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A random sample of 77 eighth grade? students' scores on a national mathematics assessment test has a mean score of 289. 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 285. Assume that the population standard deviation is 38. At α = 0.12?, is there enough evidence to support the? administrator's claim? Complete parts? (a) through? (e).
(a) Write the claim mathematically and identify H0 and Ha. 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? P-value.
?P - value = ____
?(Round to three decimal places as? needed.)
(d) Decide whether to reject or fail to reject the null hypothesis.
(e) Interpret your decision in the context of the original claim.
At the 12?% significance? level, there is or is not enough evidence to support or reject the? administrator's claim that the mean score for the? state's eighth graders on the exam is more than 285.
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