BUS 320: Sampling

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 differnet sample sizes from the virtual bowl

Segment 1: sample size = 26

1.a) Take 1100 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 = 1100)

1.b) Compute resulting 1100 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 are red", title = "26")

Segment 2: sample size = 57

2.a) Take 1100 samples of size of 57 instead of 1000 replicates of size 50. Assign the output to virtual_samples_57

virtual_samples_57 <- bowl %>% 
  rep_sample_n(size = 57, reps = 1100)

2.b) Compute resulting 1100 replicates of proportion red

• start with virtual_samples_57 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 / 57

• Assign the output to virtual_prop_red_57

virtual_prop_red_57 <- virtual_samples_57 %>% 
  group_by(replicate) %>% 
  summarize(red = sum(color == "red")) %>% 
  mutate(prop_red = red / 57)

2.c) Plot distribution of virtual_prop_red_57 via a histogram use labs to

• label x axis = “Proportion of 57 balls that were red”

• create title = “57”

ggplot(virtual_prop_red_57, aes(x = prop_red)) +
  geom_histogram(binwidth = 0.05, boundary = 0.4, color = "white") +
  labs(x = "proportion of 57 balls that were red", title = "57")

Segment 3: sample size = 110

3.a) Take 1100 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 = 1100)

3.b) Compute resulting 1100 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")

ggsave(filename = "preview.png",
       path = here::here("_posts", "2022-04-18-sampling"))

Calculate the standard deviations for your three sets of 1100 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 0.0914

n = 57

virtual_prop_red_57 %>% 
  summarize(sd = sd(prop_red))

# A tibble: 1 × 1
      sd
   <dbl>
1 0.0650

n= 110

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

# A tibble: 1 × 1
      sd
   <dbl>
1 0.0457

The distribution with sample size, n = 110, has the smallest standard deviation (spread) around the estimated proportion of red balls.