I am offered a job but I want a higher pay than the one offered, can ask for more?

Start by politely asking them if their initial construction salary offer is negotiable.  If it is, counter with a construction salary range.  Say something like, "I was anticipating an offer in the $16 to $18 per hour range," and see what they say.  In addition, if their offer is negotiable, I think you also have to be ready to state exactly why the job will be worth that much more to the construction employer because of the experience, training, skills, record of past job performance, and education you have that make your qualifications for the job a great match for the requirements of the job.  If the offer isn't negotiable, you may have to pass.