library(tidyverse)

# Example - Virus Load: n=25 Sample with Mean 32.55 and Standard Deviation 5.36
########################################################################################

# Multiplier for 95% CI
qt(.975, df=24)   # left tail area .975 = 1 - .025

# Standard Error
SE <- 5.36/sqrt(25)
# CI
c(32.55 - 2.064*SE, 32.55 + 2.064*SE)


# Example - GSS Survey Data - Mean workhours
########################################################################################

gss_survey <- read_csv("http://www.cknuckles.com/statsprogramming/data/gss_survey_data.csv")

workhours_2018 <- gss_survey |>
  filter(year == "2018") |>
  select(workhours) |>
  drop_na(workhours)

workhours_2018 |>
  summarize(
    sample_mean = mean(workhours),
    sample_sd = sd(workhours),
    n = n()
  )

ggplot(data = workhours_2018, mapping = aes(x = workhours)) +
  geom_histogram( bins=30, color = "white")

# Multiplier for 95% CI
qt(.975, df=827)   # left tail area .975 = 1 - .025

SE <- 14.483/sqrt(828)
c(41.530-1.963*SE, 41.530+1.963*SE)


# Example - T Distribution vs Z Distribution Multipliers
########################################################################################

# T distribution look-up vs Z distribution look-up
qt(.975, df=99) - qnorm(.975, mean=0, sd=1)