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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### Hypothesis Testing for Golf Ball Diameter

#### Problem Statement

Suppose a professional golfing association requires that the standard deviation of the diameter of a golf ball be less than 0.005 inch. Determine whether these golf balls conform to this requirement at the α = 0.01 level of significance. Assume that the population is normally distributed.

#### Data

The diameters of the golf balls provided for the test are as follows:
- 1.622
- 1.677
- 1.678
- 1.679
- 1.681
- 1.684
- 1.684
- 1.678
- 1.684
- 1.684
- 1.677

#### Hypothesis Formulation

- **Null Hypothesis (H₀):** 
  The standard deviation of the golf ball diameter is 0.005 inch or more.

- **Alternative Hypothesis (H₁):**
  The standard deviation of the golf ball diameter is less than 0.005 inch.

#### Instructions for Hypothesis Testing

1. **Select the Null and Alternative Hypotheses:**
   Use the drop-down menus to select the correct symbols and conditions for the null and alternative hypotheses.
   
2. **Determine the Test Statistic:**
   Calculate the standard deviation from the sample data provided and compare it to the defined threshold of 0.005 inch.

3. **Decision Rule:**
   At a significance level of α = 0.01, determine if the calculated standard deviation supports the alternative hypothesis.

4. **Conclude:**
   Based on the comparison and the level of significance, conclude whether the golf ball diameters conform to the requirement.

#### Interactive Features

- The web interface provides drop-down options for selecting hypotheses and buttons for clearing inputs or checking the correctness of selected hypotheses.

#### Additional Help

If you require further guidance, click "Get more help" for a detailed explanation or example.
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Transcribed Image Text:### Hypothesis Testing for Golf Ball Diameter #### Problem Statement Suppose a professional golfing association requires that the standard deviation of the diameter of a golf ball be less than 0.005 inch. Determine whether these golf balls conform to this requirement at the α = 0.01 level of significance. Assume that the population is normally distributed. #### Data The diameters of the golf balls provided for the test are as follows: - 1.622 - 1.677 - 1.678 - 1.679 - 1.681 - 1.684 - 1.684 - 1.678 - 1.684 - 1.684 - 1.677 #### Hypothesis Formulation - **Null Hypothesis (H₀):** The standard deviation of the golf ball diameter is 0.005 inch or more. - **Alternative Hypothesis (H₁):** The standard deviation of the golf ball diameter is less than 0.005 inch. #### Instructions for Hypothesis Testing 1. **Select the Null and Alternative Hypotheses:** Use the drop-down menus to select the correct symbols and conditions for the null and alternative hypotheses. 2. **Determine the Test Statistic:** Calculate the standard deviation from the sample data provided and compare it to the defined threshold of 0.005 inch. 3. **Decision Rule:** At a significance level of α = 0.01, determine if the calculated standard deviation supports the alternative hypothesis. 4. **Conclude:** Based on the comparison and the level of significance, conclude whether the golf ball diameters conform to the requirement. #### Interactive Features - The web interface provides drop-down options for selecting hypotheses and buttons for clearing inputs or checking the correctness of selected hypotheses. #### Additional Help If you require further guidance, click "Get more help" for a detailed explanation or example.
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