Based on Chapter 8 of ModernDive. Code for Quiz 12.

Load the R packages we will use.

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

Save a plot to be your preview plot

Look at the variable definitions in congress_age

**What is the average age of members that have served in
congress?**

Set random seed generator to 123

Take a sample of 100 from the dataset

`congress_age`

and assign it to`congress_age_100`

```
set.seed(123)
congress_age_100 <- congress_age %>%
rep_sample_n(size=100)
```

`congress_age`

is the population and`congress_age_100`

is the sample`18,635`

is number of observations in the population and`100`

is the number of observations in your sample

**Construct the confidence interval**

**1. Use specify to indicate the variable from congress_age_100
that you are interested in**

```
Response: age (numeric)
# A tibble: 100 × 1
age
<dbl>
1 53.1
2 54.9
3 65.3
4 60.1
5 43.8
6 57.9
7 55.3
8 46
9 42.1
10 37
# … with 90 more rows
```

**2. generate 1000 replicates of your sample of
100**

```
Response: age (numeric)
# A tibble: 100,000 × 2
# Groups: replicate [1,000]
replicate age
<int> <dbl>
1 1 42.1
2 1 71.2
3 1 45.6
4 1 39.6
5 1 56.8
6 1 71.6
7 1 60.5
8 1 56.4
9 1 43.3
10 1 53.1
# … with 99,990 more rows
```

The output has 100,000 rows

**3. calculate the mean for each replicate**

Assign to bootstrap_distribution_mean_age

Display bootstrap_distribution_mean_age

```
bootstrap_distribution_mean_age <- congress_age_100 %>%
specify(response = age) %>%
generate(reps = 1000, type = "bootstrap") %>%
calculate(stat = "mean")
bootstrap_distribution_mean_age
```

```
Response: age (numeric)
# A tibble: 1,000 × 2
replicate stat
<int> <dbl>
1 1 53.6
2 2 53.2
3 3 52.8
4 4 51.5
5 5 53.0
6 6 54.2
7 7 52.0
8 8 52.8
9 9 53.8
10 10 52.4
# … with 990 more rows
```

The bootstrap_distribution_mean_age has 1000 means

**4. visualize the bootstrap distribution**

```
visualize(bootstrap_distribution_mean_age)
```

**Calculate the 95% confidence interval using the percentile
method**

Assign the output to congress_ci_percentile

Display congress_ci_percentile

```
congress_ci_percentile <- bootstrap_distribution_mean_age %>%
get_confidence_interval(type = "percentile", level = 0.95)
congress_ci_percentile
```

```
# A tibble: 1 × 2
lower_ci upper_ci
<dbl> <dbl>
1 51.5 55.2
```

**Calculate the observed point estimate of the mean and assign
it to obs_mean_age**

- Display obs_mean_age

```
obs_mean_age <- congress_age_100 %>%
specify(response = age) %>%
calculate(stat = "mean") %>%
pull()
obs_mean_age
```

`[1] 53.36`

Shade the confidence interval

Add a line at the observed mean, obs_mean_age, to your visualization and color it “hotpink”

```
visualize(bootstrap_distribution_mean_age) +
shade_confidence_interval(endpoints = congress_ci_percentile) +
geom_vline(xintercept = obs_mean_age, color = "hotpink", size = 1 )
```

Calculate the population mean to see if it is in the 95% confidence interval

Assign the output to pop_mean_age

Display pop_mean_age

`[1] 53.31373`

- Add a line to the visualization at the, population mean, pop_mean_age, to the plot color it “purple”

```
visualize(bootstrap_distribution_mean_age) +
shade_confidence_interval(endpoints = congress_ci_percentile) +
geom_vline(xintercept = obs_mean_age, color = "hotpink", size = 1) +
geom_vline(xintercept = pop_mean_age, color = "purple", size = 3)
```

- Save the previous plot to preview.png and add to the yaml chunk at the top

Is population mean the 95% confidence interval constructed using the bootstrap distribution? yes

Change set.seed(123) to set.seed(4346). Rerun all the code.

When you change the seed is the population mean in the 95% confidence interval constructed using the bootstrap distribution? no

If you construct 100 95% confidence intervals approximately how many do you expect will contain the population mean? 95