This problem will investigate what exactly we mean by "Level of Confidence". a. Suppose you take 90 random samples and build 90 50% Cl's for . How many of these Cl's would you expect to successfully "capture" the true value of ? Round to one decimal if needed. Now we will test this concept. The following data is a sample of 10 values from a normally distributed population for which 5. = 48 and = 43.9 48.2 49.6 56.8 47.4 49.8 43 29.6 42.1 55.9 Build a 50% Z-interval for mu based on the sample data, using the known value of . You can use the "Z-interval" command on your calculator to make it easy. Then round to one decimal. b. Enter your CI in this format: (min, max): c. Does your Cl contain the true value of fb, which is 48? No Yes Here is a new set of random values, from the same population distribution. 48.2 39.9 45.6 46.3 54.8 53.4 46.6 49.3 41.1 43.3 d. Build a new 50% CI: e. Does your new Cl contain the true value of ? No Yes We would expect that one of the CI's above would contain and one woud not, but due to random chance it's possible that both did or neither did. Of course, usually you would not use a 50% CI, since the whole point is to try and successfully "capture"