### Testing a Statistical HypothesisYou wish to test the following claim (\( H_a \)) at a significance level of \( \alpha = 0.05 \).\[ H_0: \mu = 65.2 \\H_a: \mu < 65.2 \]You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size \( n = 571 \) with mean \( \overline{M} = 63.2 \) and a standard deviation of \( SD = 20.3 \).**Question 1:** What is the test statistic for this sample? (Report the answer accurate to three decimal places.) **Answer:** \[ \text{test statistic} = \_\_\_\_\_ \]**Question 2:** What is the p-value for this sample? (Report the answer accurate to four decimal places.)**Answer:** \[ \text{p-value} = \_\_\_\_\_ \]**Question 3:** The p-value is...- \( \) less than (or equal to) \( \alpha \)- \( \) greater than \( \alpha \)**Question 4:** This test statistic leads to a decision to...- \( \) reject the null- \( \) accept the null- \( \) fail to reject the null**Conclusion**As such, the final conclusion is that...- \( \) There is sufficient evidence to warrant rejection of the claim that the population mean is less than 65.2.- \( \) There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 65.2.- \( \) The sample data support the claim that the population mean is less than 65.2.- \( \) There is not sufficient sample evidence to support the claim that the population mean is less than 65.2.For each question, complete the analysis by calculating the necessary values and making the appropriate conclusions based on the hypothesis test.### Instructions1. **Calculate the test statistic** using the sample mean (\(\overline{M}\)), the population mean (\(\mu\)), the standard deviation (\(SD\)), and the sample size (\(n\)). Use the formula for the t-test since the population standard deviation is unknown: \[ \text{test

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You wish to test the following claim (H) at a significance level of a = 0.05. H,:µ = 65.2 HaiH < 65.2 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 571 with mean M = 63.2 and a standard deviation of SD = 20.3. 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 greater than a This test statistic leads to a decision to. reject the null 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 less than 65.2. O There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 65.2. O The sample data support the claim that the population mean is less than 65.2. There is not sufficient sample evidence to support the claim that the population mean is less than 65.2.

You wish to test the following claim (H) at a significance level of a = 0.05. H,:µ = 65.2 HaiH < 65.2 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 571 with mean M = 63.2 and a standard deviation of SD = 20.3. 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 greater than a This test statistic leads to a decision to. reject the null 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 less than 65.2. O There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 65.2. O The sample data support the claim that the population mean is less than 65.2. There is not sufficient sample evidence to support the claim that the population mean is less than 65.2.

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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