(15 points) You have data on height, in centimeters, for 61 individuals and are assuming they come from a random sample from a normally distributed population with a known standard deviation. You estimate a 95% confidence interval for the population mean, and it has a margin of error of 2. What would be the margin of error after each of the following changes? Consider the changes one at a time, not cumulatively. 3.1. You decide to estimate a 99% confidence interval instead. Note: either find an exact expression for the ratio of the new margin of error to the old margin of error (recommended) as a way of solving for the new margin of error, or be careful to preserve precision in your calculations to avoid rounding error. 3.2. You increase the sample to 210 people. 3.3. You decide to use the sample standard deviation instead of assuming the population standard deviation is known, but it turns out that ???? is equal to the value of ???? that you were initially assuming. 3.4. You are told to report the results in inches instead, using the conversion of 1 in = 2.54 cm. 3.5. You forgot to tell people to take their shoes off before their height was recorded, but you assume that shoes added exactly 2 cm to everyone's measured height.