MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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**Educational Website Text** **Testing a Statistical Claim: Aircraft Altimeters** **Scenario:** A simple random sample is selected from a normally distributed population. The goal is to test a claim using either the P-value method or the traditional method of hypothesis testing. **Context:** Company A is evaluating a new production method for manufacturing aircraft altimeters. A sample of new altimeters is analyzed to investigate if this method has a higher standard deviation in errors compared to the old method, which had a standard deviation of 32.2 ft. ### Data: Error values: -41, 78, -20, -71, -45, 10, 17, 51, -5, -50, -109, -109 ### Analysis: A significance level of 0.05 is employed to assess if the new method results in a standard deviation greater than 32.2 ft. The company needs to determine if these changes indicate the new method is better or worse, and whether any actions are necessary. ### Hypotheses: What are the null and alternative hypotheses? - **Option A:** \(H_0: \sigma = 32.2 \text{ ft}\) \(H_1: \sigma \neq 32.2 \text{ ft}\) - **Option B:** \(H_0: \sigma^2 = 32.2 \text{ ft}\) \(H_1: \sigma^2 = 32.2 \text{ ft}\) - **Option C:** \(H_0: \sigma < 32.2 \text{ ft}\) \(H_1: \sigma = 32.2 \text{ ft}\) - **Option D:** \(H_0: \sigma < 32.2 \text{ ft}\) \(H_1: \sigma = 32.2 \text{ ft}\) - **Option E:** \(H_0: \sigma = 32.2 \text{ ft}\) \(H_1: \sigma > 32.2 \text{ ft}\) - **Option F:** \(H_0: \sigma = 32.2 \text{ ft}\) \(H_1: \sigma > 32.2 \text{ ft}\) ### Statistical Test: 1.
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Transcribed Image Text:**Educational Website Text** **Testing a Statistical Claim: Aircraft Altimeters** **Scenario:** A simple random sample is selected from a normally distributed population. The goal is to test a claim using either the P-value method or the traditional method of hypothesis testing. **Context:** Company A is evaluating a new production method for manufacturing aircraft altimeters. A sample of new altimeters is analyzed to investigate if this method has a higher standard deviation in errors compared to the old method, which had a standard deviation of 32.2 ft. ### Data: Error values: -41, 78, -20, -71, -45, 10, 17, 51, -5, -50, -109, -109 ### Analysis: A significance level of 0.05 is employed to assess if the new method results in a standard deviation greater than 32.2 ft. The company needs to determine if these changes indicate the new method is better or worse, and whether any actions are necessary. ### Hypotheses: What are the null and alternative hypotheses? - **Option A:** \(H_0: \sigma = 32.2 \text{ ft}\) \(H_1: \sigma \neq 32.2 \text{ ft}\) - **Option B:** \(H_0: \sigma^2 = 32.2 \text{ ft}\) \(H_1: \sigma^2 = 32.2 \text{ ft}\) - **Option C:** \(H_0: \sigma < 32.2 \text{ ft}\) \(H_1: \sigma = 32.2 \text{ ft}\) - **Option D:** \(H_0: \sigma < 32.2 \text{ ft}\) \(H_1: \sigma = 32.2 \text{ ft}\) - **Option E:** \(H_0: \sigma = 32.2 \text{ ft}\) \(H_1: \sigma > 32.2 \text{ ft}\) - **Option F:** \(H_0: \sigma = 32.2 \text{ ft}\) \(H_1: \sigma > 32.2 \text{ ft}\) ### Statistical Test: 1.
The image presents a problem related to hypothesis testing using a simple random sample from a normally distributed population. It involves testing a claim about a new production method for manufacturing aircraft altimeters, where the errors from a sample of new altimeters are given as: \[ -41, 78, -20, -71, -45, 10, 17, 51, -5, 50, -109, -109 \] The task is to use a 0.05 level of significance to test whether the new production method has a standard deviation greater than \(32.2\) ft. This was the standard deviation for the old production method. **Hypotheses Options:** Select the appropriate null and alternative hypotheses: - A. \(H_0: \sigma = 32.2\) ft, \(H_1: \sigma > 32.2\) ft - B. \(H_0: \sigma = 32.2\) ft, \(H_1: \sigma < 32.2\) ft - C. \(H_0: \sigma = 32.2\) ft, \(H_1: \sigma \neq 32.2\) ft - D. \(H_0: \sigma > 32.2\) ft, \(H_1: \sigma = 32.2\) ft - E. \(H_0: \mu = 32.2\) ft, \(H_1: \mu \neq 32.2\) ft - F. \(H_0: \mu = 32.2\) ft, \(H_1: \mu > 32.2\) ft **Instructions for Testing:** 1. **Find the Test Statistic:** - Use the given formula and information to calculate the test statistic (rounded to two decimal places). 2. **Determine the Critical Value(s):** - Identify the critical value(s) based on the level of significance (rounded to two decimal places). 3. **Decision Rule:** - Compare the test statistic to the critical value(s) to decide whether to reject or fail to reject the null hypothesis. Use this to determine if there is evidence to support the new method's effectiveness. 4. **Assessment:** - Determine if the new production method appears better or worse than the old method based on whether
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Transcribed Image Text:The image presents a problem related to hypothesis testing using a simple random sample from a normally distributed population. It involves testing a claim about a new production method for manufacturing aircraft altimeters, where the errors from a sample of new altimeters are given as: \[ -41, 78, -20, -71, -45, 10, 17, 51, -5, 50, -109, -109 \] The task is to use a 0.05 level of significance to test whether the new production method has a standard deviation greater than \(32.2\) ft. This was the standard deviation for the old production method. **Hypotheses Options:** Select the appropriate null and alternative hypotheses: - A. \(H_0: \sigma = 32.2\) ft, \(H_1: \sigma > 32.2\) ft - B. \(H_0: \sigma = 32.2\) ft, \(H_1: \sigma < 32.2\) ft - C. \(H_0: \sigma = 32.2\) ft, \(H_1: \sigma \neq 32.2\) ft - D. \(H_0: \sigma > 32.2\) ft, \(H_1: \sigma = 32.2\) ft - E. \(H_0: \mu = 32.2\) ft, \(H_1: \mu \neq 32.2\) ft - F. \(H_0: \mu = 32.2\) ft, \(H_1: \mu > 32.2\) ft **Instructions for Testing:** 1. **Find the Test Statistic:** - Use the given formula and information to calculate the test statistic (rounded to two decimal places). 2. **Determine the Critical Value(s):** - Identify the critical value(s) based on the level of significance (rounded to two decimal places). 3. **Decision Rule:** - Compare the test statistic to the critical value(s) to decide whether to reject or fail to reject the null hypothesis. Use this to determine if there is evidence to support the new method's effectiveness. 4. **Assessment:** - Determine if the new production method appears better or worse than the old method based on whether
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