**Hypothesis Test for a Population Mean (\(\sigma\) is Known)**You wish to test the following claim (\(H_a\)) at a significance level of \(\alpha = 0.05\).- \(H_0: \mu = 53.7\)- \(H_a: \mu > 53.7\)You believe the population is normally distributed and you know the population standard deviation is \(\sigma = 10.1\). You obtain a sample mean of \(M = 57.5\) for a sample of size \(n = 63\).**What is the test statistic for this sample?** (Report answer accurate to three decimal places.)- test statistic = [ ]**What is the p-value for this sample?** (Report answer accurate to three decimal places.)- p-value = [ ]The p-value is...- ( ) less than (or equal to) \(\alpha\)- ( ) greater than \(\alpha\)This test statistic leads to a decision to...- ( ) reject the null hypothesis- ( ) accept the null hypothesis- ( ) fail to reject the null hypothesisAs such, the final conclusion is that...- ( ) There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 53.7.- ( ) There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 53.7.- ( ) The sample data support the claim that the population mean is greater than 53.7.- ( ) There is not sufficient sample evidence to support the claim that the population mean is greater than 53.7.

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Answered: Hypothesis Test for a Population Mean…

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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Test the claim that the mean GPA of night students is significantly different than 2.6 at the 0.2 significance level. Based on a sample of 50 people, the sample mean GPA was 2.55 with a standard deviation of 0.04The test statistic is: ? (2 decimals)The p-value is: ? (2 decimals)

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