A random sample of 85 eighth grade​ students' scores on a national mathematics assessment test has a mean score of 286. This test result prompts a state school administrator to declare that the mean...

(a)Write the claim mathematically and identify

and

(b)Find the standardized test statistic​ z,

(c)Find the​ P-value.

(d)Decide whether to reject or fail to reject the null hypothesis.

Extracted text: A random sample of 85 eighth grade students' scores on a national mathematics assessment test has a mean score of 286. 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 280. Assume that the population standard deviation is 40. At a = 0.11, 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. O A. Ho: µ2 280 (claim) В. Но: и3D 280 Ha: H> 280 (claim) C. Ho: μ< 280="" ha:=""><280 ha:="" µ=""> 280 (claim) Ο Ε. H : μ< 280="" ha:="" u2="" 280="" (claim)="" o="" d.="" ho:="" µ="280" (claim)="" o="" f="" ho:="" μ5="" 280="" (claim)="" hạ:="" µ=""> 280 Ha: µ> 280 (b) Find the standardized test statistic z, and its corresponding area. (Round to two decimal places as needed.) (c) Find the P-value. P-value = (Round to three decimal places as needed.) (d) Decide whether to reject or fail to reject the null hypothesis. Fail to reject Ho Reject Ho (e) Interpret your decision in the context of the original claim. At the 11% significance level, there enough evidence to the administrator's claim that the mean score for the state's eighth graders on the exam is more than 280.