a) Show (or argue technically) that the 100(1 a)% condence interval for population mean it, _ 0 _ 0' 33 Zia S H S 33 + Z1a,2n is shorter than a U 3: Zla S M S if + Z1a/3 Here, 210/2 is the (1 0.72) percentile of a stande normal distribution and o: is signicant level. b) Suppose we have a sample of size n from a p0pulation with known standard deviation 0. We build a (1 00% condence interval for H- How would this interval chance under the following circumstances? Explain how or why the change would take place. - We collect more data (11. increases), but everything else stays the same. . We increase the signicance level 0:, but everything else stays the same. . The population standard deviation or were larger, but everything else stays the same. . The populatiOn mean u. were larger, but everything else stays the same. Your answers go here for question 2