set.seed(500)
library(tidyverse)
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## ✖ dplyr::filter() masks stats::filter()
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library(openintro)
## Loading required package: airports
## Loading required package: cherryblossom
## Loading required package: usdata
library(infer)
us_adults <- tibble(
climate_change_affects = c(rep("Yes", 62000), rep("No", 38000))
)
ggplot(us_adults, aes(x = climate_change_affects)) +
geom_bar() +
labs(
x = "", y = "",
title = "Do you think climate change is affecting your local community?"
) +
coord_flip()
us_adults %>%
count(climate_change_affects) %>%
mutate(p = n /sum(n))
## # A tibble: 2 × 3
## climate_change_affects n p
## <chr> <int> <dbl>
## 1 No 38000 0.38
## 2 Yes 62000 0.62
n <- 60
samp <- us_adults %>%
sample_n(size = n)
Exercise 1
Exercise 2
I would expect another student’s sample proportion to be similar but
not identical to mine because sample proportions can vary from sample to
sample by taking smaller samples from the population. The sample is
randomly selected so the sample result would always come out a little
different everytime you run the sample code.
samp %>%
specify(response = climate_change_affects, success = "Yes") %>%
generate(reps = 1000, type = "bootstrap") %>%
calculate(stat = "prop") %>%
get_ci(level = 0.95)
## # A tibble: 1 × 2
## lower_ci upper_ci
## <dbl> <dbl>
## 1 0.517 0.767
Exercise 3
95% confidence mean 95% confident that the population mean lies
within the interval between a lower bound and an upper bound. A
confidence interval only provides a plausible range of values.
Exercise 4
Yes confidence interval capture the true population proportion of US
adults who think climate change affects their local community. If I was
working on this lab in a classroom, my neighbor’s interval would have
gotten a slightly different confidence interval. The confidence interval
is thus a statement about the estimation procedure and not about the
specific interval generated in the sample
Exercise 5
The confidence interval ranging from .55 to .783 would be expected
to cover the true population proportion 95% of the time because a
confidence interval only provides a plausible range of values. While we
might say other values are implausible based on the data, this does not
mean they are impossible.
LINK TO GITHUB FOR PICTURES OF RESULTS FROM APP
Exercise 6 (See pics at github link)
Given a sample size of 60, 1000 bootstrap samples for each interval,
and 50 confidence intervals constructed (the default values for the
above app), the proportion of my confidence intervals include the true
population proportion is 24/25 = .96. It is safe to assume 95% of the
confidence intervals demonstrated would include true populationis
proportion exactly equal to the confidence level.
Exercise 7 (See pics at github link)
I chose a different confidence level other than 95%. Given a sample
size of 60, 1000 bootstrap samples for each interval, and 50 confidene
intervals, I chose 90% confidence level. I expect a confidence interval
at this level to be narrower (plus or minus 2.5 percent, for example)
than the confidence interval I calculated at the 95% confidence level.
The reason for this is , if we want an interval with lower confidence,
such as 90%, we could use a slightly narrower interval than our original
95% interval. You have that 5% range of incorrectness in this case. When
the precision of the confidence interval increases we could assume true
population proportion interval decreases.
Exercise 8
Using the code from the infer package and data from the one sample I
have (samp), I chose a confidence level of 99% for the proportion of US
Adults who think climate change is affecting their local community. We
are 99% level of confident that the proportion of US adults who think
climate change affects their local community is between .48 adn
.81.
samp %>%
specify(response = climate_change_affects, success = "Yes") %>%
generate(reps = 1000, type = "bootstrap") %>%
calculate(stat = "prop") %>%
get_ci(level = 0.99)
## # A tibble: 1 × 2
## lower_ci upper_ci
## <dbl> <dbl>
## 1 0.483 0.817
Exercise 9 (See pics at github link)
Using the app given a sample size of 60, 1000 bootstrap samples for
each interval, and 50 confidene intervals, at the confidence level that
I chose in the previous question which was 99%, the proportion of my
confidence intervals include the true population proportion is 48/50 =
.96. Using the code from infer the percentage is lower then using the
app.
Exercise 10 (See pics at github link)
Using the code from the infer package and data from the one sample I
have (samp), I chose a confidence level of 80% for the proportion of US
Adults who think climate change is affecting their local community. I
expect a confidence interval at this level to be more narrower than all
the confidence interval I calculated before. The reason for this is , if
we want an interval with lower confidence, such as 80%, we could use a
slightly narrower interval than our original like the previous interval.
We are 80% level of confident that the proportion of US adults who think
climate change affects their local community is between .57 adn .73.
Using the app the proportion of my confidence intervals include the true
population proportion is 38/50 = .76. At a confidence level of 80% this
low.
samp %>%
specify(response = climate_change_affects, success = "Yes") %>%
generate(reps = 1000, type = "bootstrap") %>%
calculate(stat = "prop") %>%
get_ci(level = 0.80)
## # A tibble: 1 × 2
## lower_ci upper_ci
## <dbl> <dbl>
## 1 0.567 0.733
Exercise 11 (See pics at github link)
Using the app, given a sample size of 100, 1000 bootstrap samples
for each interval, and 50 confidence intervals constructed the
proportion of my confidence intervals include the true population
proportion is 46/50 = .92. Increasing the the sample size to 100 it
increased the confidence intervals to the true population porpotion to
92. The width of intervals has gotten much wider then the previous.
Exercise 12 (See pics at github link)
Using the app given a sample size of 60, 10000 bootstrap samples for
each interval, and 50 confidence intervals constructed the proportion of
my confidence intervals include the true population proportion is 41/50
= .82. Increasing the bootstrap to 10000 it increased the confidence
intervals to the true population porpotion to 82. The width of intervals
has gotten a little wider then the previous.