Lab 5 Confidence intervals

library(tidyverse)
library(openintro)
library(infer)

Exercise 1

From the sample, 55% of the population community climate change has affected their local community.

us_adults <- tibble(
  climate_change_affects = c(rep("Yes", 62000), rep("No", 38000))
)
us_adults %>%
  count(climate_change_affects) %>%
  mutate(p = n /sum(n))

## # A tibble: 2 x 3
##   climate_change_affects     n     p
##   <chr>                  <int> <dbl>
## 1 No                     38000  0.38
## 2 Yes                    62000  0.62

set.seed(60)
samp <- us_adults %>%sample_n(60)
samp%>%count(climate_change_affects)%>%mutate(p=n/sum(n))

## # A tibble: 2 x 3
##   climate_change_affects     n     p
##   <chr>                  <int> <dbl>
## 1 No                        27  0.45
## 2 Yes                       33  0.55

Exercise 2

I don’t expect a student to have identical sample proportions as the sample is randomly picked. I think its possible that other student can get the same proportion but there is more of a probability of having similar proportions.

Exercise 3

95% confident means when I run the the climate change stats over 1000 times, 95% of the 1000 samples’ proportions are exactly the true proportion.

Exercise 4

The confidence interval did captured the true proportion. However, your neighbor’s confidence will not have the exact range of yours as they have different samples. For example, the example provided range was (.55,.783).

set.seed(1000)
samp %>%
  specify(response = climate_change_affects, success = "Yes") %>%
  generate(reps = 1000, type = "bootstrap") %>%
  calculate(stat = "prop") %>%
  get_ci(level = 0.95)

## # A tibble: 1 x 2
##   lower_ci upper_ci
##      <dbl>    <dbl>
## 1    0.433    0.683

My version produced (.43,.683). Both ranges overlap each other, so the CFI’s will be similar.

Exercise 5

I believe 95% of 1000 runs, each student’s confident intervals captured the true proportion.

Exercise 6

(Note: I used the app given in the Lab 5: Pt2 template. I just like my own format )

Out of the 50 confidence intervals, only three intervals did not included the true proportion.

Exercise 7

The ranges get more narrower as the confidence level drops and wider when its most confident. The 95% confident level has a large range so it has to be the reverse for 59%. ### Exercise 8

Lets us use a confident level of .30. Only 30% of the 1000 trials have the true proportion compared to the 95% range.

samp2 <- us_adults %>%sample_n(60)
samp2%>%count(climate_change_affects)%>%mutate(p=n/sum(n))

## # A tibble: 2 x 3
##   climate_change_affects     n     p
##   <chr>                  <int> <dbl>
## 1 No                        24   0.4
## 2 Yes                       36   0.6

samp2 %>%
  specify(response = climate_change_affects, success = "Yes") %>%
  generate(reps = 1000, type = "bootstrap") %>%
  calculate(stat = "prop") %>%
  get_ci(level = 0.30)

## # A tibble: 1 x 2
##   lower_ci upper_ci
##      <dbl>    <dbl>
## 1    0.583    0.617

Exercise 9

Only 15 out of the 50 confident intervals included the true proportion. These intervals reflect the 30% confident level

Exercise 10

For this example. We can use 98% confident level. It’s range is (0.4666667,0.75 ). On the app, only one interval range of the 50 was out of range for the true proportion.

sampF <- us_adults %>%sample_n(60)
sampF%>%count(climate_change_affects)%>%mutate(p=n/sum(n))

## # A tibble: 2 x 3
##   climate_change_affects     n     p
##   <chr>                  <int> <dbl>
## 1 No                        20 0.333
## 2 Yes                       40 0.667

samp2 %>%
  specify(response = climate_change_affects, success = "Yes") %>%
  generate(reps = 1000, type = "bootstrap") %>%
  calculate(stat = "prop") %>%
  get_ci(level = 0.98)

## # A tibble: 1 x 2
##   lower_ci upper_ci
##      <dbl>    <dbl>
## 1    0.467    0.733

Exercise 11

I picked sample size of 10,200,1000 for a confident level of 95%. As the sample size increased, the bounds of matched intervals decrease.

Exercise 12

For this experiment, I picked bootstrap sizes of 700,3000,7000. As the bootstrap increased, more of the intervals hit in center of the true proportion. Like for 700, some of the correct intervals hit the mean at the ends of the interval. For 3000, the mean line hit in the middle for more of the intervals.