Load the R package we will use.
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
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 x 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 rows2. generate 1000 replicates of your sample of 100
Response: age (numeric)
# A tibble: 100,000 x 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 rowsThe output has 100,00 rows
3. calculate the mean for each replicate
Assign to bootstrap_distribution_mean_age
Display bootstrap_distribution_mean_age
# A tibble: 1,000 x 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 rowsThe bootstrap_distribution_mean_age has 1000 means
4. visualize the bootstrap distribution
Calculate the 95% confidence interval using the percentile method
Assign the output to congress_ci_percentile
Display congress_ci_percentile
# A tibble: 1 x 2
lower_ci upper_ci
<dbl> <dbl>
1 51.5 55.2Calculate the observed point estimate of the mean and assign it to obs_mean_age
- Display obs_mean_age,
[1] 53.36Shade the confidence interval
Add a line at the observed mean, obs_mean_age, to your visualization and color it “hotpink”
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”
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? ???
If you construct 100 95% confidence intervals approximately how many do you expect will contain the population mean? ???