12.45.* You form a 95% confidence interval in five different situations, with independent samples.

(a) Find the probability that (i) all five intervals contain the parameters they are designed to estimate, (ii) at least one interval is in error. (Hint: Use the binomial distribution.)

(b) If you use confidence level 0.9898 for each interval, the probability that all five intervals contain the parameters equals exactly 0.95. Explain why. (Hint: What is

(0.9898)5?) Compare 0.9898 to the confidence coefficient for each interval in the Bonferroni method.