Recently released data by the American Pet Products Association showed that in 2016 the majority (38%) of dog owners were part of Generation Y (born 1994–1980). You want to open a cage-free dog salon and in order to plan your marketing strategy for the salon, you would like to estimate the average age of dog owners in your neighborhood. Your neighborhood has 550 registered dog owners. Following a random sample of 47 dog owners at the local dog park, you found the average age of dog owners to be 28.7 years with a sample standard deviation equal to 4.8 years.

a. Construct a 95% confidence interval to estimate the average age of dog owners.

b. What assumption needs to be made for this analysis?