The sample that comes with the book expects the connection string to be in the web.config file in the web site project.
The code you're showing is for the default constructor of the DataContext. This would only be called if you didn't pass in the connection string when the DataContext is instantiated.
The sample code passes in the connection string to the constructor using a helper function in the DBHelper class.
using (HRPaidTimeOffDataContext db = new HRPaidTimeOffDataContext(DBHelper.GetHRPaidTimeOffConnectionString()))