**Hypothesis Testing Example****Problem Statement:**Suppose an airline claims that its flights are consistently on time with an average delay of at most 15 minutes. It claims that the average delay is so consistent that the variance is no more than 15 minutes. Doubting the consistency part of the claim, a disgruntled traveler calculates the delays for his next 25 flights. The average delay for those 25 flights is 22 minutes with a standard deviation of 15 minutes.**a) Hypothesis:**- **Null Hypothesis (H₀):** The population mean delay (μ) is less than or equal to 15 minutes. \( H₀: μ ≤ 15 \)- **Alternative Hypothesis (H₁):** The population mean delay (μ) is greater than 15 minutes. \( H₁: μ > 15 \)**b) Test Statistics:**To conduct the hypothesis test, we need to use the t-test for the sample mean. The test statistic is calculated using the formula:\[ t = \frac{\bar{x} - μ}{s / \sqrt{n}} \]Where:- \( \bar{x} \) is the sample mean (22 minutes)- μ is the population mean under the null hypothesis (15 minutes)- s is the sample standard deviation (15 minutes)- n is the sample size (25 flights)**c) P-value:**To find the p-value, use the calculated t-value and refer to the t-distribution table with \( n-1 = 24 \) degrees of freedom.**d) Decision about hypothesis:**Compare the p-value with the significance level (α, typically 0.05). If the p-value is less than α, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.**e) Conclusion:**Based on the decision made in part (d), we conclude whether there is enough evidence to support the disgruntled traveler's claim that the average delay is greater than 15 minutes.---This example illustrates the steps involved in hypothesis testing, a fundamental process in statistics used to infer conclusions about population parameters based on sample data.

Name: **Hypothesis Testing Example****Problem Statement:**Suppose an airlin
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Description: **Hypothesis Testing Example****Problem Statement:**Suppose an airline claims that its flights are consistently on time with an average delay of at most 15 minutes. It claims that the average delay is so consistent that the variance is no more than

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Suppose an airline claims that its flights are consistently on time with an average delay of at most 15 minutes. It claims that the average delay is so consistent that the variance is no more than 15 minutes. Doubting the consistency part of the claim, a disgruntled traveler calculates the delays for his next 25 flights. The average delay for those 25 flights is 22 minutes with a standard deviation of 15 minutes.

Suppose an airline claims that its flights are consistently on time with an average delay of at most 15 minutes. It claims that the average delay is so consistent that the variance is no more than 15 minutes. Doubting the consistency part of the claim, a disgruntled traveler calculates the delays for his next 25 flights. The average delay for those 25 flights is 22 minutes with a standard deviation of 15 minutes.

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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