a) Show (or argue technically) that the 100(1 a)% condence interval for population mean ,u is shorter than Here, 21-5% is the (1 05/2) percentile of a standard normal distribution and 0; is signicant level. In) Suppose we have a sample of size n from a population with known standard deviation 0. We build a (1 a)% condence interval for a. How would this interval chance under the following circumstances? Explain how or why the change would take place. . We collect more data (it increases), but everything else stays the same. . We increase the signicance level a, 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