One sided test for hypothesis about proportion

lecture11.jl

#=
Newborn babies are more likely to be boys than girls.
A random sample found 13 173 boys were born among 25 468
newborn children. Population: All children born that time period. Alternatively,
the unknown p could be the unknown probability.
=#

b = 13173
n = 25486

p̂ = b/n

#H0 p = 0.5
p0 = 0.5 #null value


# Check if n is large enough
n*p0 > 5
n*(1 - p0)

# Every below computed under H0
SE = sqrt(p0*(1-p0)/n)

# Compute the test statistic
z = (p̂ - p0)/SE

# z is large, evidence in favour of H1: p > 0.5
α = 0.05
z0 = quantile(Normal(0,1), 1 - α)

if z > z0
    println("Reject the null! With 0.05 significance ... p>0.5")
else
    println("Null hypothesis cannot be rejected")
end