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

- Load r packages

Modify the code for comparing different sample sizes from the virtual bowl

#Segment 1: sample size = 28

1.a) Take 1150 samples of size of 28 instead of 1000 replicates of size 25 from the bowl dataset. Assign the output to virtual_samples_28

```
virtual_samples_28 <- bowl %>%
rep_sample_n(size = 28, reps = 1150)
```

1.b) Compute resulting 1150 replicates of proportion red

start with virtual_samples_28 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 / 28 Assign the output to virtual_prop_red_28

```
virtual_prop_red_28 <- virtual_samples_28 %>%
group_by(replicate) %>%
summarize(red = sum(color == "red")) %>%
mutate(prop_red = red / 28)
```

1.c) Plot distribution of virtual_prop_red_28 via a histogram

use labs to

label x axis = “Proportion of 28 balls that were red” create title = “28”

```
ggplot(virtual_prop_red_28, aes(x = prop_red)) +
geom_histogram(binwidth = 0.05, boundary = 0.4, color = "white") +
labs(x = "Proportion of 28 balls that were red", title = "28")
```

#Segment 2: sample size = 53

2.a) Take 1150 samples of size of 53 instead of 1000 replicates of size 50. Assign the output to virtual_samples_53

```
virtual_samples_53 <- bowl %>%
rep_sample_n(size = 53, reps = 1150)
```

2.b) Compute resulting 1150 replicates of proportion red

start with virtual_samples_53 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 / 53 Assign the output to virtual_prop_red_53

```
virtual_prop_red_53 <- virtual_samples_53 %>%
group_by(replicate) %>%
summarize(red = sum(color == "red")) %>%
mutate(prop_red = red / 53)
```

2.c) Plot distribution of virtual_prop_red_53 via a histogram

use labs to

label x axis = “Proportion of 53 balls that were red” create title = “53”

```
ggplot(virtual_prop_red_53, aes(x = prop_red)) +
geom_histogram(binwidth = 0.05, boundary = 0.4, color = "white") +
labs(x = "Proportion of 53 balls that were red", title = "53")
```

#Segment 3: sample size = 118

3.a) Take 1150 samples of size of 118 instead of 1000 replicates of size 50. Assign the output to virtual_samples_118

```
virtual_samples_118 <- bowl %>%
rep_sample_n(size = 118, reps = 1150)
```

3.b) Compute resulting 1150 replicates of proportion red

start with virtual_samples_118 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 / 118 Assign the output to virtual_prop_red_118

```
virtual_prop_red_118 <- virtual_samples_118 %>%
group_by(replicate) %>%
summarize(red = sum(color == "red")) %>%
mutate(prop_red = red / 118)
```

3.c) Plot distribution of virtual_prop_red_118 via a histogram

use labs to

label x axis = “Proportion of 118 balls that were red” create title = “118”

```
ggplot(virtual_prop_red_118, aes(x = prop_red)) +
geom_histogram(binwidth = 0.05, boundary = 0.4, color = "white") +
labs(x = "Proportion of 118 balls that were red", title = "118")
```

Calculate the standard deviations for your three sets of 1150 values of prop_red using the standard deviation

n = 28

```
virtual_prop_red_28 %>%
summarize(sd = sd(prop_red))
```

```
# A tibble: 1 x 1
sd
<dbl>
1 0.0899
```

n = 53

```
virtual_prop_red_53 %>%
summarize(sd = sd(prop_red))
```

```
# A tibble: 1 x 1
sd
<dbl>
1 0.0667
```

n = 118

```
virtual_prop_red_118 %>%
summarize(sd = sd(prop_red))
```

```
# A tibble: 1 x 1
sd
<dbl>
1 0.0436
```

The distribution with sample size, n = 118, has the smallest standard deviation (spread) around the estimated proportion of red balls.