Answered: 1. To test whether a golf ball of brand…

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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$**Hypothesis Testing for Golf Ball Distances** **Objective:** The goal is to evaluate whether a golf ball from Brand A can be hit farther than a golf ball from Brand B. For the experiment, 12 golfers hit a ball from each brand. The order was switched for half of them (six golfers hit Brand A before Brand B, and the others did the opposite). **Results:** | Golfer | Distance for Brand A | Distance for Brand B | |--------|----------------------|----------------------| | 1 | 245 | 253 | | 2 | 251 | 259 | | 3 | 266 | 265 | | 4 | 254 | 274 | | 5 | 276 | 284 | | 6 | 266 | 282 | | 7 | 243 | 279 | | 8 | 239 | 260 | | 9 | 258 | 264 | | 10 | 260 | 290 | | 11 | 273 | 288 | | 12 | 244 | 264 | **Statistical Hypothesis:** - **Null Hypothesis (H₀):** The mean difference in distances (Brand A - Brand B) is zero ($ \mu_d = 0 $). - **Alternative Hypothesis (Hₐ):** The mean difference in distances is less than zero ($ \mu_d < 0 $). **Note:** For each golfer, the difference $ d $ is calculated as: \[ d = \text{Distance for Brand A} - \text{Distance for Brand B} \] **Method:** A paired t-test will be conducted with a significance level $ \alpha = 0.10 $. This involves: - Identifying the critical region for the test - Calculating the degrees of freedom - Determining the test statistic value - Drawing a conclusion based on the results This setup provides a framework for students to perform hypothesis testing using real-world data, reinforcing concepts related to statistical comparisons and decision-making.$

Transcribed Image Text:**Hypothesis Testing for Golf Ball Distances** **Objective:** The goal is to evaluate whether a golf ball from Brand A can be hit farther than a golf ball from Brand B. For the experiment, 12 golfers hit a ball from each brand. The order was switched for half of them (six golfers hit Brand A before Brand B, and the others did the opposite). **Results:** | Golfer | Distance for Brand A | Distance for Brand B | |--------|----------------------|----------------------| | 1 | 245 | 253 | | 2 | 251 | 259 | | 3 | 266 | 265 | | 4 | 254 | 274 | | 5 | 276 | 284 | | 6 | 266 | 282 | | 7 | 243 | 279 | | 8 | 239 | 260 | | 9 | 258 | 264 | | 10 | 260 | 290 | | 11 | 273 | 288 | | 12 | 244 | 264 | **Statistical Hypothesis:** - **Null Hypothesis (H₀):** The mean difference in distances (Brand A - Brand B) is zero ($ \mu_d = 0 $). - **Alternative Hypothesis (Hₐ):** The mean difference in distances is less than zero ($ \mu_d < 0 $). **Note:** For each golfer, the difference $ d $ is calculated as: \[ d = \text{Distance for Brand A} - \text{Distance for Brand B} \] **Method:** A paired t-test will be conducted with a significance level $ \alpha = 0.10 $. This involves: - Identifying the critical region for the test - Calculating the degrees of freedom - Determining the test statistic value - Drawing a conclusion based on the results This setup provides a framework for students to perform hypothesis testing using real-world data, reinforcing concepts related to statistical comparisons and decision-making.

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