In the data vit2005, found in the library PASWR, the director of urban housing in Vitoria, Spain, claims that at least 50% of all apartments have more than one bathroom and that at least 75% of all apartments have an elevator.
1. Can the director's claim about bathrooms be contradicted? Test the appropriate hypothesis using alpha = 0.10.
2. Can the director's claim about elevators be substantiated using an alpha level of 0.10? Use both an approximate method as well as an exact method to reach a conclusion. Are the methods in agreement?
3. Test whether the proportion of apartments built prior to 1980 without garages has a higher proportion with elevators than without elevators.