Question

(R) need a code for R program or solving the below question(please follow the below instruction thoroughly) and please do not copy other answers.

2. Let X1, .. . , Xn be iid. N(?, ?2). A 100(1-a)% confidence interval for ?2 is

Answer 1

library(smoothmest)
alpha=.1
mu=66
sigma=4
n=12
N=10^4
c=array(dim=1)
z1=qchisq(alpha/2,n-1,lower.tail=T)
z2=qchisq(1-alpha/2,n-1,lower.tail=T)
for(i in 1:N)
{
x=rdoublex(n,66,4)
t=0
for(j in 1:n)
{
t[j]=(x[j]-mean(x))^2
}
z=sum(t)
c[i]=ifelse((sigma^2<z/z2 && sigma^2 >z/z1),1,0)
}
p_hat=mean(c)
p_hat
p_hat+1/sqrt(N)
p_hat-1/sqrt(N)

p_hat is  0.5157 which different from (1-.1)

next programme----

alpha=.05
mu=66
sigma=1
n=10
N=10^4
c=array(dim=1)
z1=qchisq(alpha/2,n-1,lower.tail=T)
z2=qchisq(1-alpha/2,n-1,lower.tail=T)
for(i in 1:N)
{
x=rexp(n,1)
t=0
for(j in 1:n)
{
t[j]=(x[j]-mean(x))^2
}
z=sum(t)
c[i]=ifelse((sigma^2<z/z2 && sigma^2 >z/z1),1,0)
}
p_hat=mean(c)
p_hat
p_hat+1/sqrt(N) (0.7784)
p_hat-1/sqrt(N) (0.7584)

p_hat is  0.7684  .... And the other cases also done by changing the values of n and alpha