**Hypothesis Testing: Sample Mean for CEO Tenure**A shareholders’ group is lodging a protest against your company, claiming that the mean tenure for a chief executive officer (CEO) was at least 11 years. To address this claim, you decide to perform a hypothesis test using a sample survey.**Scenario:**A survey of 70 companies, reported in The Wall Street Journal, found a sample mean tenure of 10.3 years for CEOs, with a standard deviation of 4.9 years (The Wall Street Journal, January 2, 2007). Assume the population is normally distributed.**Formulating the Hypothesis:**You aim to challenge the validity of the claim made by the group at a significance level of $ \alpha = 0.005 $. Your hypotheses are as follows:- Null Hypothesis ($H_0$): $ \mu = 11 $- Alternative Hypothesis ($H_a$): $ \mu < 11 $**Statistical Tests:**1. **Test Statistic Calculation:** - The test statistic formula for the sample mean is: \[ \text{test statistic} = \frac{\bar{x} - \mu}{s / \sqrt{n}} \] - Where: - $ \bar{x}$ is the sample mean (10.3 years) - $ \mu $ is the population mean (11 years) - $ s $ is the sample standard deviation (4.9 years) - $ n $ is the sample size (70)2. **P-Value Calculation:** - Determine the p-value corresponding to the test statistic using the appropriate statistical tables or software.**Questions to Answer:**1. **What is the test statistic for this sample?** - Report the test statistic accurate to 3 decimal places.2. **What is the p-value for this sample?** - Report the p-value accurate to 4 decimal places.**Conclusion:**- Compare the p-value with the significance level $ \alpha $.**Decision Rules:**- If the p-value is less than or equal to $ \alpha $: - Reject the null hypothesis.- If the p-value is greater than $ \alpha $: - Fail to reject the null hypothesis.**Final Conclusion:**- There are multiple conclusions you can draw based on the outcomes of the

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Description: **Hypothesis Testing: Sample Mean for CEO Tenure**A shareholders’ group is lodging a protest against your company, claiming that the mean tenure for a chief executive officer (CEO) was at least 11 years. To address this claim, you decide to perform

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A shareholders' group is lodging a protest against your company. The shareholders group claimed that the mean tenure for a chief exective office (CEO) was at least 11 years. A survey of 70 companies reported in The Wall Street Journal found a sample mean tenure of 10.3 years for CEOS with a standard deviation of s = 4.9 years (The Wall Street Journal, January 2, 2007). You don't know the population standard deviation but can assume it is normally distributed. You want to formulate and test a hypothesis that can be used to challenge the validity of the claim made by the group, at a significance level of a = 0.005. Your hypotheses are: H,:µ = 11 Haiu < 11 What is the test statistic for this sample? test statistic = (Report answer accurate to 3 decimal places.) What is the p-value for this sample? p-value = (Report answer accurate to 4 decimal places.) The p-value is... less than (or equal to) a

A shareholders' group is lodging a protest against your company. The shareholders group claimed that the mean tenure for a chief exective office (CEO) was at least 11 years. A survey of 70 companies reported in The Wall Street Journal found a sample mean tenure of 10.3 years for CEOS with a standard deviation of s = 4.9 years (The Wall Street Journal, January 2, 2007). You don't know the population standard deviation but can assume it is normally distributed. You want to formulate and test a hypothesis that can be used to challenge the validity of the claim made by the group, at a significance level of a = 0.005. Your hypotheses are: H,:µ = 11 Haiu < 11 What is the test statistic for this sample? test statistic = (Report answer accurate to 3 decimal places.) What is the p-value for this sample? p-value = (Report answer accurate to 4 decimal places.) The p-value is... less than (or equal to) a

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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