5. A random sample of 2000 voters yielded 530 who reported being in favor of changing the constitution to allow foreign born people to hold the office of President.  A 99% confidence interval was constructed for the true proportion of people who are in favor of the change.  The resulting interval was as follows: [0.240, 0.290].  If an immigrant group claims that the majority of the public supports the change, does this interval contradict their claim?