Final answer:
The NJ statute authorizing reimbursement for transportation to public and religious schools does not violate the Establishment Clause of the First Amendment.
Step-by-step explanation:
In the case of Everson v. Board of Education, the Supreme Court ruled that a state law that reimburses parents for the cost of transportation to school for their children, including those attending public and religious schools, does not violate the Establishment Clause of the First Amendment.
The Court found that the law was neutral and beneficial for all K-12 students, regardless of their school type. If the law had treated religious schools differently or preferentially, it may have been found to violate the Establishment Clause. However, since the law was neutral and did not promote or inhibit religious practice, it was deemed constitutional.