Arandom sample of 78 eighth grade students' scores on a national mathematics assessment test has a mean score of 284. this test result prompts a state school administrator to declare that the mean score for the state's eighth graders on this exam is more than 275. assume that the population standard deviation is 32. at α=0.04, is there enough evidence to support the administrator's claim a) h0: μ≤275 ha: μ> 275(claim) b) find the standarized test statistic z and its corresponding area c) find the p value d) describe whether to reject or fail the null hypothesis e) interpret your decision in the context of the original claim