32. Let X1, . . . , Xn, Xn+1 denote a sample from a normal population whose mean

μ and variance σ2 are unknown. Suppose that we are interested in using the observed values of X1, . . . , Xn to determine an interval, called a prediction interval, that we predict will contain the value of Xn+1 with 100(1−α) percent confidence.

Let X n and S2 n be the sample mean and sample variance of X1, . . . , Xn.

(a) Determine the distribution of

(b) Determine the distribution of

(c) Give the prediction interval for Xn+1.

(d) The interval in part

(c) will contain the value of Xn+1 with 100(1−α) percent confidence. Explain the meaning of this statement.

Transcribed Image Text:

Xn+1-X