**Hypothesis Testing at Significance Level 0.10****Claim (Hₐ):**\( H_0: \mu = 89.2 \\H_a: \mu > 89.2 \)**Given Data:**- Population is normally distributed.- Standard deviation \( \sigma = 10.7 \).- Sample mean \( \bar{X} = 93.4 \).- Sample size \( n = 23 \).**Tasks:**1. **Calculate the Test Statistic:** - Use the formula for the test statistic for a one-sample z-test: \[ z = \frac{\bar{X} - \mu}{\sigma/\sqrt{n}} \] - Substitute the given values: \[ z = \frac{93.4 - 89.2}{10.7/\sqrt{23}} \] - Compute the value and report the test statistic accurate to three decimal places.2. **Determine the p-value:** - Based on the calculated z-value, find the corresponding p-value from the standard normal distribution. - Report the p-value accurate to four decimal places.3. **Compare p-value with α:** - The p-value is either less than (or equal to) α or greater than α.4. **Choose the Statistical Decision:** - Depending on the comparison of the p-value with α, decide to either reject the null hypothesis, accept the null hypothesis, or fail to reject the null hypothesis.**Conclusion:**- Make the final conclusion about the population mean based on the decision: - If you reject the null hypothesis, there is sufficient evidence to support that the population mean is greater than 89.2. - If you fail to reject the null hypothesis, there is not sufficient evidence to support that the population mean is greater than 89.2.**Conclusion Options:**- There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 89.2.- There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 89.2.- The sample data support the claim that the population mean is greater than 89.2.- There is not sufficient sample evidence to support the claim that the population mean is greater than 89.2.

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You wish to test the following claim (Ha) at a significance level of a = 0.10. H,:µ = 89.2 HaiH > 89.2 You believe the population is normally distributed and you know the standard deviation is a = 10.7 .You obtain a sample mean of M = 93.4 for a sample of size n = 23. 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 89.2. O There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 89.2. O The sample data support the claim that the population mean is greater than 89.2. O There is not sufficient sample evidence to support the claim that the population mean is greater than 89.2.

You wish to test the following claim (Ha) at a significance level of a = 0.10. H,:µ = 89.2 HaiH > 89.2 You believe the population is normally distributed and you know the standard deviation is a = 10.7 .You obtain a sample mean of M = 93.4 for a sample of size n = 23. 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 89.2. O There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 89.2. O The sample data support the claim that the population mean is greater than 89.2. O There is not sufficient sample evidence to support the claim that the population mean is greater than 89.2.

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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