The movie theater sates prospective people who visit the theater pay the average cost of their ticket is $52 with a standard deviation of $4.50. A group of young people renders that the average cost is higher. In order to test the movie theater's claim against their alternative, the group will select a random sample of size 100. Assume that the mean from their random sample is $52.80. Evaluate a hypothesis test at the level of significance (0.05) and state your decision.