Load the R packages we will use.
library(tidyverse)
library(moderndive) #install before loading
library(infer) #install before loading
library(fivethirtyeight) #install before loading
- 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 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
congress_age_100 %>%
specify(response = age)
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 rows#2. 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 100,000 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
# 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 rows- The bootstrap_distribution_mean_age has 1,000 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 x 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 %>%
specify(response = age) %>%
calculate(stat = "mean") %>%
pull()
obs_mean_age
[1] 53.31373- 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
pop_mean_age <- congress_age %>%
summarize(pop_mean= mean(age)) %>% pull()
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)
- Is population mean the 95% confidence interval constructed using the bootstrap distribution? ???
- 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? 95