Confidence Interval to estimate a population's standard deviation A can of latex paint is supposed to contain 32 ounces. The filling machine experiences slight deviations (sometimes too much, sometimes too little), and it is monitored by a quality control manager. In a random sample of twelve (12) cans the content of each was weighed: 31.94 ounces 31.74 32.21 31.36 31.84 31.84 31.52 32.16 31.78 31.51 32.28 32.53 Check: mean = 31.8925 std.dev. s = ? Round s to three decimal places. Do all parts (a)-(c): (a) Construct a 95% confidence interval for the population standard deviation O . You may assume the data is normally distributed, and I've provided the formulas, below, to get you started. df df S S critvalue critvalue for .025 for .975 (b) Interpret the confidence interval, "We are 95% confident that ...." (c) The filling machine will have to be shut down and recalibrated if the estimated population standard deviation is greater than .200 ounce. Will the machine be shut down for maintenance? (Yes/No)