Confidence interval for mean p when o is known Generate 1000

Confidence interval for mean p when o is known. Generate 1000 random samples of sample size 40 from a normal distribution with mu = 100 and sigma = 15. Compute sample mean (X) for each sample. There will be 1000 sample means. Compute 95% confidence interval for mu for each sample. Compute the proportion of intervals do contain the true mean mu = 100. Draw confidence intervals horizontally with a vertical line for mu = 100.

Solution

R Command:

data=matrix(0,1000,40)

for(i in 1:1000)

{

data[i,]=rnorm(40,100,15)

}

m=rep(0,1000)

for(i in 1:1000)

{

m[i]=mean(data[i,])

}

c1=rep(0,1000)

c2=rep(0,1000)

for(i in 1:1000)

{

c1[i]=mean(data[i,])-(sd(data[i,])*2.02269/sqrt(40))

c2[i]=mean(data[i,])+(sd(data[i,])*2.02269/sqrt(40))

}

c=0

for(i in 1:1000)

{

if(c1[i]<100 && c2[i]>100)

c=c+1;

}

c=c/1000

d) ans 0.953