Sampling

Code for quiz 11

1. Load the R packages we will use

library(tidyverse)
library(moderndive)

2. Quiz questions

• Replace all 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 wont work 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 ModernDive with different sample sizes and repetitions

• Make sure you have installed and loaded the tidyverse and the moderndive packages

• Fill in the blank

• Put the command you use in the Rchunks in your Rmd file fo 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 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 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 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 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(bindwith = 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 deviatoin

n = 30

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

# A tibble: 1 x 1
      sd
   <dbl>
1 0.0869

n = 55

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

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

n = 120

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

# A tibble: 1 x 1
      sd
   <dbl>
1 0.0427

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