### Hypothesis Testing with Unknown Population Standard Deviation#### Testing a Claim about a Population Mean ($H_a$) at a Significance Level of $\alpha = 0.005$Given Hypotheses:- Null Hypothesis: $H_0: \mu = 71.5$- Alternative Hypothesis: $H_a: \mu > 71.5$#### Sample Data- Sample size ($n$): 529- Sample mean ($M$): 72.9- Sample standard deviation ($SD$): 18.3### Critical Value CalculationTo find the critical value for this one-tailed test at a significance level of $\alpha = 0.005$, one would typically refer to statistical tables or use statistical software.#### Test Statistic CalculationThe test statistic for the sample is calculated using the formula:\[ \text{Test statistic (t)} = \frac{M - \mu}{(SD/\sqrt{n})} \]Here:- $ \mu $ is the population mean under the null hypothesis.- $ M $ is the sample mean.- $ SD $ is the sample standard deviation.- $ n $ is the sample size.### Decision RuleDetermine the critical value and compare the test statistic to the critical region.- **The test statistic is...** - $ \square $ in the critical region - $ \squircle $ not in the critical regionBased on whether the test statistic falls within the critical region, proceed to make a decision.### ConclusionThe decision will lead to one of the following conclusions:- **This test statistic leads to a decision to...** - $ \bigcirc $ reject the null - $ \square $ accept the null - $ \squircle $ fail to reject the nullThen, make the final conclusion based on your decision:- **As such, the final conclusion is that…** - $ \bigcirc $ There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 71.5. - $ \square $ There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 71.5. - $ \squircle $ The sample data support the claim that the population mean is greater

Given information: The sample mean is M=72.9. The population mean is μ=71.5. The sample standard…

Answered: You wish to test the following claim…

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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