Chapter 7 of ModernDive. Code for quiz 11.

Load the R packages we will use

**Question**: Modify the code for comparing different sample sizes from the virtual `bowl`

**1A.**

Take 1180 samples of size 26 instead of 1000 replicates of 25 from the

`bowl`

dataset.Assign the output to

`virtual_samples_26`

```
virtual_samples_26 <- bowl %>%
rep_sample_n(size = 26, reps = 1180)
```

**1B.**

Compute the resulting 1180 replicates of proportion Red.

Start with

`virtual_samples_26`

THEN`group_by`

replicate THENCreate variable red equal to the sum of all the red balls

Create variable

`prop_red`

equal to the variable red/26Assign the output to

`virtual_prop_red_26`

**1C.**

Plot distribution of

`virtual_prop_red_26`

via a histogramUse 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 were red", title = "26")
```

**2A.**

Take 1180 sample 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 = 1180)
```

**2B.**

Compute resulting 1180 replicates of proportion Red

Start with

`virtual_samples_55`

THEN`group_by`

replicate THENCreate variable read equal to them sum of all red balls

Create variable

`prop_red`

equal to variable red/55Assign the output to

`virtual_prop_red_55`

**2C.**

Plot distribution of

`virtual_prop_red_55`

via a histogramUse 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 bals that were read", title = "55")
```

**3A.**

Take 1180 samples of size 110 instead of 1000 replicates of size 100

Assign the output to

`virtual_samples_110`

```
virtual_samples_110 <- bowl %>%
rep_sample_n(size = 110, reps = 1180)
```

**3B.**

Compute the resulting 1180 replicates of proportion Red

Start with

`virtual_samples_110`

THEN`group_by`

replicate THENCreate variable red equal to the sum of all the red balls

Create variable

`prop_red`

equal to variable red/110Assign output to

`virtual_prop_red_110`

**3C.**

Plot distribution of

`virtual_prop_red_110`

via a histogramUse labs to:

label x-axis = “Proportion of 110 balls that were red”

create title = “110”

```
ggplot(virtual_prop_red_110, aes(prop_red)) +
geom_histogram(binwidth = 0.05, boundary = 0.4, color = "white") +
labs(x = "Proportion of 110 balls that were red", title = "110")
```

Calculate the standard deviation for samples n = 26, n = 55, and n = 110 of 1180 values of prop_red using standard deviation

**n = 26**

**n = 55**

**n = 110**

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