Use the table to test the claim using the P-value method. Tell why you made the decision you did. B) test the same claim using the critical value method if the test statictic is 0.759, x hat = 2.72424, and s =0.2956. Tell why you made the decision you did. **Title: Hypothesis Testing Using t-test and P-value****Objective:** To determine if the mean tornado length is greater than 2.5 miles using hypothesis testing with a t-test.### a) Justification for Using the t-test Instead of the z-testWhen sample sizes are small or the population standard deviation is unknown, the t-test is preferred over the z-test. The t-test is more appropriate as it accounts for additional variability when estimating population parameters from a sample.### b) Using the P-value Method for Hypothesis TestingTo test the claim, refer to the table below:#### Hypothesis Test Results:- **Population Mean (μ)** - **Null Hypothesis (H₀):** μ = 2.5 - **Alternative Hypothesis (Hₐ):** μ > 2.5| Variable | Sample Mean | Std. Err. | DF | T-Stat | P-value ||----------|-------------|-----------|-----|------------|---------|| Length | 2.72424 | 0.29557683| 499 | 0.75865215 | 0.2242 |**Analysis:**- Given the P-value = 0.2242, which is greater than a typical alpha level of 0.05, there is insufficient evidence to reject the null hypothesis. Therefore, we do not have enough evidence to claim that the mean length is greater than 2.5.### b) Testing Using the Critical Value MethodTest the same claim using the traditional critical value method.**Given:**- α = 0.05 (significance level)- Sample Mean (x̄) = 2.72424- Standard Deviation (s) = 0.2956### Explanation:1. **Calculate t-critical:** Determine the critical t-value from t-distribution tables for DF = 499 and α = 0.05.2. **Decision Rule:** If the calculated t-statistic (0.75865215) is greater than the critical t-value, reject the null hypothesis.The sample data suggests that the tornado length is greater than the assumed population mean under traditional significance testing criteria. However, P-value analysis supports sticking to the null, highlighting the importance of sample size and context in hypothesis tests.

Use the table to test the claim using the P-value method. Tell why you made the decision you did. B) test the same claim using the critical value method if the test statictic is 0.759, x hat = 2.72424, and s =0.2956. Tell why you made the decision you did.

Use the table to test the claim using the P-value method. Tell why you made the decision you did. B) test the same claim using the critical value method if the test statictic is 0.759, x hat = 2.72424, and s =0.2956. Tell why you made the decision you did.

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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