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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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$**Educational Transcription for Hypothesis Testing** **Hypothesis Testing Scenarios** For each situation, you need to state the null and alternative hypotheses using "mu" (μ) for the symbol of the mean. For example, use "mu > 1" to denote that the mean is greater than 1. Similarly, use "mu < 1" to indicate that the mean is less than 1, and "mu not = 1" for the mean not being equal to 1. Do not include units such as "mm" or "$" in your answer. **Scenario (a): Motor Spindle Diameter** The diameter of a spindle in a small motor should be 2.5 millimeters (mm) with a standard deviation of 0.14 mm. The correct operation of the motor relies on this specification; deviations can result in motor malfunction. In a sample of 13 spindles, the manufacturer measures the average diameter to be 2.38 mm. Your task is to determine whether the mean diameter has deviated from the specified 2.5 mm. - Null Hypothesis ($H_0$): - $\mu = 2.5$ - Alternative Hypothesis ($H_a$): - $\mu \neq 2.5$ **Scenario (b): Local Market Pricing** Harry suspects that prices in Caldwell are higher than the national average for a specific brand of laundry detergent. The nationwide average price is given as $19.65 with a standard deviation of $1.39. Harry collects a sample from 5 local Caldwell stores and calculates the average price for this detergent to be $18.47. Assess whether the average price in Caldwell differs from the national average. - Null Hypothesis ($H_0$): - $\mu = 19.65$ - Alternative Hypothesis ($H_a$): - $\mu \neq 19.65$ **Graphical Explanation** While this text does not provide any visual graphs or diagrams, understanding hypothesis testing typically involves interpreting data distributions, calculating standard deviations, and assessing the width of confidence intervals to determine if null hypotheses can be rejected by comparing sample means against reference values.$

Transcribed Image Text:**Educational Transcription for Hypothesis Testing** **Hypothesis Testing Scenarios** For each situation, you need to state the null and alternative hypotheses using "mu" (μ) for the symbol of the mean. For example, use "mu > 1" to denote that the mean is greater than 1. Similarly, use "mu < 1" to indicate that the mean is less than 1, and "mu not = 1" for the mean not being equal to 1. Do not include units such as "mm" or "$" in your answer. **Scenario (a): Motor Spindle Diameter** The diameter of a spindle in a small motor should be 2.5 millimeters (mm) with a standard deviation of 0.14 mm. The correct operation of the motor relies on this specification; deviations can result in motor malfunction. In a sample of 13 spindles, the manufacturer measures the average diameter to be 2.38 mm. Your task is to determine whether the mean diameter has deviated from the specified 2.5 mm. - Null Hypothesis ($H_0$): - $\mu = 2.5$ - Alternative Hypothesis ($H_a$): - $\mu \neq 2.5$ **Scenario (b): Local Market Pricing** Harry suspects that prices in Caldwell are higher than the national average for a specific brand of laundry detergent. The nationwide average price is given as $19.65 with a standard deviation of $1.39. Harry collects a sample from 5 local Caldwell stores and calculates the average price for this detergent to be $18.47. Assess whether the average price in Caldwell differs from the national average. - Null Hypothesis ($H_0$): - $\mu = 19.65$ - Alternative Hypothesis ($H_a$): - $\mu \neq 19.65$ **Graphical Explanation** While this text does not provide any visual graphs or diagrams, understanding hypothesis testing typically involves interpreting data distributions, calculating standard deviations, and assessing the width of confidence intervals to determine if null hypotheses can be rejected by comparing sample means against reference values.

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