Question: A sociologist wants information on the number of children per family in her native state of Nebraska. Forty randomly selected farm families to construct a 90% confidence interval for the mean number of children, ?? per family. She finds that the 90% confidence interval for ? is from 1.3 to 2.4 children per family.

a) Determine the margin of error (sampling error), e.

b) What is the population standard deviation ??

c) Determine the sample size required to ensure that we can be 95% confident that her estimate, \[\bar{x}\], is within 0.1 child of ?.