In this section you will try to "break" this procedure for making confidence intervals by finding a set of numbers that makes the percentage of intervals that cover the true population mean as small as possible. Fleplace the contents of the box with any combination of up to 20 integers (whole numbers) between 0 and 10 (use at least two distinct numbers). Set Sample size 5, and set Samples to take to 1000. Leave Intervals: :l: set to 2. Click Take Sample and note the percentage of the intervals that covered. Repeat the steps in the preceeding paragraph, varying the numbers you put into the box, trying to make the percentage of intervals in that cover the population mean as small as possible. Keep track of the worst list of numbers and the percentage of intervals that covered the mean of that list. Try at least 10 different sets of numbers in the box, and see if you can determine what features of the list of numbers in the box tend to make the coverage probability low. You should be able to get the percentage of intervals that cover down to 30% or less pretty easilykeep trying until you do. Then take ten sets of 1000 samples of size 5 from that box and average the percentage of the 10,000 intervals that covered the true population mean. Problem 13 The worst set of numbers was (type in the numbers separated by commas or spaces) (Q17) The fraction of the 10,000 intervals that covered the population mean of this box was only (Q18) Put the worst set of numbers you found back into the box. Increase the sample size to 200, take 1000 samples ten times, and average the ten percentages of intervals that cover to find the percentage of the 10,000 intervals that cover the true population mean. Problem 14 For sample size 200, the fraction of the 10,000 inten/als that covered the true population mean was (Q19) I hope you have just discovered that while you can "break" this procedure for finding approximate 95% confidence intervals pretty easily for small sample sizes, it is quite hard to break it for larger sample sizesabout 95% of the intervals cover the mean of the box, regardless of what numbers you put in the box, provided the sample size is large enough