Based on Chapter 7 of ModernDive. Code for Quiz 11.
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 1120
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 = 1120)
1.b) Compute resulting 1120
replicates of proportion red
virtual_samples_30
THENgroup_by
replicate THENred
equal to the sum of all the red ballsprop_red
equal to variable red / 30
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
30
balls that were red”“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 1120 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 = 1120)
2.b) Compute resulting 1120
replicates of proportion red
group_by
replicate THENred
equal to the sum of all the red ballsprop_red
equal to variable red / 55
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
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 = 114
3.a) Take 1120 samples of size of 114 instead of 1000 replicates of size 50. Assign the output to virtual_samples_114
virtual_samples_114 <- bowl %>%
rep_sample_n(size = 114, reps = 1120)
3.b) Compute resulting 1120 replicates of proportion red
virtual_samples_114
THENgroup_by
replicate THENred
equal to the sum of all the red ballsprop_red
equal to variable red / 114
virtual_prop_red_114
virtual_prop_red_114 <- virtual_samples_114 %>%
group_by(replicate) %>%
summarize(red = sum(color == "red")) %>%
mutate(prop_red = red / 114)
3.c) Plot distribution of virtual_prop_red_114
via a histogram use labs to
114
balls that were red”114
”ggplot(virtual_prop_red_114, aes(x = prop_red)) +
geom_histogram(binwidth = 0.05, boundary = 0.4, color = "white") +
labs(x = "Proportion of 114 balls that were red", title = "114")
ggsave(filename = "preview.png",
path = here::here("_posts", "2021-04-19-sampling"))
Calculate the standard deviations for your three sets of 1120 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 0.0879
n = 55
virtual_prop_red_55 %>%
summarize(sd = sd(prop_red))
# A tibble: 1 x 1
sd
<dbl>
1 0.0660
n = 114
virtual_prop_red_114 %>%
summarize(sd = sd(prop_red))
# A tibble: 1 x 1
sd
<dbl>
1 0.0439
The distribution with sample size, n = 114, has the smallest standard deviation (spread) around the estimated proportion of red balls.