Code for Quiz 11.

- Load the R package we will use.

*Question:*

7.2.4 in Modern Dive with different sample sizes and representations

Make sure you have installed and loaded the

`tidyverse`

and the`moderndive`

packagesFill 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 1200 sample sizes 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)
```

1.b) Compute resulting 1200 replicates of proportion of 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")
```

```
$x
[1] "Proportion of 30 balls that were red"
$title
[1] "30"
attr(,"class")
[1] "labels"
```

*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 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)
```

3.b) 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

```
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(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`

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

```
# A tibble: 1 x 1
sd
<dbl>
1 0.0865
```

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

```
# A tibble: 1 x 1
sd
<dbl>
1 0.0645
```

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

```
# A tibble: 1 x 1
sd
<dbl>
1 0.0432
```