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sample grade score 0 This fest resut prompl state Schoo administrator to declare that the mean score for the state's eighh graders on this exam is more than 260 Assume that the population standard deviation is 37. At 0.13, is there enough evidence to support the administrator's claim? Complete parts (a) through (e)

sample grade score 0 This fest resut prompl state Schoo administrator to declare that the mean score for the state's eighh graders on this exam is more than 260 Assume that the population standard deviation is 37. At 0.13, is there enough evidence to support the administrator's claim? Complete parts (a) through (e)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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# Statistical Analysis of Eighth Grade Students' Test Scores ## Scenario A random sample of 77 eighth-grade students' scores on a national mathematics assessment test has a mean score of 266. 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 260. Assume that the population standard deviation is 37. At α = 0.13, is there enough evidence to support the administrator’s claim? Complete parts (a) through (c): ### (a) Writing the Claim Mathematically To evaluate the claim, we need to identify the null hypothesis \(H_0\) and the alternative hypothesis \(H_1\). Choose the correct answer below: - **A. \(H_0: \mu \leq 260\) (claim)** - **\(H_1: \mu > 260\)** - B. \(H_0: \mu \geq 260\) - \(H_1: \mu = 260\) - C. \(H_0: \mu = 260\) - \(H_1: \mu > 260\) (claim) - **D. \(H_0: \mu = 260\)** - **\(H_1: \mu > 260\) (claim)** - E. \(H_0: \mu = 260\) - \(H_1: \mu \ne 260\) (claim) - F. \(H_0: \mu > 260\) - \(H_1: \mu = 260\) ### (b) Calculating the Standardized Test Statistic Find the standardized test statistic \(z\), and its corresponding area: \(z = 1.42\) (Round to two decimal places as needed.) ### (c) Finding the P-value Compute the P-value for the test. P-value = (Round to three decimal places as needed.) ### Conclusion Assess whether the P-value provides sufficient evidence to support the claim that the mean score is more than 260, given the significance level \( \alpha = 0.13 \).
Transcribed Image Text:# Statistical Analysis of Eighth Grade Students' Test Scores ## Scenario A random sample of 77 eighth-grade students' scores on a national mathematics assessment test has a mean score of 266. 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 260. Assume that the population standard deviation is 37. At α = 0.13, is there enough evidence to support the administrator’s claim? Complete parts (a) through (c): ### (a) Writing the Claim Mathematically To evaluate the claim, we need to identify the null hypothesis \(H_0\) and the alternative hypothesis \(H_1\). Choose the correct answer below: - **A. \(H_0: \mu \leq 260\) (claim)** - **\(H_1: \mu > 260\)** - B. \(H_0: \mu \geq 260\) - \(H_1: \mu = 260\) - C. \(H_0: \mu = 260\) - \(H_1: \mu > 260\) (claim) - **D. \(H_0: \mu = 260\)** - **\(H_1: \mu > 260\) (claim)** - E. \(H_0: \mu = 260\) - \(H_1: \mu \ne 260\) (claim) - F. \(H_0: \mu > 260\) - \(H_1: \mu = 260\) ### (b) Calculating the Standardized Test Statistic Find the standardized test statistic \(z\), and its corresponding area: \(z = 1.42\) (Round to two decimal places as needed.) ### (c) Finding the P-value Compute the P-value for the test. P-value = (Round to three decimal places as needed.) ### Conclusion Assess whether the P-value provides sufficient evidence to support the claim that the mean score is more than 260, given the significance level \( \alpha = 0.13 \).
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