The 2008 General Social Survey asked, "What do you think is the ideal number of children for a family to have?' ' The 678 females who responded had a median of 2, mean of 3.22, and standard deviation of 1.99. The 99% confidence interval for the population mean is (3.02,3.42). Determine whether the following statements are true or false, and explain your reasoning.

e. We are 99% confident that the average of the ideal number of children in a family answered by the 678 females in the sample is between 3.02 and 3.42. f. If a new sample was taken, we are 99% confident that the sample mean of the new sample would lie between 3.02 and 3.42. g. The margin of error of the 99% confidence interval (3.02, 3.42) is 0.2. h. A 95% confidence interval would be narrower than the 99% confidence interval since we don't need to be as sure about our estimate