Consider 95% CIs for two different parameters 1 and 2 , and let Ai (i = 1, 2) denote the event that the

Consider 95% CIs for two different parameters θ₁ and θ₂, and let Ai (i = 1, 2) denote the event that the value of θ_i is included in the random interval that results interval that results in the CI. Thus P(A_i) = .95.

a. Suppose that the data on which the CI for θ₁ is based is independent of the data used to obtain the CI for θ₂ (e.g., we might have θ₁ = l, the population mean height for American females, and θ₂ = p, the proportion of all iPhones that don’t need warranty service). What can be said about the simultaneous confidence level for the two intervals? That is, how confident can we be that the first interval contains the value of θ₁ and that the second contains the value of θ₂?

b. Now suppose the data for the first CI is not independent of that for the second one. What now can be said about the simultaneous confidence level for both intervals?

c. What can be said about the simultaneous confidence level if the confidence level for each interval separately is 100(1 − α)%? What can be said about the simultaneous confidence level if a 100(1 – α)% CI is computed separately for each of k parameters θ₁, . . ., θ_k?

Consider P(A A) C