Critical Thinking: Different Confi dence Levels

(a) Suppose that a 95% confi dence interval for a difference of proportions contains both positive and negative numbers. Will a 99% confi dence interval based on the same data necessarily contain both positive and negative numbers? Explain. What about a 90% confi dence interval? Explain.

(b) Suppose that a 95% confi dence interval for a difference of proportions contains all positive numbers. Will a 99% confi dence interval based on the same data necessarily contain all positive numbers as well? Explain.

What about a 90% confi dence interval? Explain.