## -----------------------------------------------------------------------------
#| results: hold
leadIQ <- read.delim('https://raw.githubusercontent.com/IowaBiostat/data-sets/main/lead-iq/lead-iq.txt')

mu <- 95
mu.hat <- mean(leadIQ$IQ)
s <- sd(leadIQ$IQ)
n <- length(leadIQ$IQ)
df <- n-1
t <- (mu.hat-mu)/(s/sqrt(n))
pval <- 2*pt(t,df)
pval


## -----------------------------------------------------------------------------
ci <- mu.hat + qt(c(.025,.975),n-1) * s/sqrt(n)
ci


## -----------------------------------------------------------------------------
t.test(leadIQ$IQ, mu=95)


## -----------------------------------------------------------------------------
p <- 147/200
p + c(-1, 1) * qnorm(0.975) * sqrt((p*(1-p))/200)


## -----------------------------------------------------------------------------
p_hat <- 147/200
p0 <- 0.68

z <- (p_hat - p0) / (sqrt((p0*(1-p0))/200))

2*pnorm(z, lower.tail = F) # don't forget to make it two-sided!


## -----------------------------------------------------------------------------
binom.test(x = 147, n = 200, p = 0.68)


## -----------------------------------------------------------------------------
mu <- 52
sd <- sqrt(25)
z1 <- (47 - mu) / sd
z2 <- (56 - mu) / sd

pnorm(z2) - pnorm(z1)


## -----------------------------------------------------------------------------
mu <- 52
sd <- sqrt(25)
n <- 9
z <- (60 - mu) / (sd / sqrt(n))
pnorm(z, lower.tail=FALSE)


## -----------------------------------------------------------------------------
mu <- 52
sd <- sqrt(25)
n <- 9
z <- (43 - mu) / (sd)
perc_alt_tx <- pnorm((z))
perc_alt_tx


## -----------------------------------------------------------------------------
z <- qnorm(.271, lower.tail=FALSE)
52 + z*5


## -----------------------------------------------------------------------------
pbinom(1, 
       25, 
       perc_alt_tx, # found in part c, saved to this variable
       lower.tail = FALSE) # shading to the right


## -----------------------------------------------------------------------------
z <- (16 - 18) / sqrt(4)
pnorm(z)


## -----------------------------------------------------------------------------
z <- (21 - 18) / sqrt(4)
1 - pnorm(z)


## -----------------------------------------------------------------------------
z1 <- (14 - 18) / sqrt(4)
z2 <- (20 - 18) / sqrt(4)

(p <- pnorm(z2) - pnorm(z1))
(ge2 <- pbinom(1, 5, p, lower.tail = FALSE))