A random sample of 84 eighth grade students' scores on a national mathematics assessment test has a mean score of 265. 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 260. Assume that the population standard deviation is 31. At a=0.13, is there enough evidence to support the administrator's claim? Complete parts (a) through (e).(a) Write the claim mathematically and identify Ho and Ha. Choose the correct answer below.(b) Find the standardized test statistic z, and its corresponding area.