Let’s verify the statistical assertions that we made in the course of constructing the confidence interval in equation (6.10).

(a) Prove that y , in the example of confidence intervals of section 6.3, is an unbiased estimator of μ, the expected value of earnings in the population. Begin with the definition of the average in equation (2.8). Take the expected value of both sides of the equation. Simplify the expected value to the right of the equality using equations (5.13) and (5.34). Finally, substitute E(yi) = μ.

(b) Prove equation (6.9). Begin with the definition of the average in equation€(

2.8). Take the population variance of both sides of the equation.

Simplify the population variance to the right of the equality using equations

(5.43) and (5.45).