### Hypothesis Testing for Population Mean#### Problem StatementYou wish to test the following claim ($H_a$) at a significance level of $\alpha = 0.001$:\[\begin{aligned}H_0 &: \mu = 66.6 \\H_a &: \mu > 66.6 \\\end{aligned}\]#### Given DataYou believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size $n = 75$ with:- Mean ($M$) = 69.3- Standard deviation ($SD$) = 5.4#### Finding the Test StatisticWhat is the test statistic for this sample? (Report answer accurate to three decimal places.)\[\text{test statistic} = \boxed{\hspace{1cm}}\]#### Finding the p-valueWhat is the p-value for this sample? (Report answer accurate to four decimal places.)\[\text{p-value} = \boxed{\hspace{1cm}}\]#### AnalysisThe p-value is...- $\circ$ less than (or equal to) $\alpha$- $\circ$ greater than $\alpha$#### Decision MakingThis test statistic leads to a decision to...- $\circ$ reject the null- $\circ$ accept the null- $\circ$ fail to reject the null#### ConclusionAs such, the final conclusion is that...- $\circ$ There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 66.6.- $\circ$ There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 66.6.- $\circ$ The sample data support the claim that the population mean is greater than 66.6.- $\circ$ There is not sufficient sample evidence to support the claim that the population mean is greater than 66.6.

You wish to test the following claim (Ha) at a significance level of a = 0.001. Ho: = = 66.6 Ha:µ > 66.6 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 75 with mean M = 69.3 and a standard deviation of SD = 5.4. 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 four decimal places.) p-value = The p-value is... O less than (or equal to) a O greater than a This test statistic leads to a decision to... O reject the null O accept the null O fail to reject the null As such, the final conclusion is that... O There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 66.6. O There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 66.6. O The sample data support the claim that the population mean is greater than 66.6. O There is not sufficient sample evidence to support the claim that the population mean is greater than 66.6.

You wish to test the following claim (Ha) at a significance level of a = 0.001. Ho: = = 66.6 Ha:µ > 66.6 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 75 with mean M = 69.3 and a standard deviation of SD = 5.4. 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 four decimal places.) p-value = The p-value is... O less than (or equal to) a O greater than a This test statistic leads to a decision to... O reject the null O accept the null O fail to reject the null As such, the final conclusion is that... O There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 66.6. O There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 66.6. O The sample data support the claim that the population mean is greater than 66.6. O There is not sufficient sample evidence to support the claim that the population mean is greater than 66.6.

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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