Question: A historical geographer is interested in the average number of children of households in a certain city in 1800. Rather than spend the time analyzing each entry in the city directory, she decides to sample randomly from the directory and estimate the size from this sample. In a sample of 56 households, she finds the average number of children to be 4.46 with a standard deviation of 2.06.
a. Find the 95% confidence interval, using the t-distribution.
b. Find the 95% confidence interval, using the z-distribution.
c. Which interval is more appropriate? Why?