1. Explain why we always round up when calculating a required sample size for a given confidence level. What would be the result on the level of confidence if we rounded down? 2. The mean age for all Foothill College students for a recent Fall term was 33.2. The population standard deviation has been pretty consistent at 15. Suppose that twenty-five Winter students were randomly selected. The mean age for the sample was 30.4. We are interested in the true mean age for Winter Foothill College students. Let X = the age of a Winter Foothill College student. Using this information answer the following questions. a) Construct a 95% Confidence Interval for the true mean age of Winter Foothill College students. b) Suppose we wanted to to be 95% confident that the average age of the sample is within 2 years of the population mean. i) Before computing the necessary sample size, do you expect that you will require more or less students to be sampled? Explain why. ii) Calculate the sample size necessary for the given confidence level and error bound for the mean