Expand Your Knowledge: Two Confidence Intervals What happens if we want several confidence intervals to hold at the same time (concurrently)? Do we still have the same level of confidence we had for eachindividual interval?

(a) Suppose we have two independent random variables x₁ and x₂ with respective population means μ₁ and μ₂. Let us say that we use sample data to construct two 80% confidence intervals.

Now, what is the probability that both intervals hold at the same time?

P(A₁< μ₁< B₁and A₂< μ₂< B₂) = 0.64

(b) Suppose we want both intervals to hold with 90% confidence (i.e., only 10% risk level). How much confidence c should each interval have to achieve this combined level of confidence? (Assume that each interval has the same confidence level c.)

(c) If we want both intervals to hold at the 90% level of confidence, then the individual intervals must hold at a higher level of confidence. Write a brief but detailed explanation of how this could be of importance in a large, complex engineering design such as a rocket booster or a spacecraft.