2. (15 points) You have data on height, in inches, 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% condence interval for the population mean, and it has a margin of error of 0.8. What would be the margin of error after each of the following changes? Consider the changes one at a time, not cumulatively. 2.1. You decide to estimate a 99% condence interval instead. 2.2. You increase the sample to 150 people. 2.3. You decide to use the sample standard deviation instead of assuming the population standard deviation is known, but it turns out that s is equal to the value of a that you were initially assuming. 2.4. You are told to report the results in centimeters instead, using the conversion of 1 in = 2.54 cm. 2.5. You forgot to tell people to take their shoes off before their height was recorded, but you assume that shoes added exactly 1 inch to everyone's measured height