>% 
  mutate(prop_red = red / 118)

3.c)Plot distribution of virtual_prop_red_118 via a histogram use labs to

-Label x axis = “Proportion of 118 balls that were red”

-Create title = “118”

ggplot(virtual_prop_red_118, aes(x = prop_red)) +
  geom_histogram(binwidth = 0.05, boundary = 0.4, color = "white") + 
  labs(x = "Proportion of 118 balls that were red", title = "118")

Calculate the standard deviations for your three sets of 1150 values of prop_red using the standard deviation

n = 28

virtual_prop_red_28 %>% 
  summarize(sd = sd(prop_red))

# A tibble: 1 x 1
      sd
   <dbl>
1 0.0893

n = 53

virtual_prop_red_53 %>% 
  summarize(sd = sd(prop_red))

# A tibble: 1 x 1
      sd
   <dbl>
1 0.0669

n = 118

virtual_prop_red_118 %>% 
  summarize(sd = sd(prop_red))

# A tibble: 1 x 1
      sd
   <dbl>
1 0.0429

The distribution with sample size, n = 118, has the smallest standard deviation (spead) around the estimated proportion of red balls.