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

- Load the R package we will use.

- 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

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**

1a) 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)
```

1b) 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`

1c) Plot distribution of `virtual_prop_red_30`

via a histogram

Use labs to:

- label x axis = “Proportion of 30 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**

2a) 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)
```

2b) Compute resulting 55 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`

2c) 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**

3a) 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)
```

3b) 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`

3c) 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**

**n = 55**

**n = S120**

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