Thread: confidence interval

Let X1, X2,....,Xn be a random sample of size n from the normal distribution . Calculate the expected length of a 95% confidence interval for assuming that n=5 and the variance is:

a. known
b. unknown

Thank you for any help!

Originally Posted by redpack

Let X1, X2,....,Xn be a random sample of size n from the normal distribution . Calculate the expected length of a 95% confidence interval for assuming that n=5 and the variance is:

a. known
b. unknown

Thank you for any help!

let . If X_k independent with other, then we have ~ .
In the case \sigma is known
we use ~N(0,1).
In the case \sigma is unknown
we use ~t-distribution.
From here, we get the confident interval.
Many book talk about this.