A random sample of 85 eighth grade students' scores on a national mathematics assessment test has a mean score of 2T9. 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 2TB. Assume that the population standard deviation is 38. At a = 0.12, is there enough evidence to support the administrator's claim? Complete parts [a] through (e). (a) Write the claim mathematically and identify Ho and H '1. Choose the correct answer below. 0 A He: pszro (claim) 0 B. Ho3l12?0 Ha: [122\"] (claim) Ha: p>2?0 O D. Ho: pSZTD O E. Ho: p=2T0 O F. HD: p22?(claim} Ha: p>2?0 (claim) Ha: p> 2N] (claim) Ha: p 732 O B. Ho: H 719 (claim) (b) Identify the critical value(s). Use technology. Zo = - 2.05 (Use a comma to separate answers as needed. Round to two decimal places as needed.) Identify the rejection region(s). Choose the correct answer below. O A. O B. O C. Fail to reject Ho. Fail to reject Ho. Fail to reject Ho- Reject Ho. Reject Ho- Reject Ho- Reject Ho- IN Z (c) Identify the standardized test statistic. Use technology. z= -1.01 (Round to two decimal places as needed.) (d) Decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. O A. Fail to reject Ho. There is sufficient evidence to reject the claim that mean bulb life is at O B. Reject Ho. There is sufficient evidence to reject the claim that mean bulb life is at least 732 least 732 hours. hours. O C. Fail to reject Ho. There is not sufficient evidence to reject the claim that mean bulb life is at O D. Reject Ho. There is not sufficient evidence to reject the claim that mean bulb life is at least least 732 hours. 732 hours