In reference to the title, Estonia is a country on the Baltic Sea between Latvia and Russia.
The contest categories for events at the county fair at the sign up table are: Polka Contest. Best Hog. Best Fruit Pie. The Wife Carry. Best Quilt. Best Hen. Best Cow.
Mike (Dax Shepard) to give Rio (Lake Bell) confidence tells her she is about to win her first chicken contest in the "10th biggest county in eastern Nebraska". The 10th biggest county in eastern Nebraska would be Gage County (pop 22,300) south of Lincoln.