Consider the null model, for simplicity with known ????2. After estimating ???? =

E(y) by ȳ, you plan to predict a future y from the N(????, ????2) distribution. State the formula for a 95% prediction interval for this model. Suppose, unknown to you, ȳ = ???? + zo????∕

√n for some particular zo value. Find an expression for the actual probability, conditional on ȳ, that the prediction interval contains the future y. Explain why this is not equal to 0.95 (e.g., what happens if zo = 0?)

but converges to it as n → ∞.