Based on Chapter 8 of Modern Dive. 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**

- 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
```

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

Assign to

`bootstrap_distribution_mean_age`

Display

`bootstrap_distribution_mean_age`

- 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`

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 visualiztin 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