NO, you are not correct. Look at the BLS website. Only 10% of manufacturing is unionized This is a fact.
Unions had their day and now it is quickly coming to an end, especially in the public sector where as people realize that THEY the taxpayer are funding these sweet heart contracts between the Elected Libs and the Unions, they are forcing changes ala Walker in WI.
As for the private sector I have no problems there since competition in the marketplace quickly takes care of companies who stupidly sign overly generous contracts which can only be paid by steep price increases on their products and services.
In any case I thing withi 10-15 yrs Unions will be history and every State save a very, very few will be right to work.