Check that the random variables Q1 = X and Q 2 = n(X ) are both valid pivots in Example 8.13. Example 8.13:

Check that the random variables Q1 = X̅ −θ and Q₂ = √n(X̅ − θ) are both valid pivots in Example 8.13.

Example 8.13:

Let X₁, X₂, X₃, . . ., X_n be a random sample from a normal distribution N(θ, 1). Find a 95% confidence interval for θ.