A random sample of 89 eighth grade students' scores on a national mathematics assessment test has a mean score of 277. 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 270. Assume that the population standard deviation is 38. At a = 0.06, 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: H = 270 O B. Ho: HI s 270 (claim) O C. Ho: H 2 270 (claim) Ha: H > 270 (claim) Ha: H > 270 Ha: H 270 Ha: H > 270 (claim) (b) Find the standardized test statistic z, and its corresponding area. z= 1.74 (Round to two decimal places as needed.) (c) Find the P-value. P-value = 0.959 (Round to three decimal places as needed.) (d) Decide whether to reject or fail to reject the null hypothesis. O Reject Ho O Fail to reject Ho (e) Interpret your decision in the context of the original claim. At the 6% significance level, there is not enough evidence to support the administrator's claim that the mean score for the state's eighth graders on the exam is more than 270.Use technology to help you test the claim about the population mean, , at the given level of significance, o, using the given sample statistics. Assume the population is normally distributed. Claim: p > 1290; a = 0.09; 6= 214.02. Sample statistics: x = 1312.97, n =250 Identify the null and alternative hypotheses. Choose the correct answer below. O A. Ho: HIS 1312.97 O B. Ho: H > 1312.97 Ha: H > 1312.97 Ha: Us 1312.97 O C. Ho: H 2 1290 O D. Ho: H 2 1312.97 Ha: H 1290 Ha: H > 1290 Ha: HE 1290 Calculate the standardized test statistic. The standardized test statistic is 1.70 (Round to two decimal places as needed.) Determine the P-value. P= .046 (Round to three decimal places as needed.) Determine the outcome and conclusion of the test. Reject Ho- At the 9% significance level, there is enough evidence to reject the claim