A random sample of 90 eighth grade students' scores on a national mathematics assessment test has a mean score of 262 . This fest 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 ese population standard deviation is 38. At α=0.02, is there enough evidence to support the administrator's ciaim? Complete parts (a) through (e) (a) Write the claim mathematically and identify H 0
​
and H a +
​
. Choose the correct answer below. (b) Find the standardized test statistic z, and its corresponding area. z= (Round to two decimal places as needed.) (c) Find the th-value.