A random sample of 78 eighth grade students' scores on a national mathematics assessment test has a mean score of 273. 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 31. At a = 0.14, is there enough evidence to support the administrator's claim? Complete parts (a) through (e). [A. Ho: H 2 270 (claim) B. Ho: HS 270 (claim) ( C. Ho: H = 270 Has p 270 Ha: H> 270 (claim) D. Hous270 V E. Ho: H 270 (claim) Ha: H 2 270 (claim) Ha: HI > 270 (b) Find the standardized test statistic z. z= Of (Round to two decimal places as needed.) A random sample of 78 eighth grade students' scores on a national mathematics assessment test has a mean score of 273. 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 31. At a =0.14, is there enough evidence to support the administrator's claim? Complete parts (a) through (e). Has H > 270 (claim) Ha: H 2 270 (claim) Ha: H > 270 (b) Find the standardized test statistic z. z=(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. A random sample of 78 eighth grade students' scores on a national mathematics assessment test has a mean score of 273. 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 31. At a = 0.14, is there enough evidence to support the administrator's claim? Complete parts (a) through (e). (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 14% 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 270. X (1,8) support reject Next for part (e) options are is/ is not . support/ reject