2. (20 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 devia- tion. You estimate a 95% confidence interval for the population mean; let the margin of error be denoted by M1. For each of the following changes, say how the numeric value of the new margin of error, M2, compares to M1. Consider the changes one at a time, not cumulatively. 2.1. You decide to estimate a 99% confidence interval instead. (a) M2 M1 (d) M2 could be smaller than, equal to, or greater than M1. 2.2. You increase the sample to 150 people. (a) M2 M1 (d) M2 could be smaller than, equal to, or greater than M1. 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 o that you were initially assuming. (a) M2 M1 (d) M2 could be smaller than, equal to, or greater than M1. 2.4. You are told to report the results in centimeters instead, using the conversion of 1 in = 2.54 cm. (a) M2 M1 (d) M2 could be smaller than, equal to, or greater than M1. 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. (a) M2 M1 (d) M2 could be smaller than, equal to, or greater than M1